# Concepts and Paradoxes in a Quantum Universe

Conference Date:
Monday, June 20, 2016 (All day) to Friday, June 24, 2016 (All day)
Scientific Areas:
Quantum Foundations

By developing new approaches to quantum measurement that don't disturb the quantum system, and by using pre- and post-selection, Yakir Aharonov and group were able to show that one can develop a new way to think about quantum mechanics that is intuitive, consistent, and free of paradoxes.

This is a joint conference between:

Sponsorship for this conference has been provided by:

• Yakir Aharonov, Chapman University
• Alonso Botero, Universidad de los Andes
• Robert Boyd, University of Ottawa & University of Rochester
• Boris Braverman, Massachusetts Institute of Technology
• Andrew Briggs, University of Oxford
• Roman Buniy, Chapman University
• Eli Cohen, Bristol University
• Lajos Diosi, Wigner Research Centre for Physics
• Justin Dressel, Chapman University
• Avshalom Elitzur, Israeli Institute for Advanced Research
• Yuval Gefen, Weizmann Institute
• John Gray, Naval Surface Warfare Center, Dahlgren
• Armen Gulian, Chapman University
• Lucien Hardy, Perimeter Institute
• Yuji Hasegawa, Vienna University of Technology
• Holger Hofmann, Hiroshima University
• John Howell, University of Rochester
• Andrew Jordan, University of Rochester
• Tirzah Kaufherr, Tel Aviv University
• Sir Anthony Leggett, University of Illinois at Urbana-Champaign
• Matthew Leifer, Chapman University
• Gus Lobo, Universidade Federal de Ouro Preto
• Kelvin McQueen, Tel Aviv University
• Ali Nayeri, Chapman University
• Arun Pati, Harish-Chandra Research Institute
• Philip Pearle, Hamilton College
• Marlan Scully, Texas A&M University
• Yutaka Shikano, Institute for Molecular Science, National Institutes of Natural Sciences
• Lee Smolin, Perimeter Institute
• Robert Spekkens, Perimeter Institute
• Aephraim Steinberg, University of Toronto
• Jeff Tollaksen, Chapman University
• Mauricio Torres, Darmstadt University of Technology
• James Troupe, University of Texas
• Neil Turok, Perimeter Institute
• Bill Unruh, University of British Columbia
• Lev Vaidman, Tel Aviv University
• Cai Waegell, Chapman University

• Yakir Aharonov, Chapman University
• David Albert, Columbia University
• James Bardeen, University of Washington
• Alonso Botero, Universidad de los Andes
• Frederic Bouchard, University of Ottawa
• Cristian Bourgeois, Chapman University
• Robert Boyd, University of Ottawa & University of Rochester
• Boris Braverman, Massachusetts Institute of Technology
• Andrew Briggs, University of Oxford
• Roman Buniy, Chapman University
• Areeya Chantasri, University of Rochester
• Eli Cohen, Bristol University
• Ismaell DePaiva, Chapman University
• Lajos Diosi, Wigner Research Centre for Physics
• Justin Dressel, Chapman University
• Avshalom Elitzur, Israeli Institute for Advanced Research
• Robert Fickler, University of Ottawa
• Luis Pedro Garcia-Pintos, Bristol University
• Yuval Gefen, Weizmann Institute
• John Gray, Naval Surface Warfare Center, Dahlgren
• Lucien Hardy, Perimeter Institute
• Jeremie Harris, University of Ottawa
• Yuji Hasegawa, Vienna University of Technology
• Holger Hofmann, Hiroshima University
• John Howell, University of Rochester
• Andrew Jordan, University of Rochester
• Tirzah Kaufherr, Tel Aviv University
• Tim Koslowski, Universidad Nacional Autónoma de México (UNAM)
• Tomer Landsberger, Tel Aviv University
• Sir Anthony Leggett, University of Illinois at Urbana-Champaign
• Matthew Leifer, Chapman University
• Philippe Lewalle, University of Rochester
• Gus Lobo, Universidade Federal de Ouro Preto
• Kelvin McQueen, Tel Aviv University
• Alvaro Mozota, Perimeter Institute
• Markus Mueller, Perimeter Institute & University of Western Ontario
• Ali Nayeri, Chapman University
• Shengshi Pang, University of Rochester
• Arun Pati, Harish-Chandra Research Institute
• Taylor Patti, Chapman University
• Philip Pearle, Hamilton College
• Marlan Scully, Texas A&M University
• Yutaka Shikano, Institute for Molecular Science, National Institutes of Natural Sciences
• Tomer Shushi, University of Haifa
• Lee Smolin, Perimeter Institute
• Robert Spekkens, Perimeter Institute
• Aephraim Steinberg, University of Toronto
• Jeff Tollaksen, Chapman University
• Mauricio Torres, Darmstadt University of Technology
• James Troupe, University of Texas
• Neil Turok, Perimeter Institute
• Bill Unruh, University of British Columbia
• Lev Vaidman, Tel Aviv University
• Luz Jimenez Vela, Chapman University
• Cai Waegell, Chapman University
• Elie Wolfe, Perimeter Institute

Monday, June 20, 2016

 Time Event Location 8:30 – 9:00am Registration Reception 9:00 – 9:10am Welcome and Opening Remarks Bob Room SESSION 1:  Foundational questions 9:10 – 10:00am Yakir Aharonov, Chapman UniversityFinally making sense of Quantum Mechanics, part 1 Bob Room 10:00 – 10:45am Aephraim Steinberg, University of TorontoHow to count one photon and get a(n average) result of 1000... Bob Room 10:45 – 11:00am Coffee Break Bistro – 1st Floor 11:00 – 11:45am Marlan Scully, Texas A&M UniversityTBA Bob Room 11:45 – 12:30pm Avshalom Elitzur, Israeli Institute for Advanced ResearchThe Quantum Tip of the Two-Vector Iceberg Bob Room 12:30 – 2:00pm Lunch Bistro – 2nd Floor SESSION 2:  Quantum correlation 2:00 – 2:30pm Andrew Jordan, University of RochesterThe arrow of time for continuous quantum measurements Bob Room 2:30pm – 3:00pm Yutaka Shikano, Institute for Molecular Science,National Institutes of Natural SciencesObservation of Aharonov-Bohm effect with quantum tunneling Bob Room 3:00 – 3:30pm Coffee Break Bistro – 1st Floor 3:30 – 4:00pm Cai Waegell, Chapman UniversityConfined contextuality:  How specific counterfactual paradoxes in pre- and post-selected Kochen-Specker sets give rise to experimentally observable consequences. Bob Room 4:00 – 4:30pm Justin Dressel, Chapman UniversityWeak and continuous measurements in superconducting circuits Bob Room 4:30 – 4:45pm Coffee Break Bistro – 1st Floor 4:45 – 5:30pm Sir Anthony Leggett, University of Illinois at Urbana-ChampaignRealism Versus Quantum Mechanics: Implications of Recent Experiments Bob Room

Tuesday, June 21, 2016

 Time Event Location SESSION 3:  Implementations 9:00 – 9:45am Yakir Aharonov, Chapman UniversityFinally making sense of Quantum Mechanics, part 2 Bob Room 9:45 – 10:30am Andrew Briggs, University of OxfordThe Unreasonable Effectiveness of Curiosity Bob Room 10:30 – 11:00am Coffee Break Bistro – 1st Floor 11:00 – 11:45am Robert Boyd, University of Ottawa/ University of RochesterTBA Bob Room 11:45 – 12:30pm John Howell, University of RochesterTBA Bob Room 12:30 – 2:00pm Lunch Bistro – 2nd Floor SESSION 4:  Quantum phases 2:00 – 2:30pm Roman Buniy, Chapman UniversityHigher order topological actions Bob Room 2:30pm – 3:00pm Gus Lobo, Universidade Federal de Ouro PretoPhase Space Methods in Quantum Mechanics and Weak Values Bob Room 3:00 – 3:10pm Conference Photo TBA 3:10 – 3:30pm Coffee Break Bistro – 1st Floor 3:30 – 4:00pm Tirzah Kaufherr, Tel Aviv UniversityGauge invariant nonlocal nonlocal quantum dynamics of the Aharonov-Bohm effect and how it may be tested Bob Room 4:00 – 4:30pm Alonso Botero, Universidad de los AndesUbiquity of Weak Values Bob Room 4:30 – 4:45pm Coffee Break Bistro – 1st Floor 4:45  – 5:30pm Philip Pearle, Hamilton CollegeQuantized Vector Potential and the Magnetic Aharonov-Bohm Effect Bob Room

Wednesday, June 22, 2016

 Time Event Location SESSION 5:  Interpretations/Philosophy 9:00 – 9:45am Yakir Aharonov, Chapman UniversityFinally making sense of Quantum Mechanics, part 3 Bob Room 9:45 – 10:30am Lajos Diosi, Wigner Research Centre for PhysicsFeatures of Sequential Weak Measurements Bob Room 10:30 – 11:00am Coffee Break Bistro – 1st Floor 11:00 – 11:45am Arun Pati, Harish-Chandra Research InstituteUncertainty and Complementarity Relations with Weak values Bob Room 11:45 – 12:30pm Lev Vaidman, Tel Aviv UniversityThe meaning of weak values Bob Room 12:30 – 2:00pm Lunch Bistro – 2nd Floor SESSION 6:  Interpretations/Philosophy 2:00 – 2:30pm Armen Gulian, Chapman University10 Minutes of the Aharonov-Bohm effect and 20 minutes of a new superconducting gravitational-wave detector Bob Room 2:30pm – 3:00pm Boris Braverman, Massachusetts Institute of TechnologyOur Quantum World, Contextuality, and Bohmian Mechanics Bob Room 3:00 – 3:30pm Coffee Break Bistro – 1st Floor 3:30 – 4:00pm Kelvin McQueen, Tel Aviv UniversitySelf-locating uncertainty and the many worlds interpretation Bob Room 4:00 – 4:30pm Matt Leifer, Chapman UniversityDoes time-symmetry in quantum theory imply retrocausality? Bob Room 4:30 – 4:45pm Coffee Break Bistro – 1st Floor 4:45  – 5:30pm Rob Spekkens, Perimeter InstituteTBA Bob Room

Thursday, June 23, 2016

 Time Event Location SESSION 7:  General relativity/Cosmology 9:00 – 9:45am Yakir Aharonov, Chapman UniversityFinally making sense of Quantum Mechanics, part 4 Bob Room 9:45 – 10:30am Bill Unruh, University of British ColumbiaQuantum Mechanics is Not Non-Local Bob Room 10:30 – 11:00am Coffee Break Bistro – 1st Floor 11:00 – 11:45am Neil Turok, Perimeter InstituteA Perfect Quantum Cosmological Bounce Bob Room 11:45 – 12:30pm Lee Smolin, Perimeter InstituteQuantum mechanics and the principle of maximal variety Bob Room 12:30 – 2:00pm Lunch Bistro – 2nd Floor SESSION 8:  General relativity/Cosmology 2:00 – 2:30pm Eli Cohen, University of BristolA Final Boundary Condition: Several Implications for the Universe Bob Room 2:30pm – 3:00pm Ali Nayeri, Chapman UniversityInstability of Flatspace and the Early Quantum Fluctuations by Considering an Unbounded Hamiltonian Bob Room 3:00 – 3:30pm Coffee Break Bistro – 1st Floor 3:30 – 4:00pm Juan Mauricio Torres, Darmstadt University of TechnologyAtomic two-qubit quantum operations with ancillary multiphoton states Bob Room 4:00 – 4:45pm David Albert, Columbia UniversityTBA Bob Room 5:30 – 8:00pm Banquet Bistro – 2nd Floor

Friday, June 24, 2016

 Time Event Location SESSION 9:  Implementations 9:00 – 9:45am Yakir Aharonov, Chapman UniversityFinally making sense of Quantum Mechanics, part 5 Bob Room 9:45 – 10:30am Yuji Hasegawa, Vienna University of TechnologyQuantum paradoxes emerging in matter-wave interferometer experiments Bob Room 10:30 – 11:00am Coffee Break Bistro – 1st Floor 11:00 – 11:45am Yuval Gefen, Weizmann InstituteTBA Bob Room 11:45 – 12:30pm Holger Hoffman, Hiroshima UniversityWhy interactions matter: How the laws of dynamics determine the shape of physical reality Bob Room 12:30 – 2:00pm Lunch Bistro – 2nd Floor SESSION 10:  Applications 2:00 – 2:30pm James Troupe, University of TexasA Contextuality Based Quantum Key Distribution Protocol Bob Room 2:30pm – 3:00pm John Gray, Naval Surface Warfare Center, DahlgrenSome Implications of the Aharonov Ansatz to Sensing Bob Room 3:00 – 3:30pm Coffee Break Bistro – 1st Floor 3:30 – 4:00pm Lucien Hardy, Perimeter InstituteTBA Bob Room 4:00 – 4:45pm Panel Discussion Bob Room 4:45pm Good-bye Bob Room

Yakir Aharonov, Chapman University

Finally making sense of Quantum Mechanics

Alonso Botero, Universidad de los Andes

Ubiquity of Weak Values

In this brief talk we will show how weak values appear in a wide range of physical contexts beyond the usual context of weak measurements. Among others, we will discuss how weak values appear in: the physics of classical parameters in a quantum evolution; the statistics of strong measurements; formulas for probability amplitudes in quantum mechanics; and finally, in the classical correspondence of quantum mechanics.

Boris Braverman, Massachusetts Institute of Technology

Our Quantum World, Contextuality, and Bohmian Mechanics

Our universe is at its heart quantum mechanical, yet classical behaviour is seen everywhere. I will discuss the scales that determine the quantum to classical transition and the prospects for the observation of ever more macroscopic quantum behaviour. I will then discuss how paradoxes in quantum mechanics can be understood and visualized with Bohmian trajectories, how these trajectories can be measured, and the implications for the ontology of the Bohmian picture.

Andrew Briggs, University of Oxford

The Unreasonable Effectiveness of Curiosity

Curiosity about how the world works can lead to beneficial progress in technology, and vice-versa. This kind of interplay can be found in quantum nanoscience, where foundationally motivated experiments and technologically motivated experiments often use similar materials and techniques, because both involve extending the realm of non-classical behaviour. At a higher level, curiosity about ultimate questions such as meaning and purpose can create an environment that is conducive to scientific breakthroughs, and many of the best minds in science have also been curious about deeper realities. Eugene Wigner described the miracle of the effectiveness of mathematics as a wonderful gift which we neither understand nor deserve. The same could be said of curiosity.

Roman Buniy, Chapman University

Higher order topological actions

In classical mechanics, an action is defined only modulo additive terms which do not modify the equations of motion; in certain cases, these terms are topological quantities. We construct an infinite sequence of higher order topological actions and argue that they play a role in quantum mechanics, and hence can be accessed experimentally.

Eli Cohen, University of Bristol

A Final Boundary Condition: Several Implications for the Universe

In classical mechanics, only the initial state of the system is needed to determine its time evolution. Additional information on the final state is either redundant or inconsistent. In quantum mechanics, however, the initial state does not convey all measurements’ outcomes. Only when augmented with a final quantum state, which can be understood as propagating backwards in time, a richer, more complete picture of quantum reality is portrayed.
This time-symmetric view leads to a subtle kind of a local hidden-variables theory, where true collapse never occurs, yet can be effectively observed. Moreover, the Born rule and the borderline between classical and quantum systems can be derived from, respectively, the requirements of stability and “macroscopic robustness under time-reversal.’’ The significant role of macroscopic systems in amplifying and recording quantum outcomes then directly follows.
Some possible cosmological consequences of this construction are discussed, especially those related to the breakdown of the “Pigeonhole principle” and our on-going work on the concept of  “Quantum Holism”.

The talk will be partially based on:
1. Y. Aharonov, E. Cohen, E. Gruss, T. Landsberger, Quantum Stud.: Math. Found. 1 (2014) 133-146.
2. Y. Aharonov, E. Cohen, A.C. Elitzur, Ann. Phys. 355 (2015) 258-268.
3. Y. Aharonov, E. Cohen, to be published in “Quantum Nonlocality and Reality”, M. Bell and S. Gao (Eds.), Cambridge University Press, arXiv:1504.03797.
4. E. Cohen, Y. Aharonov, to be published in “Quantum Structural Studies: Classical Emergence from the Quantum Level”, R.E. Kastner, J. Jeknic-Dugic, G. Jaroszkiewicz (Eds.), World Scientific Publishing Co., arXiv:1602.05083.

Lajos Diosi, Wigner Research Centre for Physics

Features of Sequential Weak Measurements

I discuss the outcome statistics of sequential weak measurement of general observables.

In sequential weak measurement of canonical variables, without post-selection, correlations yield the corresponding correlations of the Wigner function.
Outcome correlations in spin-1/2 sequential weak measurements without post-selection coincide with those in strong measurements, they are constrained kinematically so that they yield as much information as single measurements. In sequential weak measurements with post-selection, a new anomaly occurs, different from the weak value anomaly in single weak measurements. I consider trivial post-selection, i.e.:
re-selection |f>=|i>,
which should intuitively not differ from no post-selection since weak measurements are considered non-invasive. Indeed, re-selection does not matter, compared with no-selection, for single weak measurement. It does so, however, for sequential ones. I illustrate it in spin-1/2 weak measurement.

Justin Dressel, Chapman University

Weak and continuous measurements in superconducting circuits

Superconducting circuit technology has rapidly developed over the past several years to become a leading contender for realizing a scalable quantum computer. Modern circuit designs are based on the transmon qubit, which coherently superposes macroscopic charge oscillations. Measurements of a transmon are fundamentally weak and continuous in time, with projective measurements emerging only after a finite duration. Adding gates, such measurements may then implement ancilla-based measurements of controllable strength. Recent experiments have used both types of weak measurement to great effect: for monitoring qubit evolution, and for showing violations of a hybrid Bell-Leggett-Garg inequality.

John Gray, Naval Surface Warfare Center, Dahlgren

Some Implications of the Aharonov Ansatz to Sensing

There is a common framework for the measurement problem for sensors such as radars, sonars, and optics in a common language by casting analysis of signals in the language of quantum mechanics (Rigged Hilbert Space). The use of this language can reveal a more detailed understanding of the underlying interactions of a return signal that are not usually brought out by standard signal processing design techniques. The weak measurement Ansatz first provided by the Aharonov, Albert and Vaidman paper (A2V) that introduced weak values to the world provides an explicit means to consider all interactions of a signal with an object by using what we term the Aharonov Ansatz. The Aharonov Ansatz for sensing can summarized as:

1. Any sensor measurement process, whether active or passive can be thought of as determining the mathematical operator's characteristics of a signal's interaction with a object.

2. Certain types of interaction operators can be "post-selected" for in the return signal when the broadcast signal is known for either a single or multiple operators so receiver design can be optimized.

3. In principle detectors can design can be optimized, "matched" to signal interaction for these operators (operator matched filter), so mathematical solutions to receiver (in the classical sense) design or the design of apparatus of difficult to measure quantum interactions can be improved as has been reported in the literature.

4. Matching or post-selection to a given operator, when possible, maximizes ability to detect a "signal" or the characteristics of an interaction.

Finally, in this talk we note a connection between this work and a the variational functional used in perturbation theory in quantum mechanics.

Holger Hofmann, Hiroshima University

Why interactions matter: How the laws of dynamics determine the shape of physical reality

Measurements performed at variable strengths show that non-commuting physical properties are related by complex-valued statistics, where the complex phase expresses the action of transformations along orbits represented by the eigenstates. In strong measurements, the dynamics along the orbits is completely randomized, which means that the pure states prepared by such a measurement actually represent ergodic statistics where the coherence between components originates from quantum dynamics. The complex algebra of Hilbert space inner products describes the intersection of two ergodically randomized orbits, where the complex phase describes the action of propagation along the orbits. Since the same action also appears in classical descriptions of the dynamics it is possible to derive quantum states and their time evolution directly from the classical equations of motion, without the abstractions of operator algebra.

A representative example of this fundamental relation between classical dynamics and quantum coherence is the multi-photon interference in two-path interferometers, where the multi-photon interference fringes can be explained by the action enclosed by two classical orbits corresponding to the input and output photon number states. This example shows how the non-classical features of quantum statistics emerge from the effects of enclosed actions on the causality relations between the initial orbit prepared by ergodic randomization and the final orbit along which the system was sampled during the measurement. Since action relations take the same form in quantum mechanics and in the classical limit, any attempt to explain quantum mechanics should start with an analysis of the dynamics.

The conventional sense of reality only emerges from the consistency of causality relations,not from any abstract knowledge of reality''. Our concepts of particles and trajectories only have an approximate validity which breaks down in the limit of small action. Reality always requires the dynamics of interaction, and hbar is an absolute limitation of physical reality. In this presentation, I hope to clarify that this absence of a microscopic material reality can be understood quite naturally in terms of the well known physics of dynamics and interactions, removing the need for any untestable platonic assumptions about a hypothetical reality out there''.

Yuji Hasegawa, Vienna University of Technology

Quantum paradoxes emerging in matter-wave interferometer experiments

Peculiarities of quantum mechanical predictions on a fundamental level are investigated intensively in matter-wave optical setups; in particular, neutron interferometric strategy has been providing almost ideal experimental circumstances for experimental demonstrations of quantum effects. In this device quantum interference between beams spatially separated on a macroscopic scale is put on explicit view.

Recently, a new counter-intuitive phenomenon, called quantum Cheshire-cat, is observed in a neutron interferometer experiment. Weak measurement and weak values justify the access of the neutrons’ dynamics in the interferometer. Moreover, another experiment reported full determination of weak-values of neutron’s ½-spin; this experiment is further applied to demonstrate quantum Pigeonhole effect and quantum contextual. In my talk, I am going to give an overview of neutron interferometry for investigation of quantum paradoxes.

Andrew Jordan, University of Rochester

The arrow of time for continuous quantum measurements

The question of the time reversibility of quantum mechanics with measurements is one that has been debated for some time.  In this talk, I will present new work exploring our ability to distinguish the forward from the time-reverse measurement records of continuous quantum measurements.  The question involves both the conditions for the time-reversibility of the quantum trajectory equations of motion, as well as statistical distinguishability of the arrow of time. I will present the case with and without postselection on the final state, and connect the issue to a similar topic in nonequilibrium statistical physics.  This work generalizes and pushes the two-time reformulation of quantum mechanics developed by Yakir Aharonov and collaborators beyond arbitrarily weak measurements. I will also discuss how this proposal can be implemented with continuously monitored superconducting quantum circuits.

In collaboration with Alexander Korotkov, Justin Dressel, Areeya Chantasri, and Kater Murch

Funded by the John Templeton Foundation.

Tirzah Kaufherr, Tel Aviv University

Gauge invariant nonlocal nonlocal quantum dynamics of the Aharonov-Bohm effect and how it may be tested

The gauge invariant nonlocal quantum dynamics that is responsible for the Aharonov-Bohm effect is described. It is shown that it may be verified experimentally.

Sir Anthony Leggett, University of Illinois at Urbana-Champaign

Realism Versus Quantum Mechanics: Implications of Recent Experiments

Matthew Leifer, Chapman University

Does time-symmetry in quantum theory imply retrocausality?

The two-state vector formalism of Aharonov and collaborators introduces a backwards-evolving state in order to restore time symmetry to quantum measurement theory.  The question then arises, does any time-symmetric account of quantum theory necessarily involve retrocausality (influences that travel backwards in time)?  In [1], Huw Price argued that, under certain assumptions about the underlying ontology, an interpretation of quantum theory that is both realist and time-symmetric must be retrocausal.  Price’s argument is based on an analysis of a photon travelling between two polarizing beam-splitters. One of his assumptions is that the usual forward-evolving polarization vector of the photon is a beable, i.e. part of the ontology. He argues, on the basis of this and his other assumptions, that a backward-evolving polarization vector must also be a beable.

The assumption that the forward evolving polarization vector is a beable is an assumption of the reality of the quantum state. But one of the reasons for exploring retrocausal interpretations of quantum theory is that they offer the potential for evading the unpleasant conclusions of no-go theorems, such as Bell’s theorem and, in particular, recent proofs of the reality of the quantum state [2]. In this talk, I will show how Price’s argument can, in fact, be generalized so that it does not assume the reality of the quantum state. I also reformulate the common assumptions of Price’s and our arguments to make them more generally applicable and to pin down the notion of time-symmetry involved more precisely. The notion of time-symmetry used in the argument is stronger than the notion of time-symmetry usually used in physics, but is still a true symmetry of quantum theory that ought to be taken seriously.

This talk is based on joint work with Matt Pusey.

[1] H. Price. Does time-symmetry imply retrocausality? How the quantum world says “maybe”. Stud. Hist. Phil. Mod. Phys., 43(2):75–83, 2012. arXiv:1002.0906

[2] For a review see M. Leifer. Is the quantum state real? An extended review of psi-ontology theorems. Quanta, 3:67-155, 2014. arXiv:1409.1570

Gus Lobo, Universidade Federal de Ouro Preto

Phase Space Methods in Quantum Mechanics and Weak Values

Phase space methods are ubiquitous in quantum mechanics. From the Weyl-Wigner Moyal formalism to coherent states and discrete phase spaces we see the imprints of the classical world again and again. In this presentation, we address one of two major developments introduced by Aharonov and his collaborators: The concept of weak values that stems from a time-symmetric view of quantum physics. We look at the weak measurement through two distinct geometric frames: The geometry of the measuring apparatus and the geometry of the measured system. We nalize with some brief comments on the second major conceptual due to Aharonov and collaborators: the theory of modular variables and how Schwinger´s discrete phase space structure helps to shed light on it. We conclude then with the following mantra: It´ s all about phase space.

Kelvin McQueen, Tel Aviv University

Self-locating uncertainty and the many worlds interpretation

According to the many worlds interpretation (MWI), quantum mechanics in its simplest form (no collapse or hidden variables) is complete. A primary objection to the MWI is that it fails to account for the Born rule. The most prominent response to this objection comes from the decision-theoretic program, which aims to derive a rationality postulate according to which a believer in the MWI ought to act as if the Born rule is true. I argue that the existence of alternative coherent rationality postulates undermines this response. A different response, based on self-locating uncertainty, avoids this objection and may explain the Born rule in the MWI. I conclude by considering whether this framework is capable of explaining the weak trace of particles in certain difficult cases.

Ali Nayeri, Chapman University

Instability of Flatspace and the Early Quantum Fluctuations by Considering an Unbounded Hamiltonian

Introducing a new field which makes the Hamiltonian unbounded, we show that vacuum fluctuations of a scalar field destabilized the flatspace. Perturbation in this new scalar field, may also explain some astrophysical phenomena in the galactic scale.

Arun Pati, Harish-Chandra Research Institute

Uncertainty and Complementarity Relations with Weak values

The products of weak values of quantum observables have interesting implications in deriving quantum uncertainty and complementarity relations for both weak and  strong measurement statistics.  We show that a product representation formula allows the standard Heisenberg uncertainty relation to be derived from a  classical uncertainty relation for complex random variables. This formula also leads to a strong uncertainty relation for unitary operators which displays a new preparation uncertainty relation for quantum systems.

Furthermore, the two system observables that are weakly and strongly measured in a weak measurement context are shown to obey a complementarity relation under the interchange of these observables, in the form of an upper bound on the product of the corresponding weak values.

Moreover, we derive general tradeoff relations, between weak purity, quantum purity and quantum incompatibility using the weak value formalism.

Our results may open up new ways of thinking about uncertainty and complementarity relations using products of weak values.

Philip Pearle, Hamilton College

Quantized Vector Potential and the Magnetic Aharonov-Bohm Effect

The state vector describing the physical situation of the magnetic A-B effect should depend upon all three quantizeable entities in the problem, the electron orbiting the solenoid, the moving charged particles in the solenoid and the vector potential. One may imagine three approximate solutions to the exact dynamics, where two of the three entities do not interact at all, and the third, quantized, entity interacts with a classical approximation. Thus, fifty-five years ago, A-B showed that, if the interaction is between the quantized electron current and the classical approximation to the solenoid’s vector potential, the state vector acquires a measurable phase shift. Four years ago Vaidman showed that, if the interaction is between the quantized solenoid current and the classical approximation to the electron’s vector potential, the state vector acquires the

A-B phase shift. I shall first show why these two results have to be the same. Then, I shall show that, if the interaction is between the quantized vector potential and the classical approximation to the electron and solenoid currents, the state vector acquires the A-B phase shift. Lastly, I shall show how to reconcile these three mathematically and conceptually different calculations.

Yutaka Shikano Institute for Molecular Science, National Institutes of Natural Sciences

Observation of Aharonov-Bohm effect with quantum tunneling

Quantum tunneling is one such phenomenon that is essential for a number of devices that are now taken for granted. However, our understanding of quantum tunneling dynamics is far from complete, and there are still a number of theoretical and experimental challenges. The dynamics of the quantum tunneling process can be investigated if we can create a large tunneling region. We have achieved this using a linear Paul trap and a quantum tunneling rotor, which has resulted in the successful observation of the Aharonov–Bohm effect in tunneling particles. Also, this result shows that the spatially separated phonon can be interfered.

Aephraim Steinberg, University of Toronto

How to count one photon and get a(n average) result of 1000...

I will present our recent experimental work using electromagnetically induced transparency in laser-cooled atoms to measure the nonlinear phase shift created by a single post-selected photon, and its enhancement through "weak-value amplification."  Put simply, due to the striking effects of "post-selective" quantum measurements, a (very uncertain) measurement of photon number can yield an average value much larger than one, even when it is carried out on a single photon.  I will say a few words about possible practical applications of this "weak value amplification" scheme, and their limitations.

Time permitting, I will also describe other future and past work using "weak measurement," such as our studies quantifying the disturbance due to a measurement and what happens when it destroys interference; and our project to measure "where a particle has been" as it tunnels through a classically forbidden region – our prediction being that it will make it from one side of the barrier to the other without spending any significant time in the middle.

Juan Mauricio TorresDarmstadt University of Technology

Atomic two-qubit quantum operations with ancillary multiphoton states

We propose and theoretically investigate the implementation of entangling operations on two two-level atoms using cavity-QED scenarios. The atoms interact with an optical cavity and their state is postselected in a noninvasive way by measuring the optical field after the interaction. We show that the resulting quantum operation can be exploited to implement an entanglement purification protocol, where a fidelity larger than one half with respect to any Bell state is not a necessary condition.

James Troupe, University of Texas

A Contextuality Based Quantum Key Distribution Protocol

In 2005 R. Spekkens presented a generalization of noncontextuality that applies to imperfect measurements (POVMs) by allowing the underlying ontological model to be indeterministic. Unlike traditional Bell-Kochen-Specker noncontextuality, ontological models of a single qubit were shown to be contextual under this definition. Recently, M. Pusey showed that, under certain conditions, exhibiting an anomalous weak value implies contextuality. We will present a single qubit prepare and measure QKD protocol that uses observation of anomalous weak values of particular observables to estimate the quantum channel error rate and certify the security of the channel. We will also argue that it is the “degree” of contextuality of the noisy qubits exiting the channel that fundamentally determine the secure key rate. A benefit of this approach is that the security does not depend on the fair sampling assumption, and so is not compromised by Eve controlling Bob’s measurement devices. Thus it retains much of the benefit of “Measurement Device Independent” QKD protocols while only using single photon preparation and measurement.

Lev Vaidman, Tel Aviv University

The meaning of weak values

The weak value, as an expectation value, requires an ensemble to be found. Nevertheless, we argue that the physical meaning of the weak value is much more close to the physical meaning of an eigenvalue than to the physical meaning of an expectation value. Theoretical analysis and experimental results performed in the MPQ laboratory of Harald Weinfurter are presented. Quantum systems described by numerically equal eigenvalue, weak value and expectation value cause identical average shift of an external system interacting with them during an infinitesimal time. However, there are differences between the final states of the external system. In the case of an eigenvalue, the shift is the only change in the wavefunction of the external system. In case of the expectation value, there is an additional change in the quantum state of the same order, while in the case of the weak value the additional distortion is negligible.  The understanding of weak value as a property of a single system refutes recent claims that there exist classical statistical analogue to the weak value.

Bill Unruh, University of British Columbia

Quantum Mechanics is Not Non-Local

Bell's inequality is often stated as proving that quantum mechanics is non-local (rather than non-realistic, which apparently shows that physicists have more problems with non-realism than with non-locality). I will argue that the purpose of the use of locality in Bell's argument (in the CHSH form) is to make the classical system as close to the quantum system as possible, not to differentiate it from the quantum, and that non-realism is a more reasonable interpretation than is non-locality.

## Panel Discussion

Friday Jun 24, 2016
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## TBA

Friday Jun 24, 2016
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## Some Implications of the Aharonov Ansatz to Sensing

Friday Jun 24, 2016
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There is a common framework for the measurement problem for sensors such as radars, sonars, and optics in a common language by casting analysis of signals in the language of quantum mechanics (Rigged Hilbert Space). The use of this language can reveal a more detailed understanding of the underlying interactions of a return signal that are not usually brought out by standard signal processing design techniques.

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## A Contextuality Based Quantum Key Distribution Protocol

Friday Jun 24, 2016
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In 2005 R. Spekkens presented a generalization of noncontextuality that applies to imperfect measurements (POVMs) by allowing the underlying ontological model to be indeterministic. Unlike traditional Bell-Kochen-Specker noncontextuality, ontological models of a single qubit were shown to be contextual under this definition. Recently, M. Pusey showed that, under certain conditions, exhibiting an anomalous weak value implies contextuality.

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## Why interactions matter: How the laws of dynamics determine the shape of physical reality

Friday Jun 24, 2016
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Measurements performed at variable strengths show that non-commuting physical properties are related by complex-valued statistics, where the complex phase expresses the action of transformations along orbits represented by the eigenstates. In strong measurements, the dynamics along the orbits is completely randomized, which means that the pure states prepared by such a measurement actually represent ergodic statistics where the coherence between components originates from quantum dynamics.

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Friday Jun 24, 2016
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## Quantum paradoxes emerging in matter-wave interferometer experiments

Friday Jun 24, 2016
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Peculiarities of quantum mechanical predictions on a fundamental level are investigated intensively in matter-wave optical setups; in particular, neutron interferometric strategy has been providing almost ideal experimental circumstances for experimental demonstrations of quantum effects. In this device quantum interference between beams spatially separated on a macroscopic scale is put on explicit view.

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## Finally making sense of Quantum Mechanics, part 5

Friday Jun 24, 2016
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## TBA

Thursday Jun 23, 2016
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## Atomic two-qubit quantum operations with ancillary multiphoton states

Thursday Jun 23, 2016

We propose and theoretically investigate the implementation of entangling operations on two two-level atoms using cavity-QED scenarios. The atoms interact with an optical cavity and their state is postselected in a noninvasive way by measuring the optical field after the interaction. We show that the resulting quantum operation can be exploited to implement an entanglement purification protocol, where a fidelity larger than one half with respect to any Bell state is not a necessary condition.

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## Pages

Scientific Organizers:

• Yakir Aharonov, Chapman University
• Justin Dressel, Chapman University
• Lucien Hardy, Perimeter Institute
• Matthew Leifer, Chapman University
• Jeff Tollaksen, Chapman University