# Relativistic Quantum Information

Conference Date:
Monday, June 25, 2012 (All day) to Thursday, June 28, 2012 (All day)
Scientific Areas:
Quantum Information
Quantum Gravity
Quantum Foundations

Over the past few years, a new field of high research intensity has emerged, known as Relativistic Quantum Information (RQI). The field of RQI aims to understand the relationship between special and general relativity, and quantum information. In particular, so-called quantum entanglement bits (e-bits) are a necessary resource in all of quantum communication and quantum computation. One of the key goals of the field of RQI is to develop a theory of e-bits in realistic spacetimes described by Lorentzian manifolds. This offers exciting new challenges because it combines information theory with quantum theoretic and general relativistic questions. Deep questions concerning the relationship between information processing and the structure of spacetime will be considered. This conference will bring together the most prominent researchers in RQI, as well as some of their best postdoctoral fellows and graduate students. The workshop is timely because of newly emerging prospects for experimental tests of phenomena of relativistic quantum information, for example, using quantum communication with satellite-based instruments or Berry’s phase tests of the Unruh effect.

• David Aasen, University of Waterloo
• Paul Alsing, Air Force Research Laboratory, Information Directorate
• Shrobona Bagchi, Harish-Chandra Research Institute
• Hector Bombin, Perimeter Institute
• Leron Borsten, Imperial College London
• Wilson Brenna, University of Waterloo
• Eric Brown, University of Waterloo
• Caslav Brukner, University of Vienna
• David Edward Bruschi, University of Nottingham
• Hilary Carteret, Wilfrid Laurier University
• Horacio Casini, Centro Atomico Bariloche
• Aidan Chatwin-Davies, University of Waterloo
• Linqing Chen, Perimeter Institute
• Luca Di Fiore, Hewlett-Packard
• John Dixon, Toronto
• William Donnelly, University of Maryland
• Jason Doukas, National Institute for Informatics
• Andrzej Dragan, University of Warsaw
• Michael Duff, Imperial College, London
• Christopher Erven, Institute for Quantum Computing
• Felix Flicker, Perimeter Institute
• Doreen Fraser, University of Waterloo
• Nicolai Friis, University of Nottingham
• Daniel Gottesman, Perimeter Institute
• Lucien Hardy, Perimeter Institute
• Patrick Hayden, McGill University
• Thomas Jennewein, University of Waterloo
• Robert Jonsson, University of Waterloo
• Achim Kempf, Perimeter Institute, University of Waterloo
• Adrian Kent, University of Cambridge
• Piotr Kolenderski, Institute for Quantum Computing
• Dawood Kothawala, University of New Brunswick
• Antony Lee, University of Nottingham
• Juan Leon, Instituto de Fisica Fundamental, CSIC, Madrid
• Peter Levay, Budapest University of Technology and Economics
• Adam Lewis, University of Toronto
• Shih-Yuin Lin, National Changhua University
• Seth Lloyd, Massachusetts Institute of Technology
• Jorma Louko, University of Notthingham
• Robert Mann, Perimeter Institute, University of Waterloo
• Iman Marvian, Perimeter Institute
• Robert Martin, University of Cape Town
• Eduardo Martin-Martinez, University of Waterloo
• William McHarris, Michigan State University
• Nicolas Menicucci, University of Sydney
• Avijit Misra, Harish-Chandra Research Institute
• Miguel Montero, Instituto de Fisica Fundamental (CSIC)
• Evgeny Mozgunov, California Institute of Technology
• Markus Mueller, Perimeter Institute
• Casey Myers, Centre for Engineered Quantum Systems
• Rob Myers, Perimeter Institute
• Mikhail Panine, University of Waterloo
• Jacques Pienaar, University of Queensland
• Eric Poisson, University of Guelph
• Sandu Popescu, University of Bristol
• Christopher Pugh, University of Waterloo
• Robabeh Rahimi Darabad, University of Waterloo
• Tim Ralph, University of Queensland
• Sepehr Rashidi, University of Waterloo
• Katja Reid, Perimeter Institute
• Benni Reznik, Tel-Aviv University
• Carlos Sabin, University of Notthingham
• Grant Salton, McGill University
• Fabio Scardigli, Academia Sinica Institute of Physics Taipei
• Alexander Smith, University of Toronto
• Laurel Stephenson Haskins, University of California
• Tayebeh Tahmtan, Eastern Mediterranean University
• Daniel Terno, Macquarie University
• Paulina Corona Ugalde, Perimeter Institute
• Anton van Niekerk, Perimeter Institute
• Juven Wang, MIT
• Eric Webster, University of Waterloo
• Peng Xiao, Brock University
• Rong Zhou, University of Maryland, College Park
• Nosiphiwo Zwane,Perimeter Institute

David Aasen, University of Waterloo

Towards Universal Quantum Computation Out of Relativistic Motion of Particle Detectors
In the field of Relativistic Quantum information, general relativistic effects such as ultrarelativistic accelerations or intense gravitational fields have been often considered in the past as a source of noise, decoherence and entanglement degradation. In this talk we will see how general relativistic effects can actually be taken advantage of in order to process quantum information by means of particle detectors. We will show that the motion of such detectors through spacetime could be used to build quantum gates and outperform equivalent settings that do not make use of quantum effects induced by relativity.

Paul Alsing, Air Force Research Laboratory, Information Directorate
Nonlocality, Entanglement Witnesses and Supra-Correlations
While entanglement is believed to underlie the power of quantum computation and communication, it is not generally well understood for multipartite systems. Recently, it has been appreciated that there exists proper no-signaling probability distributions derivable from operators that do not represent valid quantum states.  Such systems exhibit supra-correlations that are stronger than allowed by quantum mechanics, but less than the algebraically allowed maximum in Bell-inequalities (in the bipartite case). Some of these probability distributions are derivable from an entanglement witness W, which is a non-positive Hermitian operator constructed such that its expectation value with a separable quantum state (positive density matrix) rho_sep is non-negative (so that Tr[W rho]< 0 indicates entanglement in quantum state rho). In the bipartite case, it is known that by a modification of the local no-signaling measurements by spacelike separated parties A and B, the supra-correlations exhibited by any W can be modeled as derivable from a physically realizable quantum state ρ. However, this result does not generalize to the n-partite case for n>2. Supra-correlations can also be exhibited in 2- and 3-qubit systems by explicitly constructing "states" O (not necessarily positive quantum states) that exhibit PR correlations for a fixed, but arbitrary number, of measurements available to each party. In this paper we examine the structure of "states" that exhibit supra-correlations. In addition, we examine the affect upon the distribution of the correlations amongst the parties involved when constraints of positivity and purity are imposed. We investigate circumstances in which such "states" do and do not represent valid quantum states.

Leron Borsten, Imperial College, London
Causal Constraints on Possible Measurements
A crucial question in any approach to quantum information processing is:  first, how are classical bits encoded physically in the quantum system, second, how are they then manipulated and, third,  how are they finally read out?   These questions are particularly challenging when investigating quantum information processing in a relativistic spacetime. An obvious framework for such an investigation is relativistic quantum field theory.  Here, progress is hampered by the lack of a universally applicable rule for calculating the probabilities of the outcomes of ideal measurements on a relativistic quantum field in a collection of spacetime regions. Indeed, a straightforward relativistic generalisation of the non-relativistic formula for these probabilities leads to superluminal signalling.

Motivated by these considerations we ask what interventions/ideal measurements can we in principle make, taking  causality as our guiding criterion. In the course of this analysis we reconsider various aspects of ideal measurements in QFT, detector models and the probability rules themselves. In particular, it is shown that an ideal measurement of a one–particle wave packet state of a relativistic quantum field in Minkowski spacetime enables superluminal signalling. The result holds for a measurement that takes place over an intervention region in spacetime whose extent in time in some frame is longer than the light crossing time of the packet in that frame.

Eric Brown, University of Waterloo
Geometric Discord in Non-Inertial Frames
I review the recent work performed on computing the geometric discord in non-inertial frames. We consider the well-known case of an inertially maximally entangled state shared by inertial Alice and non-inertial Robb. It is found that for high accelerations the geometric discord decays to a negligible amount; this is in stark contrast to the entropic definition of quantum discord which asymptotes to a finite value in the same limit. Such a result has two different implications: the first being that usable quantum correlations are more limited in this regime than previously thought and the second being that geometric discord may not be a sufficient measure of quantum correlations. I will discuss both of these perspectives.

Caslav Brukner, University of Vienna
Quantum Interference of “Clocks”
Experimental tests of general relativity performed so far involve systems that can be effectively described by classical physics. On the other hand, observed gravity effects on quantum systems do not go beyond the Newtonian limit of the theory. In light of the conceptual differences between general relativity and quantum mechanics, as well as those of finding a unified theoretical framework for the two theories, it is of particular interest to look for feasible experiments that can only be explained if both theories apply.   We propose testing general relativistic time dilation with a single “clock” in a superposition of two paths in space-time, along which time flows at different rates. We show that the interference visibility in such an experiment will decrease to the extent to which the path information becomes available from reading out the time from the “clock”. This effect would provide the first test of the genuine general relativistic notion of time in quantum mechanics. We consider implementation of the “clock” in evolving internal degrees of freedom of a massive particle and, alternatively, in the external degree of a photon and analyze the feasibility of the experiment.

David Edward Bruschi, University of Nottingham
Entanglement Resonances
We investigate entanglement creation between modes of a quantum field contained within a cavity which undergoes noninertial motion. We find that, in the the low acceleration regime, or equivalently in the small cavity regime, entanglement can be created from initially separable states and it can be linearly increased by repeating travel scenarios. We are able to fin analytically how all the parameter involved affect the entanglement. We suggest that this can be of interest when looking for experimental veriications of predictions within the field of relativistic quantum information.

Aidan Chatwin-Davies, University of Waterloo
A Fully-Relativistic Bandlimit on Quantum Fields' Two-Point Correlation Functions
The bridge between continuous information and discrete information is provided by sampling theory. In this talk, I will discuss an application of covariant sampling theory to cosmology (see the previous talk by Dr. R. Martin). In cosmology, the two-point correlation function of a quantum field is of central importance because it is a measure of the size of the fluctuations of the quantum field and of the entanglement of the vacuum in a given spacetime. Furthermore, the two-point function is experimentally accessible through the cosmic microwave background. Using covariant sampling theory, I will show how an information-theoretic bandlimit imposed at the Planck scale manifests itself in the two-point function. We will examine this bandlimit in Minkowski space and in de Sitter space.

William Donnelly, University of Maryland
Vacuum Entanglement and Gauge Symmetry
The entanglement entropy associated to a region of space is a quantity of great interest in black hole thermodynamics, quantum information and condensed matter theory. But when the fields in question have a gauge symmetry, the physical observables are nonlocal and there is a question of what we mean by the Hilbert space corresponding to a region of space. I will give a natural definition of the Hilbert space associated to a region of space in lattice gauge theory. The Hilbert space includes edge states similar to those that appear in 2+1 gravity and quantum Hall systems. The gauge symmetry allows for a decomposition of the entanglement entropy into the sum of a bulk entropy, and an entropy localized on the boundary.

Jason Doukas, National Institute for Informatics
Localised Detection of the Unruh Effect
I will discuss a new proposal with the potential to experimentally probe the validity of Rindler quantisation from the recent completely localized framework of non-inertial projective detectors of quantum fields.

Andrzej Dragan, University of Warsaw
Localised Detection of Relativistic Quantum Fields in Non-Inertial Frames
We introduce a novel approach to measurements in QFT in non-inertial frames. A simple, localised, analytical model of state detection allows us to study all the standard questions of RQI and yielding simple answers with a clear physical interpretation. We apply the model to investigate extraction of the entanglement from the vacuum, completely characterize entangled state of two localised inertial wave-packets in the accelerating frame and study the entanglement degradation as a function of the proper acceleration of the detector.

Michael Duff, Imperial College London
Black Holes and Qubits
Two different branches of theoretical physics, string theory and quantum information theory (QIT), share many of the same features, allowing knowledge on one side to provide new insights on the other. In particular the matching of the classification of stringy black holes and the classification of four-qubit entanglement provides a falsifiable prediction in the field of QIT.

Nicolas Friis, University of Nottingham
Entanglement Generation in Relativistic Quantum Fields
We present a general, analytic recipe to compute the entanglement that is generated between arbitrary, discrete modes of bosonic quantum fields by Bogoliubov transformations. Our setup allows the complete characterization of the quantum correlations in all Gaussian field states. Additionally, it holds for all Bogoliubov transformations. These are commonly applied in quantum optics for the description of squeezing operations, relate the modedecompositions of observers in different regions of curved spacetimes, and describe observers moving along non-stationary trajectories. We focus on a quantum optical example in a cavity quantum electrodynamics setting: an uncharged scalar field within a cavity provides a model for an optical resonator, in which entanglement is created by non-uniform acceleration.We show that the amount of generated entanglement can be magnified by initialsingle-mode squeezing, for which we provide an explicit formula.Applications to quantum fields in curved spacetimes, such as an expanding universe, are discussed.

Patrick Hayden, McGill University
Holographic Mutual Information is Monogamous
I'll describe a special information-theoretic property of quantum field theories with holographic duals: the mutual informations among arbitrary disjoint spatial regions A,B,C obey the inequality I(A:BC) >= I(A:B)+I(A:C), provided entanglement entropies are given by the Ryu-Takayanagi formula. Inequalities of this type are known as monogamy relations and are characteristic of measures of quantum entanglement. This suggests that correlations in holographic theories arise primarily from entanglement rather than classical correlations. Moreover, monogamy property implies that the Ryu-Takayanagi formula is consistent with all known general inequalities obeyed by the entanglement entropy, including an infinite set recently discovered by Cadney, Linden, and Winter; this constitutes significant evidence in favour of its validity.

Photon Location in Rindler Coordinates
Bases of orthonormal localized states are constructed in Rindler coordinates and applied to an Unruh detector with good time resolution and an accelerated rod-like array detector.

Patrick Hayden, McGill University
Holographic Mutual Information is Monogamous
I'll describe a special information-theoretic property of quantum field theories with holographic duals: the mutual informations among arbitrary disjoint spatial regions A,B,C obey the inequality I(A:BC) >= I(A:B)+I(A:C), provided entanglement entropies are given by the Ryu-Takayanagi formula. Inequalities of this type are known as monogamy relations and are characteristic of measures of quantum entanglement. This suggests that correlations in holographic theories arise primarily from entanglement rather than classical correlations. Moreover, monogamy property implies that the Ryu-Takayanagi formula is consistent with all known general inequalities obeyed by the entanglement entropy, including an infinite set recently discovered by Cadney, Linden, and Winter; this constitutes significant evidence in favour of its validity.

Thomas Jennewein, University of Waterloo
Towards Quantum Science Experiments with Satellites
Space offers a very unique environment for quantum physics experiments at regimes for distance and velocity not possible on ground. In the recent years there have been a range of theoretical and experimental studies towards the feasibility of performing quantum physics and quantum information science experiments in space.   The most advanced quantum application is quantum cryptography,  known as quantum key distribution (QKD),  which can be extended to global distances by bringing suitable quantum systems into space.  It is interesting to note that with quantum satellites in Earth's orbit, we will be able to perform tests on the validity of quantum physics and entanglement at huge length scales and velocities. This could provide a possible route towards gaining  insights into the interplay of quantum physics and relativity. I will review some of the interesting quantum entanglement tests that can be performed with satellites in space. I will also outline a proposed satellite mission that is based on existing technology on a small-scale satellite, and could be a first important step into this direction.

The fundamental properties of quantum information and its applications to computing and cryptography have been greatly illuminated by considering information-theoretic tasks that are provably possible or impossible within non-relativistic quantum mechanics.  In this talk I describe a general framework for defining tasks within (special) relativistic quantum theory and illustrate it with examples from relativistic quantum cryptography.

Antony Lee, University of Nottingham
Finite Size Detectors in RQI
Unruh-DeWitt detectors interacting with a quantum field promise to be suitable systems for relativistic quantum information processing. since the detectors are point-like, they couple with the same strength to all modes of the filed spectrum. In this work we consider a more realistic model in which the detector has a finite size implemented by a chosen spatial profile. Therefore, the detector couples to a distribution of field modes which depends on the detector's shape. The spatial profile of the detector can be fine-tuned to couple to peaked distributions of Minkowski, Unruh or Rindler modes. Our model will be used to deepen our understanding of free mode entanglement in non-inertial frames.

Juan Leon, Instituto de Fisica Fundamental, CSIC, Madrid
The Quest for Localization
This talk aims to review the obstacles met in QFT to reach an appropriate definition for such a basic concept as localization. The anti-local character of the square root of the "- Laplace-Beltrami + mass^2" operator prevents the existence of localized states with a finite number of quanta. (Bosonic) quantum fields describe elementary excitations of an extended system whose ground state is the vacuum. No wonder, there is a complicated relationship between the cardinal (quantal) and continuous (spatial) sides of the theory. We will also analyze the roles (if any) played in RQI by the localized excitations of the vacuum.

Peter Levay, Budapest University of Technology and Economics
Black Hole Entrophy Related to Measures of Entanglement
Recently striking connections have been discovered between the research fields of black hole soultions in string theory and the one of entanglement measures in quantum entanglement theory.For the emerging research field the term The Black Hole/Qubit Correspondence has been coined. The basic idea is that wrapping configurations of extended objects in extra dimensions can  give rise to interesting realizations of entangled systems and black holes at the same time. The geometry of the extra dimensions and the wrapping type determines the entangled system in question. Usually as the extra dimensional spaces Calabi-Yau manifolds are chosen. In this talk I give some hints how this constraint could be relaxed. These considerations might substantially generalize the range of validity of the Black-Hole/Qubit correspondence.

Shih-Yuin Lin, National Changhua University
Quantum Teleportation from Alice to Rob in Vacuum
We consider quantum teleportation of continuous variables in a relativistic system with the Unruh-DeWitt detectorscoupled to a common quantum field initially in the Minkowski vacuum. An unknown coherent state of an Unruh-DeWitt detector is teleported from one inertial agent (Alice) to an almost uniformly accelerated agent (Rob), using a detector pair initially entangled and shared by these two agents. Results for the averaged physical fidelity of quantum teleportation will be discussed.

Seth Lloyd, Massachusetts Institute of Technology
Quantum Limits to the Measurement of Spacetime Geometry
This talk analyzes the limits that quantum mechanics imposes on the accuracy to which spacetime geometry can be measured.  By applying the fundamental physical bounds to measurement accuracy ensembles of clocks and signals, as in the global positioning system, I present a covariant version of the quantum geometric limit, which states that the total number of ticks of clocks and clicks of detectors that can be contained in a four volume of spacetime of radius R and temporal extent is less than or equal to RT divided by the Planck length times the Planck time. The quantum  geometric bound limits the number of events or ops' that can take place in a four-volume of spacetime and is consistent with and complementary to the holographic bound which limits the number of bits that can exist within a three-volume of spacetime.

Jorma Louko, University of Nottingham
Future-past Correlations in Relativistic Quantum Information
In the Unruh effect, long-distance correlations in a pure quantum state cause accelerated observers to experience the state as a thermal bath. We discuss a similar phenomenon for quantum states that contain correlations between the distant future and the distant past. Examples include Minkowski half-space with a static mirror and an eternal black hole with an unusual global structure behind the horizon. The question of utilising the future-past correlations in quantum information tasks is raised.

Robert Martin, University of Cape Town
A Fully Covariant Information Theoretic Ultraviolet Cutoff for Fields on Expanding FRW Spacetimes
A covariant ultra-violet cutoff on the modes of physical fields on a given space-time can be achieved by cutting off the spectrum of the D'Alembertian of the manifold. This cutoff is a natural generalization of the naive ultra-violet cutoff inEuclidean space which is obtained by simply projecting out frequencies greater in magnitude than a given maximum frequency. Here it is shown that for flat spacetime and expanding FRW spacetimes thiscutoff manifests itself as a decrease in temporal degrees of freedom for large spatial modes. In a large class of expanding FRW spacetimes where the proper time co-ordinate ends at a finite value, it is shown how the numberof temporal degrees of freedom of a fixed spatial mode depends on the magnitude of the spatial mode. We further indicate how the effects of this ultra-violet cutoff on the dynamics of field theories can be studied, and how the resulting modifications to inflationary predictions of the CMB spectrum could be calculated. This talk is based on ongoing joint work with Prof. Achim Kempf (University of Waterloo) and Aidan Chatwin-Davies (UW).

Robert Mann, University of Waterloo, Perimeter Institute
Tripartite Entanglement, Svetlichny Inequalities, and Non-inertial Observers
I discuss the behaviour of bipartite and tripartite non-locality between fermionic entangled states shared by observers, one of whom uniformly accelerates. Although fermionic entanglement persists for arbitrarily large acceleration, the Bell/CHSH inequalities cannot be violated for sufficiently large but finite acceleration. However the Svetlichny inequality, which is a measure of genuine tripartite non-locality, can be violated for any finite value of the acceleration.

Eduardo Martin-Martinez, University of Waterloo
Relativistic Quantum Information and Relativistic Quantum Optics: Towards Experiments to Reveal Quantum Effects Provoked by Gravity
We will explore different results on  relativistic quantum information and general relativistic quantum optics whose aim is to provide scenarios where relativistic quantum effects can be experimentally accessible. Traditionally, relativistic quantum information has been far away from the experimental test, but the discipline is close to the transition point where experimental outcomes will soon arise. Not only to bestow experimental proof on long ago predicted but still undetected phenomena (such as the Unruh and Hawking effects), but also to provide insight into the relationship of general relativity  and quantum theory, and to serve as a  source of new quantum technologies.
We will show how it is possible to extract timelike and  spacelike quantum correlations from the vacuum state of the field in a tabletop experiment, and how to use it to build a quantum memory. We will see how geometric phases can help to detect the Unruh effect and how to use what we learn from that setting to build a quantum thermometer. Finally we will discuss how quantum simulators can be applied to the study of quantum effects of gravity, and used to predict experimental scenarios way beyond current computational power of classical computers.

Nicolas Menicucci, University of Sydney
On the Preparation of States in Nonlinear Quantum Mechanics
Recent analysis of closed timelike curves from an information-theoretic perspective has led to contradictory conclusions about their information-processing power. One thing is generally agreed upon, however, which is that if such curves exist, the quantum-like evolution they imply would be nonlinear, but the physical interpretation of such theories is still unclear. It is known that any operationally verifiable instance of a nonlinear, deterministic evolution on some set of pure states makes the density matrix inadequate for representing mixtures of those pure states. We re-cast the problem in the language of operational quantum mechanics, building on previous work to show that the no-signalling requirement leads to a splitting of the equivalence classes of preparation procedures. This leads to the conclusion that any non-linear theory satisfying certain minimal conditions must be regarded as inconsistent unless it contains distinct representations for the two different kinds of mixtures, and incomplete unless it contains a rule for determining the physical preparations associated with each type. We refer to this as the preparation problem' for nonlinear theories.

Miguel Montero, Instituto de Fisica Fundamental (CSIC)
Physical Results with Fermions in RQI
A number of works in the field of relativistic quantum information have been devoted to the study of entanglement on certain simple families of Unruh-mode entangled states in non-inertial frames. In the fermionic case remarkable results such as the survival of entanglement at infinite acceleration have been obtained. In this talk we will present and analyze some issues related to the anticommuting character of fermionic field operators, which  have been overlooked in the past, sometimes leading to unphysical results.  We provide a simple way of obtaining physical results, yielding interesting consequences such as convergence of field entanglement for different families of Unruh mode-entangled states in the infinite acceleration limit.

Casey Myers, Centre for Engineered Quantum Systems
Any Quantum State Can be Cloned in the Presence of a Closed Timelike Curve
Using the Deutsch approach, we show that the no-cloning theorem can be circumvented in the presence of closed timelike curves, allowing the perfect cloning of a quantum state chosen randomly from a finite alphabet of states. Further, we show that a universal cloner can be constructed that when acting on a completely arbitrary qubit state, exceeds the no-cloning bound on fidelity. Since the “no cloning theorem” has played a central role in the development of quantum information science, it is clear that the existence of closed timelike curves would radically change the rules for quantum information technology.

Jacques Pienaar, University of Queensland
Quantum Time-Like Curves: From Thought Experiment to Real Experiment
Thought experiments involving quantum mechanics in the presence of closed time-like curves (CTCs) seem to have little to do with reality. However, even particles that traverse the CTC passively and without interactions can lead to highly non-trivial effects, such as the maximal violation of the uncertainty principle. Moreover, these effects may carry over to curved space-times without CTCs, presenting novel opportunities for testing non-standard physics in the relativistic regime.

Tim Ralph, University of Queensland
Quantum Communication Between Localized, Non-Inertial Observers
An unsolved problem in relativistic quantum information research is how to model efficient, directional quantum communication between localised parties in a fully quantum field theoretical framework. We propose a tractable approach to this problem based on calculating expectation values of localized field observables in the Heisenberg Picture. We illustrate our approach by analysing, and obtaining approximate analytical solutions to, the problem of communicating quantum states between an inertial sender, Alice and an accelerated homodyne receiver, Rob. We discuss the effect on quantum protocols carried out over such a communication channel.

Benni Reznik, Tel-Aviv University
Entanglement of a Relativistic Field in the Vacuum State
We discuss gedanken experiments for measuring local and non-local observables in QFT that
respect causality, and can by used to test the entanglement between two spatially distant regions in the vacuum. It is shown that the entanglement decays exponentially with the distance between the regions and does not vanish, in contrast to the case of lattice models. We discuss in this respect a possible mechanism which might explain this persistence effect, and a connection between the Reeh-Schlieder theorem and superoscillations.

Carlos Sabin, University of Nottingham
On-chip Extraction of Quantum Correlations from the Vacuum
On-chip extraction of quantum correlations from the vacuumCarlos Sabn, Borja Peropadre, Marco del Rey, Eduardo Martn-MartnezCircuit Quantum Electrodynamics provides a framework in which the interaction of two-level systems with a quantum field can be naturally considered [1]. The combination of superconducting qubits with transmission lines implement an artificial 1-D matter-radiation interaction, with the advantage of a large experimental accessibility and tunability of the physical parameters. Using these features, fundamental problems in Quantum Field Theory hitherto considered as ideal are now accessible to experiment, as in the recent celebrated test of the Dynamical Casimir Effect.In this talk we will exploit the possibility of achieving an ultrastrong coupling regime  in circuit QED to propose a feasible test of the extraction of vacuum entanglement to a pair of qubits [2]. First, we will analyze a  setup in which the qubits are spacelike separated and interact with the vacuum of the quantum field at the same time. After that we will focus on an even more intriguing possibility [3]: that the qubits interact with the field at different time intervals -one in the past and the other one in the future- with an intermezzo of no interaction at all. We will see how the qubits can get entangled while remaining spacelike or timelike separated and in the latter case with or without a certain probability of photon exchange. In addition to its interest from the fundamental viewpoint, the extraction of past-future quantum correlations enables its use as a quantum channel for quantum teleportation in time''.  We will show how this opens the door  to a novel kind of quantum memory in which the information of the quantum state of some ancillary qubit P' is codified in the  field during a certain time and then recovered in F using classical information stored in the past - regardless whatever may happen to P after its interaction with the field. Our scheme is fully within reach of current circuit QED technologies. [1] Carlos Sabn, Marco del Rey, Juan Jos Garca-Ripoll, Juan Len, Phys. Rev. Lett. 107, 150402 (2011).[2]  Carlos Sabn, Juan Jos Garca-Ripoll, Enrique Solano, Juan Len, Phys. Rev. B 81, 184501 (2010).[3] Carlos Sabn, Borja Peropadre, Marco del Rey, Eduardo Martn-Martnez, arXiv: 1202.1230.

Grant Salton, McGill University
Measuring Distance with Acceleration-assisted Entanglement Harvesting
We show that entanglement harvested from a quantum field by interaction with local detectors undergoing anti-parallel acceleration can be used to measure the distance of closest approach between the two detectors. Information about the separation is stored nonlocally in the phase of the joint state of the detectors after the interaction; a single detector alone contains none. We model the detectors as two-level quantum systems accelerating uniformly  through the Minkowski vacuum while interacting for a short time with a massless scalar field. This interaction allows entanglement to be swapped locally from the field to the detectors. Although each detector alone sees the same thermal spectrum (due to Unruh radiation), the joint state between them may be entangled. In the vicinity of a critical distance of closest approach between the detectors, the phase of the entangled state depends sensitively on the distance. We contrast this with the case of parallel acceleration, in which no such critical distance exists, and we discuss the connection of this case with entanglement harvested from an expanding universe.

Fabio Scardigli, Academia Sinica Institute of Physics Taipei
Uncertainty Relations on a Planck Lattice and Black Hole Temperature
After an introduction to generalized uncertainty principle(s), we study uncertainty relations as formulated in a crystal-like universe, whose lattice spacing is of order of  Planck length. For Planckian energies, the uncertainty relation for position and momenta has a lower bound equal to zero. Connections of this result with 't Hooft's deterministic quantization proposal, and with double special relativity are briefly presented. We then apply our formulae to (micro) black holes, we derive a new mass-temperature relation for Schwarzschild black holes, and we discuss the new thermodynamic entropy and heat capacity. In contrast to standard results based on Heisenberg and stringy uncertainty relations, we obtain both a finite Hawking's temperature and a zero rest-mass remnant at the end of the (micro) black hole evaporation. [Ref.Paper: PRD 81, 084030 (2010). arXiv:0912.2253]

Daniel Terno, McQuarie University
Quantum Information in Gravitational Field
Both spin of massive particles and politicization of light are affected by gravity. I discuss different levels of the approximation involved in studies of qubits that are encoded into spin and polarization, the impact of gravity on single qubits and entanglement and how quantum experiments can help us to test gravity.

Rong Zhou, University of Maryland, College Park
Boundary Effects on Quantum Entanglement and its Dynamics in a Detector-Field System
We analyze an exactly solvable model consisting of an inertial Unruh-DeWitt detector which interacts linearly with a massless quantum field in Minkowski spacetime with a perfectly reflecting flat plane boundary. This model is related to proposed mirror-field superposition and relevant experiments in macroscopic quantum phenomena, as well as atomic fluctuation forces near a conducting surface. Firstly a coupled set of equations for the detector’s and the field’s Heisenberg operators are derived. After coarse graining the field, the dynamics of the detector’s internal degreeof freedom is described by a quantum Langevin equation, where the dissipation and noise kernels respectively correspond to the retarded Green’s functions and Hadamard elementary functions of the free quantum field in half space. We use the linear entropy as measures of entanglement between the detector and the quantum field under mirror reflection, then solve the early-time detector-fieldentanglement dynamics. At late times when the combined system is in a stationary state, we obtain exact expressions for the detector’s covariance matrix and show that the detector-field entanglement decreases for smaller separation between the detector and the mirror.We explain the behavior of detector-field entanglement qualitatively with the help of a detector’s mirror image, compare them with the case of two real detectors and explain the differences.

## Tripartite Entanglement, Svetlichny Inequalities, and Non-inertial Observers

Monday Jun 25, 2012
Speaker(s):

I discuss the behaviour of bipartite and
tripartite non-locality between fermionic entangled states shared by observers,
one of whom uniformly accelerates. Although fermionic entanglement persists for
arbitrarily large acceleration, the Bell/CHSH inequalities cannot be violated
for sufficiently large but finite acceleration. However the Svetlichny
inequality, which is a measure of genuine tripartite non-locality, can be violated
for any finite value of the acceleration.

## Geometric Discord in Non-Inertial Frames

Monday Jun 25, 2012
Speaker(s):

I review the recent work performed on computing the geometric
discord in non-inertial frames. We consider the well-known case of an
inertially maximally entangled state shared by inertial Alice and non-inertial
Robb. It is found that for high accelerations the geometric discord decays to a
negligible amount; this is in stark contrast to the entropic definition of
quantum discord which asymptotes to a finite value in the same limit. Such a
result has two different implications: the first being that usable quantum

## Quantum Teleportation from Alice to Rob in Vacuum

Monday Jun 25, 2012
Speaker(s):

We consider quantum teleportation of continuous variables in a relativistic system with the Unruh-DeWitt detectorscoupled to a common quantum field initially in the Minkowski vacuum. An unknown coherent state of an Unruh-DeWitt detector is teleported from one inertial agent (Alice) to an almost uniformly accelerated agent (Rob), using a detector pair initially entangled and shared by these two agents. Results for the averaged physical fidelity of quantum teleportation will be discussed.

## Physical Results with Fermions in RQI

Monday Jun 25, 2012
Speaker(s):

A number of works in the field of relativistic quantum information have been devoted to the study of entanglement on certain simple families of Unruh-mode entangled states in non-inertial frames. In the fermionic case remarkable results such as the survival of entanglement at infinite acceleration have been obtained.

## Entanglement of a Relativistic Field in the Vacuum State

Monday Jun 25, 2012
Speaker(s):

We discuss gedanken
experiments for measuring local and non-local observables in QFT that

respect causality, and can by used to test the entanglement between two spatially distant regions in the vacuum. It is shown that the entanglement
decays exponentially with the distance between the regions and does not vanish, in contrast to the
case of lattice models. We discuss in this respect a possible mechanism which might
explain this persistence effect, and a connection between the Reeh-Schlieder

Scientific Areas:

## The Quest for Localization

Monday Jun 25, 2012
Speaker(s):

This talk aims to review the obstacles met in QFT to
reach an appropriate definition for such a basic concept as localization. The
anti-local character of the square root of the "- Laplace-Beltrami +
mass^2" operator prevents the existence of localized states with a finite
number of quanta. (Bosonic) quantum fields describe elementary excitations of
an extended system whose ground state is the vacuum. No wonder, there is a
complicated relationship between the cardinal

## Pages

Paul Alsing, Air Force Research Laboratory, Information Directorate

Organizers:

Robert Mann, University of Waterloo

Funding provided in part by: