Bulletin of the American Physical Society
APS March Meeting 2011
Volume 56, Number 1
Monday–Friday, March 21–25, 2011; Dallas, Texas
Session H29: Focus Session: Quantum Information for Quantum Foundations - Axiomatics and Toy Models |
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Sponsoring Units: GQI Chair: Oscar Dahlsten, Oxford University Room: C148 |
Tuesday, March 22, 2011 8:00AM - 8:36AM |
H29.00001: Toward a conceptual foundation of Quantum Information Processing Invited Speaker: Quantum Information Science has brought to light an enormous amount of new protocols showing that the structure of quantum theory dramatically impacts the way in which information can be processed. It also made clear that the rules of information processing are dictated by physics and that different physical theories entail different models of information processing. Quantum Information poses an exciting challenge to foundational research: the challenge is to reduce the multiplicity of quantum protocols to a small number of basic physical principles and to answer questions like ``What are the physical roots of the power of quantum information?'' A satisfactory answer to these questions calls for the solution of a long-standing problem: deriving quantum theory from physical principles, as opposed to the abstract mathematical principles of the Hilbert space formulation. In this talk I will show that quantum theory can be derived from few principles about information processing. The central principle of the derivation will be the purification principle, stating that ignorance about a part (subsystem) is always compatible with maximal knowledge of the whole (compound system). A large number of quantum information features, including e.g. teleportation and no-cloning, are direct consequences of the purification principle, which appears a strong candidate for the conceptual foundation of Quantum Information Processing. Moreover, the derivation of quantum theory from purely informational principles provides a rigorous justification of the diffuse claim that quantum theory is ultimately a theory of information. [Preview Abstract] |
Tuesday, March 22, 2011 8:36AM - 8:48AM |
H29.00002: Physics as Information Giacomo Mauro D'Ariano The experience from Quantum Information has lead theorists to look at Quantum Theory and the whole Physics from a different angle. A new information-theoretic paradigm is emerging, long time ago prophesied by John Archivald Wheeler with his popular coinage ``It from bit.'' Theoretical groups are now addressing the problem of deriving Quantum Theory from informational principles, and similar lines are investigated e.g. in new approaches to Quantum Gravity. In my talk I will review some recent advances on these lines. The general idea synthesizing the new paradigm is that there is only Quantum Theory (without quantization rules), and the whole Physics---including space-time and relativity--is emergent from the quantum-information processing. And, since Quantum Theory itself is made with purely informational principles, the whole Physics must be reformulated in information-theoretical terms. The review is divided into four parts: a) Very short review of the informational axiomatization of Quantum Theory; b) How space-time and relativistic covariance emerge from the quantum computation; c) What is the information-theoretical meaning of inertial mass and Planck constant, and how the Dirac field emerges; d) Observable consequences of the new theory. I will then conclude with some possible future research lines. [Preview Abstract] |
Tuesday, March 22, 2011 8:48AM - 9:00AM |
H29.00003: A derivation of quantum theory from physical requirements Markus Mueller, Lluis Masanes Quantum theory is usually formulated by postulating the mathematical structure and representation of states, transformations, and measurements. The general physical consequences that follow (like violation of Bell-type inequalities, the possibility of performing state tomography with local measurements, or factorization of integers in polynomial time) come as theorems which use the postulates as premises. In this work, this procedure is reversed: we impose five simple physical requirements, and this suffices to single out quantum theory and derive its mathematical formalism uniquely. This is more similar to the usual formulation of special relativity, where two simple physical requirements ---the principles of relativity and light speed invariance--- are used to derive the mathematical structure of Minkowski space-time and its transformations. [Preview Abstract] |
Tuesday, March 22, 2011 9:00AM - 9:12AM |
H29.00004: Homogeneous Self-Dual Cones and the Structure of Quantum Theory Alexander Wilce This talk reviews recent and on-going work with Howard Barnum on the origins of the Jordan-algebraic structure of finite-dimensional quantum theory. I begin by surveying various principles --- e.g., that every state of a bipartite system arise as the marginal of a ``steering" bipartite state -- - that force the cone of (un-normalized) states of a finite-dimensional probabilistic system to be homogenous and {\em weakly} self-dual, that is, isomorphic to its dual cone. Where this weak self-duality can be implemented by an inner product, the cone is {\em strongly} self dual. In this case, classical results of Koecher and Vinberg show that it is isomorphic to the cone of squares in a formally real Jordan algebra. If this is the case, then (using a theorem of H. Hanche-Olsen) one can show that the only locally-tomographic theory containing at least one qubit is finite-dimensional Complex QM. I conclude with a brief discussion of how one might motivate strong self-duality. [Preview Abstract] |
Tuesday, March 22, 2011 9:12AM - 9:24AM |
H29.00005: Quaternions and the Quantum Matthew Graydon Birkhoff and von Neumann pointed out that quantum probability calculi could be formulated over rings admitting involutory anti-automorphisms [1]. We discuss a model for generalized quantum measurements and quantum states based on quaternionic matrix algebras. We show that the usual Born rule for calculating probabilities for outcomes of quantum measurements can be carried over into quaternionic quantum theories within a Jordan-algebraic framework. We exploit a group isomorphism between Sp(1) and SU(2) to show that single-system unitary dynamics and generalized measurements in a quaternionic quantum theory can be simulated by corresponding processes in usual quantum mechanics. We resurvey the divide between quaternionic and complex quantum theories given this quadit-qudit correspondence. Reference: [1] G. Birkhoff and J. Von Neumann, ``The logic of quantum mechanics'', Ann. Math., 37, 823-843 (1936). [Preview Abstract] |
Tuesday, March 22, 2011 9:24AM - 9:36AM |
H29.00006: Quantum theory cannot be extended Roger Colbeck, Renato Renner Predictions made by quantum theory are generally not deterministic: the theory tells us only how to calculate the probabilities with which measurement outcomes occur. This indeterminism is one of the key differences from classical mechanics and one can ask whether this is the best any theory can offer, or whether observable quantities could be better predicted by some higher theory. In a famous work, Bell considered extensions of quantum theory in the form of local hidden variables and showed that these cannot determine the outcomes of measurements on maximally entangled particles. Here, we go beyond the case of such classical extensions and ask whether any improved predictions can be achieved by any extension of quantum theory. We answer this question in the negative. More precisely, under the assumption that measurement settings can be chosen freely, there cannot exist any extension of quantum theory that provides us with any additional information about the outcomes of future measurements. [Preview Abstract] |
Tuesday, March 22, 2011 9:36AM - 9:48AM |
H29.00007: Eliminating remnants of classical mechanics and the birth of the Schr\"odinger equation Wolfgang P. Schleich, Daniel Greenberger, Donald H. Kobe We show that the Schr\"odinger equation emerges from the Hamilton-Jacobi equation for a specific choice of the amplitude $R$ of a wave $\psi\equiv R\exp[I S/\hbar]$ where $S$ is the classical action. This choice eliminates in the wave equation for $\psi$ all remnants of classical mechanics associated with $S$ but at the same time builds via the wave equation for $R$ a bridge to classical mechanics and to the de Broglie pilot wave theory. [Preview Abstract] |
Tuesday, March 22, 2011 9:48AM - 10:00AM |
H29.00008: Modal Quantum Theory Michael Westmoreland, Benjamin Schumacher We present a class of toy model theories similar in structure to ordinary quantum mechanics. Some of these models are based on finite fields instead of complex amplitudes. The interpretation of such theories involves only the ``modal'' concepts of possibility and necessity rather than quantitative probability measures. Despite its very simple structure, our toy model nevertheless includes many of the key phenomena of actual quantum systems: interference, complementarity, entanglement, nonlocality, and the impossibility of cloning. These results are detailed in arXiv:1010.2929 and arXiv:1010.5452. [Preview Abstract] |
Tuesday, March 22, 2011 10:00AM - 10:12AM |
H29.00009: Time-asymmetry and causal structure Bob Coecke, Raymond Lal We consider devices with two inputs and two outputs, Alice and Bob each having access to one input and one output. To such a device we associate time-reverses by exchanging the roles of the inputs and the outputs. We find that there are devices which admit a local hidden variable representation, but for which time- reverses enable perfect signaling between Alice and Bob. That is, a ``perfect channel in one time direction'' becomes a ``non-channel in the other direction.'' Also, for PR boxes time-reverses enable signaling between Alice and Bob, but never as a perfect channel. This result has several consequences. Firstly, it establishes that the arrow of time can be read from signaling structure: signaling means backward in time. It undermines the representation of causal structures as partial orders or similar `time-symmetric structures', as is often assumed in search of a theory of quantum gravity. They also provide new insights into the structure of the polytope of generalized probabilistic correlations, hence on theories more general than quantum theory. Finally, it contributes to the growing area of research into quantum information processing in relativistic spacetimes. Ref: arXiv:1010.4572 [Preview Abstract] |
Tuesday, March 22, 2011 10:12AM - 10:24AM |
H29.00010: Topos formulation of History Quantum Theory Cecilia Flori In this talk I will describe a topos formulation of consistent histories obtained using the topos reformulation of standard quantum mechanics put forward by Doering and Isham. Such a reformulation leads to a novel type of logic with which to represent propositions. In the first part of the talk I will introduce the topos reformulation of quantum mechanics. I will then explain how such a reformulation can be extended so as to include temporally-ordered collection of propositions as opposed to single time propositions. Finally I will show how such an extension will lead to the possibility of assigning truth values to temporal propositions. [Preview Abstract] |
Tuesday, March 22, 2011 10:24AM - 10:36AM |
H29.00011: Causal Tapestries William Sulis Causal sets provide one of many approaches to the problem of quantum gravity. Causal tapestries generalize the concept of a causal set, extending the range of putative dynamics from sequential growth to include iterative and non deterministic methods, and the range of embedding manifolds to include those with curvature. Like causal sets, causal tapestries are manifestly Lorentz invariant in spite of possessing a form of ``transient now''. It is shown that the order relations of the local causal structures must possess an order theoretic (Dushnik {\&} Miller) dimension not exceeding the topological dimension of the embedding manifold and the finite free dimension is bounded by the number of elementary processes generating the causal relations. [Preview Abstract] |
Tuesday, March 22, 2011 10:36AM - 10:48AM |
H29.00012: ABSTRACT WITHDRAWN |
Tuesday, March 22, 2011 10:48AM - 11:00AM |
H29.00013: The quantal algebra and abstract equations of motion Samir Lipovaca Classical and quantum mechanics common characteristics reveal core physics features that are hidden by the details related to the realizations of those theories in phase and Hilbert space respectively. The quantal algebra combines classical and quantum mechanics into an abstract structurally unified structure. It is based on two observations which can be made about classical and quantum mechanics. The first observation is that classical and quantum mechanics use two products: one symmetric and one anti-symmetric. The second observation is that classical and quantum mechanics obey the so-called composability principle: any two physical systems can interact with each other. The local structure of spacetime is contained in the quantal algebra without having been postulated. We will generalize classical and quantum mechanics equations of motion to abstract equations of motion in which the anti-symmetric product of the quantal algebra plays a central role. We will express the defining identities of the quantal algebra in terms of the abstract derivation. In this form it is easy to see that the first defining identity (the Jacobi identity) captures the essence of the Bianchi identity in general relativity which is one set of gravitational field equations for the curvature tensor. [Preview Abstract] |
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