Bulletin of the American Physical Society
2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007; Denver, Colorado
Session B33: Focus Session: Quantum Foundations I |
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Sponsoring Units: GQI Chair: Carlton Caves, University of New Mexico Room: Colorado Convention Center 403 |
Monday, March 5, 2007 11:15AM - 11:51AM |
B33.00001: Almost quantum theory: classical theories with a constraint on knowledge Invited Speaker: What kind of theory would be appropriate for an agent living in a world that is essentially classical but where there is a fundamental restriction on how much knowledge can be acquired about the physical state of any system? Formalizing such a restriction, one can define several toy theories that are found to have a rich structure similar to that of quantum theory, including a notion of coherent superposition and entanglement. These theories are also found to have analogues of a wide variety of quantum phenomena, such as complementarity, interference, teleportation, no-cloning, and many quantum cryptographic and communication protocols. The diversity and quality of these analogies provides compelling evidence for the view that quantum states are not states of reality -- as most interpretations suggest -- but rather states of knowledge that are incomplete (and cannot be completed). The question ``what is the nature of the reality to which this knowledge refers?" remains open in this research program but the phenomenon of contextuality (a consequence of the Bell-Kochen-Specker theorem) provides, I argue, our best clue for how to answer it. [Preview Abstract] |
Monday, March 5, 2007 11:51AM - 12:03PM |
B33.00002: Cloning, Broadcasting and the de Finetti theorem in Generalized Probablistic Theories Matthew Leifer, Howard Barnum, Jonathan Barrett, Alexander Wilce We give a lightning overview of a framework for generalized probablistic theories, proposed by Barrett, that includes classical probability and quantum theory as special cases. The framework also includes theories that support ``superquantum'' correlations, which violate Bell inequalities to a larger extent than quantum theory whilst still not allowing signalling. In recent years, many similarities between quantum entanglement/nonlocality and ``superquantum'' correlations have been found by researchers studying quantum information and foundations. These can be seen to emerge from the common structure of all theories in Barrett's framework. In particular, some results from quantum information that can be generalized to all theories in the framework are described, including versions of the no-cloning theorem, the no-broadcasting theorem and the de Finetti theorem. [Preview Abstract] |
Monday, March 5, 2007 12:03PM - 12:15PM |
B33.00003: Quantum Mechanics on Phase Space and Informational Completeness Franklin E. Schroeck, Jr. The formalism of quantum mechanics on phase space is reviewed and the informational completeness of it is discussed. Applications to quantum computing will be mentioned. [Preview Abstract] |
Monday, March 5, 2007 12:15PM - 12:27PM |
B33.00004: Quasi-Orthonormal Bases for the Space of Density Operators Christopher A. Fuchs, D. M. Appleby, Hoan B. Dang Recently there has been much interest in the quantum information community to prove (or find a counterexample to) the existence of so-called symmetric informationally complete measurements (SICs). In this talk we show that there should be even more interest. For, under a robust measure of orthonormality for operator bases (one that does not build in any symmetry at the outset), one can show that SICs, if they exist, come as close as possible to being orthonormal bases for the space of density operators. Moreover, in contrast to the usual expression of the superposition principle (where bases are taken to be orthogonal sets of state vectors), writing a superposition principle in terms of SICs leads to a more intrinsically-quantum representation for quantum states. This is because the basis states, rather than being the easiest to eavesdrop on, are actually the hardest. Moreover, they fulfill a few other extreme quantum properties which will be outlined. [Preview Abstract] |
Monday, March 5, 2007 12:27PM - 12:39PM |
B33.00005: Macrorealism Emerging from Quantum Physics Caslav Brukner, Johannes Kofler I will give a novel theoretical approach to macroscopic realism and classical physics within quantum theory. While conceptually different from the decoherence program, it is not at variance with it. It puts the stress on the required precision of our measurement apparatuses such that quantum effects can still be observed. In the first part of the talk I will show that for unrestricted measurement accuracy a violation of macrorealism (i.e., a violation of the Leggett-Garg inequalities) is possible for arbitrary large systems. In the second part, I will show that, given the restriction of coarse-grained measurement resolution, not only macrorealism becomes valid but even the classical Newtonian laws emerge out of the quantum laws. Thus, even if an object were sufficiently isolated from its environment to avoid decoherence and fully obeys the laws of quantum physics, it will appear to behave classically under coarse-grained measurements. In the final part of the talk I will argue that since larger and larger systems require better and better measurement precision to see quantum effects -- and infinite precision cannot be reached in a world with finite resources --, there could be a fundamental limit on the dimensionality of the object above which its quantum features cannot be observed. [Preview Abstract] |
Monday, March 5, 2007 12:39PM - 12:51PM |
B33.00006: Critical sets of rays in four dimensions proving the Bell-Kochen-Specker theorem P.K. Aravind In recent years several sets of rays have been discovered in four and more dimensions that provide illustrations of the Bell-Kochen-Specker (BKS) theorem. These demonstrations acquire additional significance through the fact that they provide proofs of Bell's nonlocality theorem as well if used in conjunction with the right kind of entanglement. This talk will provide a brief overview of this field and then concentrate on two 60-ray sets in four dimensions recently discovered by the author. Both sets embed a geometrical structure within them, known as Reye's configuration, that permits the identification of smaller subsets (``critical sets'') that provide noncoloring proofs of the BKS theorem. (Reye's configuration is a set of 12 points and 16 lines with the property that four lines pass through every point and three points lie on every line. A ``critical set'' of rays is one that provides a minimalist noncoloring proof of the BKS theorem in the sense that the deletion of even a single ray from it makes the proof fail). This talk will discuss the ``quantum geometry'' of the two 60-ray sets and their relationship to each other. The application of these results to quantum information processing will be briefly considered. [Preview Abstract] |
Monday, March 5, 2007 12:51PM - 1:03PM |
B33.00007: Probing Contextuality with Pre- and Post-selection Jeff Tollaksen By analyzing the concept of contextuality (Bell-Kochen-Specker) in terms of pre-and-post-selection (PPS), it is possible to assign definite values to observables in a new way. Physical reasons are presented for restrictions on these assignments. When measurements are performed which do not disturb the pre- and post-selection (i.e. weak measurements), then novel {\it experimental} aspects of contextuality can be demonstrated including a proof that every PPS-paradox with definite predictions implies contextuality. Certain results of these measurements (eccentric weak values with e.g. negative values outside the spectrum), however, cannot be explained by a ``classical-like'' hidden variable theory. Surprising theoretical implications are discussed. [Preview Abstract] |
Monday, March 5, 2007 1:03PM - 1:15PM |
B33.00008: On the logical structure of Bell theorems. Jonathan Walgate, Anne Broadbent, Hilary Carteret, Andre Methot Some specific predictions of quantum mechanics are inconsistent with local realism, a phenomenon known as nonlocality. Despite overwhelming evidence for quantum mechanics, the practical difficulties of detector efficiency and coordinating space-like separated measurements have provided loopholes for a classical worldview. New experiments have been proposed to meet these challenges, based around a new kind of nonlocality proof called an ``EPR Bell inequality''. Much investment is now being made to realize these proofs experimentally. We show all these proposals are fundamentally flawed. We focus on a series of designs that have appeared in \textit{PRL} and \textit{PRA} for loophole-free Bell experiments. These experiments use hyperentangled two-photon quantum states to generate experimental data supposedly at odds with local realism. We show how to produce identical results using a single coin, and explain where the logical flaw can be found. To understand our nonclassical world, we must understand precisely the experimental evidence for nonlocality. This tempting shortcut is a logical, theoretical and experimental dead end. http://www.arxiv.org/abs/quant-ph/0512201. [Preview Abstract] |
Monday, March 5, 2007 1:15PM - 1:27PM |
B33.00009: Tests of local realism and the coincidence-time problem Jan-{\AA}ke Larsson This paper analyzes effects of time-dependence in the Bell inequality, and other tests of local realism. Generalized tests are derived for the case when coincidence and non-coincidence [and hence whether or not a pair, or triplet, contributes to the actual data] is controlled by timing that depends on the detector settings. Needless to say, these tests are violated by quantum mechanics and could be violated by experimental data provided that the loss of measurement data through failure of coincidence is small enough, but the quantitative bound is more restrictive in this case than in the previously analyzed ``efficiency loophole.'' [Preview Abstract] |
Monday, March 5, 2007 1:27PM - 1:39PM |
B33.00010: Entanglement and correlations in mixed-state quantum computation Animesh Datta, Steven Flammia, Carlton Caves, Guifre Vidal A very intriguing model of mixed-state quantum computation is the `power of one qubit' [E. Knill and R. Laflamme, Phys. Rev. Lett 81, 5672 (1998)], which has one pure qubit and n qubits in the completely mixed state. This model is known to evaluate the normalized trace of a unitary matrix with fixed accuracy efficiently, and offers an exponential speed-up over the best known classical algorithm. We show that this model involves entangled states. We also show that, on one hand, these states have no more than a constant amount of entanglement (as measured by the negativity), while on the other, they have an exponentially high operator Schmidt rank. Since quantum systems with limited Schmidt rank are known to be simulatable classically in an efficient manner, this suggests that the advantage of mixed-state quantum computation may stem not from the amount of entanglement but the degree of correlations (as quantified by the operator Schmidt rank) the system possesses. [Preview Abstract] |
Monday, March 5, 2007 1:39PM - 1:51PM |
B33.00011: Multiply constrained bounds on measures of entanglement Anil Shaji We place bounds on non-operational measures of entanglement using multiple operational measures as constraints. Non-operational measures like the entanglement of formation, tangle and concurrence are physically significant, but they do not admit efficient procedures for computing because computing them involves finding optimal pure state decompositions for mixed states. On the other hand, there are operational measures of entanglement that can be computed relatively easily for arbitrary states. Bounding non-operational measures using a single operational measure as constraint has previously been done. We generalize this method to more than one constraint. We work out examples in which bounds are obtained for the entanglement of formation, tangle and concurrence of a family of states using the operational entanglement measures constructed from two positive, but not completely positive maps as constraints. The two maps are the partial transpose map and the $\Phi$-map introduced by Breuer [H-P. Breuer, e-print, quant-ph/0605036]. [Preview Abstract] |
Monday, March 5, 2007 1:51PM - 2:03PM |
B33.00012: Graphical description of the action of Clifford operators on stabilizer states Matthew Elliott, Bryan Eastin, Carlton Caves We introduce a graphical representation of stabilizer states, which reduces to standard graphs for graph states. The effects of Clifford operators on stabilizer states are then translated into graph operations on the corresponding stabilizer state graphs, and we find that they are completely described in terms of loop complementation and local complementation. [Preview Abstract] |
Monday, March 5, 2007 2:03PM - 2:15PM |
B33.00013: Entanglement and the second law Ian Durham The second law of thermodynamics is, in reality, a strong argument about the nature of probabilities. In essence, the same can be said of Bell's inequalities, of which thermodynamic variations have been found. The tantalizingly close nature of these two arguments has potentially profound implications for quantum theory and, in particular, practical quantum computing. This presentation explores this relationship and its potential implications. [Preview Abstract] |
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