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Workshop on Reference Frames and Superselection Rules in Quantum Information Theory
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Efficient alignment of reference frames with and without shared
entanglement
Emili Bagan
Universitat Autonoma Barcelona, Spain
A system of spin 1/2 particles can be used to establish a common reference frame between two distant
parties. The optimal strategy exploits entanglement much in the same way as dense coding does. It requires
that each party has the same number N of spins (2N in total) which have to be prepared beforehand in a
specific maximally entangled state. The first part of this talk will review the key points of the optimal
strategy. In the second part it will be shown that one can in principle attain the asymptotic fidelity of the
optimal strategy with just half the number of spins (N in total) and, moreover, with no shared entanglement.
The relation of this work with the estimation of unknown one qubit gates will be also discussed.
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Generalized entanglement and superselection rules
Howard Barnum
Los Alamos National laboratory, USA
I review notions of generalized entanglement and generalized LOCC relative to a subspace of observables
introduced in order to understand information processing with various restrictions on the means available
for observation and control of a system. When the distinguished observable space admits nontrivial
invariant subspaces, this notion corresponds to information-processing subject to superselection rules; I
will examine this situation in detail, give some applications, and relate the notion to others' work on
superselection rules in quantum information. Joint work with E. Knill, G. Ortiz, R. Somma, and L. Viola
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Mixed-state entanglement in the light of pure-state entanglement constrained by superselection rules
Stephen Bartlett
University of Queensland, Australia
All pure bipartite states that cannot be locally prepared can, through local operations, be distilled into a
maximally entangled state. On the other hand, there exist mixed bipartite states that are neither locally
preparable nor distillable; these are the bound entangled states. For reasons such as this, characterising
mixed state entanglement (MSE) is a notoriously difficult problem. I show that pure state entanglement
constrained by superselection rules (SSRs) possesses a similar structure to MSE, but is much easier to
characterise, in particular if the SSR is Abelian. Also, unsolved questions in MSE have analogous
questions in the context of constrained pure state entanglement which can be answered. Our results may
suggest future directions for progress in the study of MSE.
Joint work with Howard Wiseman and Robert Spekkens
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Maximum likelihood and efficient use of quantum resources in the alignment of reference frames
Giulio Chiribella
University of Pavia, Italy
The absolute alignment of reference frames using quantum systems can be viewed as a particular case of
group parameter estimation, involving the rotation group. In the first part of the talk, I will review some
simple results about covariant measurements which maximize the likelihood. The maximization of the
likelihood provides a clear insight about the group theoretical structure involved in estimation problems. In
the second part, the mentioned results will be used as guidelines in the alignment problem. This approach
leads directly to the best efficiency known for absolute alignment, without the need of using entanglement
between sender and receiver.
Joint work with G.M.D'Ariano, P.Perinotti, and M.F.Sacchi.
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Quantum Reference Frames and Uncertainty
Michael Dickson
Indiana University, USA
Attending carefully to the role that reference frames play in the definition of physical concepts in quantum
theory can lead us to a clearer understanding of the uncertainty relations, and the connection that they have
with the fact that physical quantities are defined in terms of, and measured relative to, reference frames. I
shall begin with a brief historical look at the role of reference frames in classical physics, then show how
taking that role seriously in the context of quantum mechanics sheds some light on the uncertainty
relations.
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On quantum alignment of chiralities of distant frameworks
Lajos Diosi
Research Institute for Particle and Nuclear Physics, Hungary
Entangled quantum states are extraordinary sensitive to independent reflections of local reference frames.
One might think this sensitivity enhances the capacity of quantum communication in alignment of, e.g., the
chiralities of distant reference frames. This challenging idea will be discussed and conditions of such
enhancement will be explored.
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Quantum reference frames and relative states
Nicolas Gisin
University of Geneva, Switzerland
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