Bulletin of the American Physical Society
APS March Meeting 2016
Volume 61, Number 2
Monday–Friday, March 14–18, 2016; Baltimore, Maryland
Session L44: Quantum Information Theory and Quantum Foundations |
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Sponsoring Units: GQI Chair: Bei Zeng, University of Guelph Room: 347 |
Wednesday, March 16, 2016 11:15AM - 11:27AM |
L44.00001: Quantum Speed Limits, coherence and asymmetry Iman Marvian, Robert Spekkens, Paolo Zanardi The resource theory of asymmetry is a framework for classifying and quantifying the symmetry-breaking properties of both states and operations relative to a given symmetry. In the special case where the symmetry is the set of translations generated by a fixed observable, asymmetry can be interpreted as coherence relative to the observable eigenbasis, and the resource theory of asymmetry provides a framework to study this notion of coherence. We here show that this notion of coherence naturally arises in the context of quantum speed limits. Indeed, the very concept of speed of evolution, i.e., the inverse of the minimum time it takes the system to evolve to another (partially) distinguishable state, is a measure of asymmetry relative to the time translations generated by the system Hamiltonian. Furthermore, the celebrated Mandelstam-Tamm and Margolus-Levitin speed limits can be interpreted as upper bounds on this measure of asymmetry by functions which are themselves measures of asymmetry in the special case of pure states. Using measures of asymmetry that are not restricted to pure states, such as the Wigner-Yanase skew information, we obtain extensions of the Mandelstam-Tamm bound which are significantly tighter in the case of mixed states. [Preview Abstract] |
Wednesday, March 16, 2016 11:27AM - 11:39AM |
L44.00002: A Strong Loophole-Free Test of Local Realism Peter Bierhorst, Lynden Shalm, Martin Stevens, Thomas Gerrits, Scott Glancy, Michael Allman, Kevin Coakley, Shellee Dyer, Carson Hodge, Adriana Lita, Varun Verma, Richard Mirin, Emanuel Knill, Sae Woo Nam We discuss theoretical and statistical aspects of a recent loophole-free violation of local realism using entangled photon pairs. The experiment ensures that all relevant events in the Bell test are spacelike separated by placing the parties far enough apart and using fast random number generators and high-speed polarization measurements. A high-quality polarization-entangled source of photons, combined with high-efficiency, low-noise, single-photon detectors, allows us to make measurements without requiring any fair-sampling assumptions. We collected six data sets, and for each data set we used a hypothesis test to compute the maximum probability (the p-value) that our experiment, if it had been governed by local realism, would produce a violation as large or larger than we observed. The smallest p-value we observed is 5.9 X 10\textasciicircum -9. [Preview Abstract] |
Wednesday, March 16, 2016 11:39AM - 11:51AM |
L44.00003: Implications of Einstein-Weyl Causality on Quantum Mechanics David BenDaniel A fundamental physical principle that has consequences for the topology of space-time is the principle of Einstein-Weyl causality. This also has quantum mechanical manifestations. Borchers and Sen have rigorously investigated the mathematical implications of Einstein-Weyl causality and shown the denumerable space-time Q$^{\mathrm{2}}$ would be implied. They were left with important philosophical paradoxes regarding the nature of the physical real line E, e.g., whether E $=$ R, the real line of mathematics. In order to remove these paradoxes an investigation into a constructible foundation is suggested. We have pursued such a program and find it indeed provides a dense, denumerable space-time and, moreover, an interesting connection with quantum mechanics. We first show that this constructible theory contains polynomial functions which are locally homeomorphic with a dense, denumerable metric space R* and are inherently quantized. Eigenfunctions governing fields can then be effectively obtained by computational iteration. Postulating a Lagrangian for fields in a compactified space-time, we get a general description of which the Schrodinger equation is a special case. From these results we can then also show that this denumerable space-time is relational (in the sense that space is not infinitesimally small if and only if it contains a quantized field) and, since Q$^{\mathrm{2}}$ is imbedded in R*$^{\mathrm{2}}$, it directly fulfills the strict topological requirements for Einstein-Weyl causality. Therefore, the theory predicts that E $=$ R*. [Preview Abstract] |
Wednesday, March 16, 2016 11:51AM - 12:03PM |
L44.00004: Entanglement Entropy and Mutual Information of Circular Entangling Surfaces in 2+1d Quantum Lifshitz Model Tianci Zhou, Xiao Chen, Eduardo Fradkin We investigate the entanglement entropy(EE) of circular entangling surfaces in the 2+1d quantum Lifshitz model, where the spatially conformal invariant ground state is a Rokhsar-Kivelson state with Gibbs weight of 2d free Boson. We use cut-off independent mutual information regulator[1] to define and calculate the subleading correction in the EE. The subtlety due to the Boson compactification in the replica trick is carefully taken care of. Our results show that for circular entangling surface, the subleading term is a constant on both the sphere of arbitrary radius and infinite plane. For the latter case, it parallels the constancy of disk EE in 2+1d conformal field theory, despite the lack of full space time conformal invariance. In the end, we present the mutual information of two disjoint disks and compare its scaling function in the small parameter regime (radii much smaller than their separation) with Cardy's general CFT results [2]. 1. H. Casini, M. Huerta, R. Myers, A. Yale, arXiv: 1506.06195 (2015). 2. J. Cardy, J. Phys. A: Math. Theor. 46, 285402 (2013) [Preview Abstract] |
Wednesday, March 16, 2016 12:03PM - 12:15PM |
L44.00005: Monogamy of quantum steering Antony Milne, David Jennings, Sania Jevtic, Terry Rudolph, Howard Wiseman The quantum steering ellipsoid formalism naturally extends the Bloch vector picture for qubits to provide a visualisation of two-qubit systems. If Alice and Bob share a correlated state then a local measurement by Bob steers Alice’s qubit inside the Bloch sphere; given all possible measurements by Bob, the set of states to which Alice can be steered form her steering ellipsoid. We apply the formalism to a three-party scenario and find that steering ellipsoid volumes obey a simple monogamy relation. This gives us a novel derivation of the well-known CKW (Coffman-Kundu-Wootters) inequality for entanglement monogamy. The geometric perspective also identifies a new measure of quantum correlation, `obesity', and a set of `maximally obese' states that saturate the steering monogamy bound. These states are found to have extremal quantum correlation properties that are significant in the steering ellipsoid picture and for the study of two-qubit states in general. [Preview Abstract] |
Wednesday, March 16, 2016 12:15PM - 12:27PM |
L44.00006: Conflict between the Uncertainty Principle and wave mechanics Antony Bourdillon The traveling wave group that is defined on conserved physical values is the vehicle of transmission for a unidirectional photon or free particle having a wide wave front. As a stable wave packet, it expresses internal periodicity combined with group localization. Heisenberg's Uncertainty Principle is precisely derived from it. The wave group demonstrates serious conflict between the Principle and wave mechanics. Also derived is the phase velocity beyond the horizon set by the speed of light. In this space occurs the reduction of the wave packet which occurs in measurement and which is represented by comparing phase velocities in the direction of propagation with the transverse plane. The new description of the wavefunction for the stable free particle or antiparticle contains variables that were previously ignored. Deterministic physics must always appear probabilistic when hidden variables are bypassed. Secondary hidden variables always occur in measurement. The wave group turns out to be probabilistic. It is ubiquitous in physics and has many consequences. [Preview Abstract] |
Wednesday, March 16, 2016 12:27PM - 12:39PM |
L44.00007: Coherence-path-information duality relation for N paths Mark Hillery, Emilio Bagan, Janos Bergou For an interferometer with two paths, there is a duality relation between the information about which path the particle took and the visibility of the interference pattern at the output. The more path information we have, the smaller the visibility, and vice versa. We generalize this relation to a multi-path interferometer, and we substitute a recently defined measure of quantum coherence for the visibility. The path information is provided by attaching a detector to each path and applying the minimum-error state discrimination procedure to the detector states. [Preview Abstract] |
Wednesday, March 16, 2016 12:39PM - 12:51PM |
L44.00008: Axioms for quantum mechanics: relativistic causality, retrocausality, and the existence of a classical limit Daniel Rohrlich Y. Aharonov and A. Shimony both conjectured that two axioms -- relativistic causality (``no superluminal signalling'') and nonlocality -- so nearly contradict each other that only quantum mechanics reconciles them. Can we indeed derive quantum mechanics, at least in part, from these two axioms? No: ``PR-box'' correlations show that quantum correlations are not the most nonlocal correlations consistent with relativistic causality. Here we replace ``nonlocality'' with ``retrocausality'' and supplement the axioms of relativistic causality and retrocausality with a natural and minimal third axiom: the existence of a classical limit, in which macroscopic observables commute. That is, just as quantum mechanics has a classical limit, so must any generalization of quantum mechanics. In this limit, PR-box correlations \textit{violate }relativistic causality. Generalized to all stronger-than-quantum bipartite correlations, this result is a derivation of Tsirelson's bound (a theorem of quantum mechanics) from the three axioms of relativistic causality, retrocausality and the existence of a classical limit. Although the derivation does not assume quantum mechanics, it points to the Hilbert space structure that underlies quantum correlations. [Preview Abstract] |
Wednesday, March 16, 2016 12:51PM - 1:03PM |
L44.00009: J-holomorphic maps and the uncertainty principle in geometric quantum mechanics Barbara Sanborn The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a complex projective Hilbert space as its phase space. The K\"{a}hler structure of the projective space provides quantum mechanics with a Riemannian metric in addition to the symplectic structure characteristic of classical mechanics. By including aspects of the symplectic topology of the quantum phase space, the geometric theory is extended and enriched. In particular, the quantum uncertainty principle is naturally expressed as an inequality from J-holomorphic map theory. [Preview Abstract] |
Wednesday, March 16, 2016 1:03PM - 1:15PM |
L44.00010: A proposed physical analog for a quantum probability amplitude Jeffrey Boyd What is the physical analog of a probability amplitude? All quantum mathematics, including quantum information, is built on amplitudes. Every other science uses probabilities; QM alone uses their square root. Why? This question has been asked for a century, but no one previously has proposed an answer. We will present cylindrical helices moving toward a particle source, which particles follow backwards. Consider Feynman’s book QED. He speaks of amplitudes moving through space like the hand of a spinning clock. His hand is a complex vector. It traces a cylindrical helix in Cartesian space. The Theory of Elementary Waves changes direction so Feynman’s clock faces move toward the particle source. Particles follow amplitudes (quantum waves) backwards. This contradicts wave particle duality. We will present empirical evidence that wave particle duality is wrong about the direction of particles versus waves. This involves a paradigm shift; which are always controversial. We believe that our model is the ONLY proposal ever made for the physical foundations of probability amplitudes. We will show that our “probability amplitudes” in physical nature form a Hilbert vector space with adjoints, an inner product and support both linear algebra and Dirac notation. [Preview Abstract] |
Wednesday, March 16, 2016 1:15PM - 1:27PM |
L44.00011: Quantum enhanced estimation of a multi-dimensional field. Animesh Datta, Tillmann Baumgratz We present a framework for the quantum-enhanced estimation of multiple parameters corresponding to non-commuting unitary generators. We derive the quantum Fisher information matrix to put a lower bound on the total variance of all the parameters involved. We present the conditions for the attainment of the multi-parameter bound, which is not guaranteed unlike the quantum metrology of single parameters. Our study also reveals that too much quantum entanglement may be detrimental to attaining the Heisenberg scaling in the estimation of unitarily generated parameters. One particular case of our framework is the simultaneous estimation of all three components of a magnetic field. We propose a probe state that demonstrates that the simultaneous estimation of the three components is better than the precision of estimating the three components individually. We provide realistic measurements that come close to attaining the quantum limit, exhibiting the advantage of simultaneous quantum estimation even in the case of non-commuting generators. Our work applies to precision estimation any Hamiltonian, and may be employed in efficient process tomography and verification. Our theoretical proposal can be implement in any finite dimensional quantum system such as trapped ions and nitrogen vacancy centres in diamond. [Preview Abstract] |
Wednesday, March 16, 2016 1:27PM - 1:39PM |
L44.00012: Fisher symmetry and the geometry of quantum states Jonathan A. Gross, Howard Barnum, Carlton M. Caves The quantum Fisher information (QFI) is a valuable tool on account of the achievable lower bound it provides for single-parameter estimation. Due to the existence of incompatible quantum observables, however, the lower bound provided by the QFI cannot be saturated in the general multi-parameter case. A bound demonstrated by Gill and Massar (GM) captures some of the limitations that incompatibility imposes in the multi-parameter case. We further explore the structure of measurements allowed by quantum mechanics, identifying restrictions beyond those given by the QFI and GM bound. These additional restrictions give insight into the geometry of quantum state space and notions of measurement symmetry related to the QFI. [Preview Abstract] |
Wednesday, March 16, 2016 1:39PM - 1:51PM |
L44.00013: Information Thermodynamics applied to the MERA quantum circuit. Vasilios Passias, Victor Chua, Apoorv Tiwari, Shinsei Ryu We interpret the MERA (Multiscale Entanglement Renormalization Ansatz) tensor network as a unitary quantum circuit to study excited states of quantum spin-chains. Contrary to the common use of MERA as a variational ground state ansatz, the quantum circuit defined by MERA -- adapted to a fixed ground state -- is employed as a diagnostic tool to study dynamically evolving excited state wavefunctions. Outputs of the quantum computation emanating from the isometry tensors, which are normally approximate tensor product states, now fluctuate strongly. These ``bulk" degrees of freedom in the MERA which act as logical qubits are studied using tools from quantum information theory and information thermodynamics. A local temperature scale based on Landauer's information erasure principle is defined to measure their degree of fluctuation. We investigate properties of this temperature against the expectations of Luttinger's theorem which relates weak field gravity to heat flow. [Preview Abstract] |
Wednesday, March 16, 2016 1:51PM - 2:03PM |
L44.00014: The Dimensions of Emergent Spacetime in the Influence Network Kevin Knuth It has been previously demonstrated that the consistent quantification of a causally ordered set of events (influence network) with respect to observers represented by embedded chains results in a unique consistent quantification scheme that reproduces the Minkowski metric in the case of coordinated chains and Lorentz transformations in the case of linearly-related chains (Knuth and Bahreyni 2014). Here we demonstrate that quantification by multiple coordinated chains can only be consistent in the cases of two and four chains resulting in emergent 1$+$1 and 3$+$1 dimensional spacetimes, respectively. Odd numbers of chains are specifically ruled out and numbers of chains greater than four lead to a system that is not closed under chain permutation symmetry in a manner consistent with Galois theory. As a result, the spacetime framework that emerges from the consistent quantification of a causally ordered set of events with respect to embedded observers provides a potential foundation for emergent spacetime as well as an explanation as to the significance and nature of 3$+$1 spacetime dimensions. [Preview Abstract] |
Wednesday, March 16, 2016 2:03PM - 2:15PM |
L44.00015: Locality and entanglement in bandlimited quantum field theory Jason Pye, William Donnelly, Achim Kempf We consider a model for a Planck scale ultraviolet cutoff which is based on Shannon sampling. Shannon sampling originated in information theory, where it expresses the equivalence of continuous and discrete representations of information. When applied to quantum field theory, Shannon sampling expresses a hard ultraviolet cutoff in the form of a bandlimitation. This introduces nonlocality at the cutoff scale in a way that is more subtle than a simple discretization of space: quantum fields can then be represented as either living on continuous space or, entirely equivalently, as living on any one lattice whose average spacing is sufficiently small. We explicitly calculate vacuum entanglement entropies in 1+1 dimensions and we find a transition between logarithmic and linear scaling of the entropy, which is the expected 1+1 dimensional analog of the transition from an area to a volume law. We also use entanglement entropy and mutual information as measures to probe in detail the localizability of the field degrees of freedom. We find that, even though neither translation nor rotation invariance are broken, each field degree of freedom occupies an incompressible volume of space, indicating a finite information density. [Preview Abstract] |
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