Bulletin of the American Physical Society
2008 APS March Meeting
Volume 53, Number 2
Monday–Friday, March 10–14, 2008; New Orleans, Louisiana
Session L14: Focus Session: Foundations of Quantum Theory II |
Hide Abstracts |
Sponsoring Units: GQI Chair: Julio Gea-Banacloche, University of Arkansas Room: Morial Convention Center 205 |
Tuesday, March 11, 2008 2:30PM - 3:06PM |
L14.00001: General probabilistic theories for quantum foundations and quantum information Invited Speaker: Jonathan Barrett Is there any reason why the universe should obey the laws of quantum theory, as opposed to any other possible theory? Is quantum theory special in any way? The best way to address these questions is to view quantum theory as just one point in an entire space of possible theories, and to compare and contrast quantum theory with its rivals. As the success of quantum information theory makes clear, one means by which different theories may be compared and contrasted is via their information processing capabilities. To this end, following early work of Mackey, Ludwig and others, I show how to write down essentially arbitrary probabilistic models, based on the conditions that state spaces are convex and that separated systems cannot be used for instantaneous signalling. Both the classical and quantum theories are special cases. With a focus on information processing, I then describe (i) some features of quantum theory that one might have expected to be uniquely quantum, but turn out to be highly generic, and (ii) some features that do mark quantum theory as special. Some of this is work done in collaboration with Howard Barnum, Matthew Leifer and Alexander Wilce. [Preview Abstract] |
Tuesday, March 11, 2008 3:06PM - 3:18PM |
L14.00002: Fully epistemic toy theory Michael Skotiniotis, Aidan Roy, Barry C. Sanders The Spekkens toy model is an interesting example of how to modify classical physics in order to perform several quantum information processing tasks. Spekkens' toy model has four axioms concerning toy states, valid operations, measurements, and composition of single toy systems. Motivated by the empirical indistinguishability of epistemic vs. ontic states in the toy universe, we show that relaxing valid operations to mappings of epistemic rather than ontic states preserves the features of the toy model. Similarly we show that relaxing the axiom regarding the composition of single toy systems also preserves the toy model. Relaxing both axioms simultaneously, however, breaks the correspondence of the toy model with quantum theory because the tensor product composition rule is violated, but these two relaxations together produce a group of operations on epistemic states that is isomorphic to the projected extended Clifford Group. [Preview Abstract] |
Tuesday, March 11, 2008 3:18PM - 3:30PM |
L14.00003: Tensor products and teleportation protocols for abstract state spaces Alexander Wilce In a well-known generalization of classical probability theory, arbitrary compact convex sets serve as abstract ``state spaces'' for (hypothetical) physical systems, with classical systems corresponding to simplices and quantum systems, to state spaces of C*-algebras. One can define natural tensor products for abstract state spaces, modeling composite systems subject to a no-signaling condition. Remarkably, many basic quantum-information theoretic phenomena, including the no-cloning and no-broadcasting theorems, already appear at this level of generality. However, the existence of a teleportation protocol is a strong constraint, moving us closer to quantum theory. In this talk, after a brief summary of the framework, I will outline what we currently understand about teleportation in this setting. This represents recent and ongoing joint work with Howard Barnum, Jonathan Barrett and Matthew Leifer [Preview Abstract] |
Tuesday, March 11, 2008 3:30PM - 3:42PM |
L14.00004: The Density Matrix and the Interpretation of Quantum Theory Owen Maroney Can a density matrix be regarded as a description of the physically real properties of an individual system? If so, it may be possible to attribute the same objective significance to statistical mechanical properties, such as entropy or temperature, as to properties such as mass or energy. Non-linear modifications to unitary evolution can be proposed, based upon this idea, to account for thermodynamic irreversibility. Traditional approaches to interpreting quantum phenomena assume that an individual system is described by a pure state, with density matrices arising only through a statistical mixture or through tracing out entangled degrees of freedom. We discuss how treating the density matrix as fundamental can affect the viability of some of these interpretations, and how the thermodynamically motivated non-linearities do not, in themselves, help in solving the quantum measurement problem. [Preview Abstract] |
Tuesday, March 11, 2008 3:42PM - 4:18PM |
L14.00005: An Approach to Quantum State Pooling from Quantum Conditional Independence Invited Speaker: Matthew Leifer In approaches to quantum theory in which the quantum state is taken to represent an agent's belief, knowledge or information about a physical system, it is legitimate for different agents to assign different states to one and the same physical system. The question then arises of what state they should assign if they get together and share their information about the system. This is the problem of quantum state pooling. The classical counterpart of this problem for probability distributions only has a unique solution under additional assumptions about how the data are collected, such as conditional independence constraints. Recently, Spekkens and Wiseman found a quantum pooling rule analogous to the classical one, which is valid if the differing state assignments arise from making indirect measurements on special classes of tripartite quantum state. We show that this pooling rule applies to a much wider class of tripartite states, and that its validity rests on quantum analogs of conditional independence recently studied by one of the authors, as well as a generalization of the notion of a sufficient statistic to the quantum case. Work done in collaboration with Robert Spekkens, University of Cambridge. [Preview Abstract] |
Tuesday, March 11, 2008 4:18PM - 4:30PM |
L14.00006: New results in the category-theoretic approach to foundations of quantum physics Bob Coecke We report on some recent results in the category theoretic approach quantum physics, which aims to provide an operational foundation, a logical axiomatics as well as a purely diagrammatic language for it. Firstly, we were able to unify several measurement-based quantum computational schemes; in particular, the categorical language is sufficient to provide proofs of universality for each of these. Secondly, we have a manner to abstractly generate arbitrary multi-partite entangled states; hence equipping multi-partite entanglement with a formal interpretation in terms of information-flow. Also, we axiomatised Spekkens' model in purely category-theoretic terms; its quantum-like behaviors are now consequences merely of abstract category-theoretic structure. [Preview Abstract] |
Tuesday, March 11, 2008 4:30PM - 4:42PM |
L14.00007: Graphical Calculi and Mutually Unbiassed Embeddings of Classical Logic Ross Duncan While arbitrary quantum states may not be freely cloned or deleted [1], we note, following [2], that these distinctively classical operations may be performed on states which lie within a given basis. Each basis therefore provides an embedding of classical logic into a quantum state space. This work provides a categorical axiomatisation (cf [3]) of the interaction of such embeddings when distinct mutually unbiassed bases [4] are used. We provide a graphical language (cf. [5]) for the classical operations that each embedding provides, and demonstrate that this system captures many properties of multi-partite entangled states and can simulate quantum algorithms. [1] W. Wootters and W. Zurek. A single quantum cannot be cloned, 1982. A.K. Pati and S. L. Braunstein. Impossibility of deleting an unknown quantum state, 2000. [2] B. Coecke and D. Pavlovic (2007) Quantum measurements without sums. arXiv:quant-ph/0608035. [3] S. Abramsky and B. Coecke (2004) A categorical semantics of quantum protocols. arXiv:quant-ph/0402130. [4] J. Schwinger (1960) Unitary operator bases. Proceedings of the National Academy of Sciences of the U.S.A. 46 [5] B. Coecke (2005) Kindergarten quantum mechanics. arXiv:quant-ph/0510032 [Preview Abstract] |
Tuesday, March 11, 2008 4:42PM - 4:54PM |
L14.00008: Basing quantum theory on information processing Howard Barnum I consider information-based derivations of the quantum formalism, in a framework encompassing quantum and classical theory and a broad spectrum of theories serving as foils to them. The most ambitious hope for such a derivation is a role analogous to Einstein's development of the dynamics and kinetics of macroscopic bodies, and later of their gravitational interactions, on the basis of simple principles with clear operational meanings and experimental consequences. Short of this, it could still provide a principled understanding of the features of quantum mechanics that account for its greater-than-classical information-processing power, helping guide the search for new quantum algorithms and protocols. I summarize the convex operational framework for theories, and discuss information-processing in theories therein. Results include the fact that information that can be obtained without disturbance is inherently classical, generalized no-cloning and no-broadcasting theorems, exponentially secure bit commitment in all non-classical theories without entanglement, properties of theories that allow teleportation, and properties of theories that allow ``remote steering'' of ensembles using entanglement. Joint work with collaborators including Jonathan Barrett, Matthew Leifer, Alexander Wilce, Oscar Dahlsten, and Ben Toner. [Preview Abstract] |
Tuesday, March 11, 2008 4:54PM - 5:06PM |
L14.00009: Quantum mechanics and the nature of the second law of thermodynamics Ian T. Durham The second law of thermodynamics is inherently a classical law, though quantum analogues have been suggested. What are these quantum analogues and what is their relation to the classical version of the second law? In particular, what can Bell's inequalities tell us about this relation? This continues ongoing work, some of which has been presented at previous APS meetings, and makes a stronger argument on the thermodynamic nature of Bell's inequalities. [Preview Abstract] |
Tuesday, March 11, 2008 5:06PM - 5:18PM |
L14.00010: Many worlds and the appearance of probability in quantum mechanics Robert A. Van Wesep The theory of measurement has posed a conceptual problem since the beginning of quantum mechanics (QM). One the one hand, the quantum theory of interacting systems says that when a system $\mathcal O$ measures the value of a quantity $A$ associated with a system $\mathcal S$, the state of the compound system $\mathcal S \mathcal O$ following the measurement is a superposition of pure product states, one for each eigenvalue of $A$. On the other hand, one's subjective experience (as the observer $\mathcal O$) is that this statevector ``collapses'' nondeterministically to a pure state with probability given by the Born rule. The \emph{Copenhagen interpretation} (CI) says that this collapse actually occurs. The \emph{many-worlds view} (MW) is that it doesn't. The defects of CI are obvious: there is no way to say which interactions are measurements to which the interpretation applies, and there is no way to describe the process of collapse that it calls for. MW, on the other hand, does not seem able to incorporate the Born rule. If this were true, it would rule out MW as a description of reality. We show that it is not true, in the strongest possible way: the Born rule is actually a derivable consequence of the quantum theory of measurement \emph{as long as we accept the theory as is}, i..e, as long as we accept MW[1]. The proof uses the strong law of large numbers, which is the link between the abstract notion of probability and the concrete properties of sequences of observations.\newline [1] R.A. Van Wesep, Ann. Phys. 321 (10) (2006) 2438--2452. [Preview Abstract] |
Tuesday, March 11, 2008 5:18PM - 5:30PM |
L14.00011: Quantum catalysis of information Koji Azuma, Masato Koashi, Nobuyuki Imoto In quantum information science, it has been long believed that no one can access quantum information in a system without disturbing it. In fact, the belief has been corroborated by several no-go theorems such as the no-cloning theorem and the no-deleting theorem. Here, however, we show that the belief is incorrect, by exhibiting a novel process, `quantum catalysis of information', in which, without receiving any disturbance, a system certainly exchanges a type of information that cannot be transmitted without quantum communication channel. [Preview Abstract] |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2021 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
1 Research Road, Ridge, NY 11961-2701
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700