QUOXIC

This meeting was held on Wednesday 12th December at Imperial College in the Institute for Mathematical Sciences.

Talk titles and abstracts are below.

Schedule

• 12:00 Alexander Retzker (Imperial) -- Detection of Acceleration Radiation in a Bose-Einstein Condensate.
• 12:45 Libby Heaney (Leeds) -- Entanglement in the Bose-Einstein Condensate Phase Transition.
• LUNCH
• 14:30 Joe Fitzsimons (Oxford) -- TBA
• 15:00 Etienne Brion (Imperial) -- Quantum Computing with Collective Ensembles of Multi-Level Systems.
• COFFEE
• 16:00 Rob Spekkens (Cambridge) -- Negativity and Contextuality Are Equivalent Notions of Nonclassicality.
• 16:30 Bob Coecke (Oxford) -- The logic of Spekkens' toy model

Abstracts

We propose and study methods for detecting the Unruh effect in a Bose-Einstein condensate. The Bogoliubov vacuum of a Bose-Einstein condensate is used here to simulate a scalar field-theory, and accelerated atom dots or optical lattices as means for detecting phonon radiation due to acceleration effects. We study Unruh's effect for linear acceleration and circular acceleration. In particular, we study the dispersive effects of the Bogoliubov spectrum on the ideal case of exact thermalization. Our results suggest that Unruh's acceleration radiation can be tested using current accessible experimental methods.

As a Bose gas is cooled below the transition temperature for condensation strong correlations begin to form between all points in space. This spatial coherence is mathematically described by the one-bodied reduced density matrix, which measures the overlap of a particles wavefunction at two different points in space. As previous work has indicated that particle number entanglement also exists between regions of space in a BEC, it is interesting to ask whether the phenomena of spatial coherence and entanglement are related. The aim of this talk is to explore this relationship. Intriguingly, I will show that entanglement in the gas can be detected by quantities that are dependent on the one-bodied reduced density matrix and we will see that spatial coherence between regions of space is necessary but by no means sufficient for entanglement.

In this talk, I shall present a new physical approach for encoding and processing of quantum information in ensembles of multi-level quantum systems. In this new framework, the different bits are not carried by individual particles but associated with the collective population of different internal levels. One- and two-bit gates are implemented by collective internal state transitions taking place in the presence of an excitation blockade mechanism which restricts the population of each internal state to the values zero and unity. Via this scheme, 10-20 bit quantum computers can be built in single trapped clouds of ground state atoms subject to the Rydberg excitation blockade mechanism, and the linear dependence between register size and the number of internal quantum states in atoms offers realistic means to reach larger registers.

It is common to assert that the discovery of quantum theory overthrew our classical conception of nature. But what, precisely, was overthrown? Two notions of nonclassicality that have been investigated intensively are: (1) negativity, that is, the need to posit negative probabilities when representing quantum states by real functions on classical state spaces, for instance, when using Wigner's representation on phase space, and (2) contextuality, that is, the impossibility of a hidden variable model of quantum theory wherein the representation of measurements does not depend on the context of the measurement. Although both of these notions were meant to characterize the conditions under which a classical explanation cannot be provided, I demonstrate that they are inadequate to the task and I argue for a particular way of generalizing and revising them. With the refined version of each in hand, it becomes apparent that they are in fact one and the same.

We recast Spekkens' toy model [Spek] as a categorical construction on the category Rel of sets, relations and cartesian product. This category Rel, by being a so-called `dagger-compact category' [AC], already supports typical quantum structural features such as full-blown Dirac notation including inner-product, adjoints, projectors, unitarity, trace, map-state duality [Kind], as well as the construction of mixed-states and completely positive maps [Sel], and in particular, tensor structure, which is in fact the source to all the above. Rel also contains a classical objects [CP1] from which arise superpositions, GHZ-states, POVMs, decoherence structure and corresponding emergent classicality [CP2, CPP]. What Rel however manifestly lacks is `the' key quantum concept of complementarity: each system comes with only a single observable. What Spekkens' construction adjoins to Rel is exactly Pauli-type complementarity. We contrast the way in which complementarity arise from a propositional structure (= question set) as compared to the Birkhoff-von Neumann-Piron conception of how quantumness (superposition and complementarity that is in this case) arises from propositional structure [Moo, CMW].

[Spek] R. Spekkens (...) ... toy-theory ...
[AC] S. Abramsky and B. Coecke (2004) A categorical semantics of quantum protocols. arXiv:quant-ph/0402130
[Coe] B. Coecke (2005) Kindergarten quantum mechanics. arXiv:quant-ph/0510032
[Sel] P. Selinger (2007) Dagger compact categories and completely positive maps. Electronic Notes in Theoretical Computer Science 170, 139--163.
[CP1] B. Coecke and D. Pavlovic (2006) Quantum measurements without sums. arXiv:quant-ph/0608035
[CP2] B. Coecke and E. O. Paquette (2006) POVMs and Naimark's theorem without sums. arXiv:quant-ph/0608072
[CPP] B. Coecke, E. O. Paquette and D. Pavlovic (2008) Classical structures from tensorial quantum structures. Draft paper.
[Moo] D. J. Moore (1999) On State Spaces and Property Lattices. Studies in the History and Philosophy of Modern Physics 30, 61--83.
[CMW] B. Coecke, D.J. Moore and A. Wilce (2000) Operational quantum logic: An overview. arXiv:quant-ph/0008019