Bulletin of the American Physical Society
APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017; New Orleans, Louisiana
Session A52: Quantum Information Theory |
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Sponsoring Units: GQI Chair: Todd Brun, University of Southern California Room: 399 |
Monday, March 13, 2017 8:00AM - 8:12AM |
A52.00001: Toward a quasi-probability representation of matchgate circuits Ninnat Dangniam, Christopher Ferrie, Carlton Caves Quantum circuits composed of a particular class of gates called matchgates range from circuits that are classically simulatable to those that can perform universal quantum computation. Matchgate computation can also be understood from a more physical point of view as a computation with fermionic modes. We attempt to construct a quasi-probability (phase space) representation of quantum theory in which classically simulatable matchgate circuits are represented positively i.e. non-contextually. [Preview Abstract] |
Monday, March 13, 2017 8:12AM - 8:24AM |
A52.00002: Rank deficiency and the Euclidean geometry of quantum states Jonathan A Gross, Carlton M Caves Quantum state tomography requires characterizing a collection of parameters whose size grows rapidly with the size of the quantum system under consideration. In practice one hopes that prior information about the system can reduce the number of parameters in need of characterization---for example, one might expect to find high-quality quantum systems in states of low rank. Interest in tomographic schemes that return rank-deficient estimates leads us to explore some geometric properties of the space of quantum states that are analogous to solid angles in three-dimensional Euclidean geometry. [Preview Abstract] |
Monday, March 13, 2017 8:24AM - 8:36AM |
A52.00003: Emergence of geometry in quantum states Katharine Hyatt, James Garrison, Bela Bauer Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks as tractable models for holographic dualities. Conventionally, the structure of the network -- and hence the geometry -- is largely fixed a priori by the choice of tensor network ansatz. Here, we evade this restriction and describe an unbiased approach that allows us to extract the appropriate geometry from a given quantum state. This is based on an algorithm to iteratively find a unitary circuit that transforms a given quantum state into an unentangled state. We then analyze the structure of the resulting unitary circuits. In the case of critical systems in one dimension, we recover signatures of scale-invariance in the unitary network, and show that appropriately defined geodesic paths between physical degrees of freedom exhibit properties of a hyperbolic geometry. [Preview Abstract] |
Monday, March 13, 2017 8:36AM - 8:48AM |
A52.00004: Resource destroying maps Zi-Wen Liu, Xueyuan Hu, Seth Lloyd Resource theory is a widely-applicable framework for analyzing the physical resources required for given tasks, such as computation, communication, and energy extraction. In this paper, we propose a general scheme for analyzing resource theories based on resource destroying maps, which leave resource-free states unchanged but erase the resource stored in all other states. The linearity of the resource destroying map depends on the convexity of the set of free states, but the scheme can be applied to any resource. In particular, we introduce a group of simple and general conditions that determine whether a quantum operation exhibits certain resource-free properties. Our theory reveals fundamental connections among basic elements of resource theories, namely free states, free operations and resource measures. Notably, we find a class of simple measures without optimization that are monotone nonincreasing under operations that commute with the resource destroying map. We explicitly discuss our theory in the contexts of coherence and discord-type quantum correlations, two prominent features of nonclassicality, to illustrate properties of resource destroying maps and provide new insights into these highly active fields. [Preview Abstract] |
Monday, March 13, 2017 8:48AM - 9:00AM |
A52.00005: Qudit quantum computation on matrix product states with global symmetry Dongsheng Wang, David Stephen, Robert Raussendorf Resource states that contain nontrivial symmetry-protected topological order are identified for universal measurement-based quantum computation. Our resource states fall into two classes: one as the qudit generalizations of the qubit cluster state, and the other as the higher-symmetry generalizations of the spin-1 Affleck-Kennedy-Lieb-Tasaki (AKLT) state, namely, with unitary, orthogonal, or symplectic symmetry. The symmetry in cluster states protects information propagation (identity gate), while the higher symmetry in AKLT-type states enables nontrivial gate computation. This work demonstrates a close connection between measurement-based quantum computation and symmetry-protected topological order. [Preview Abstract] |
Monday, March 13, 2017 9:00AM - 9:12AM |
A52.00006: CHSH Violation for All Two-Qubit Measurement Settings Daniel Dilley, Eric Chitambar It is well-known that certain two-qubit quantum states demonstrate nonlocal correlations when Alice and Bob measure the spin of their systems in particular directions. This is shown by a violation of the so-called CHSH Inequality. Necessary and sufficient conditions have previously been established for when measurement directions exist that violate the CHSH Inequality for a given two-qubit state. In this talk we turn the question around and ask whether or not an entangled quantum state exists that demonstrates nonlocal correlations for a given choice of local measurement directions. We show that the CHSH Inequality can be violated by some quantum state for any choice of distinct local measurement directions, and we explicitly describe the state that violates the inequality. Furthermore, we show that a maximally entangled state generates the greatest violation of the CHSH Inequality for any choice of measurements. This provides a stronger type of equivalence between maximal entanglement and maximal nonlocality in CHSH experiments. [Preview Abstract] |
Monday, March 13, 2017 9:12AM - 9:24AM |
A52.00007: Approximate reversal of quantum Gaussian dynamics Ludovico Lami, Siddhartha Das, Mark Wilde Recently, there has been focus on determining the conditions under which the data processing inequality for quantum relative entropy is satisfied with approximate equality. The solution of the exact equality case is due to the work of Petz, who showed that the quantum relative entropy between two states stays the same after the action of a quantum channel if and only if there is a {\it reversal channel} that recovers the original states after the channel acts. Furthermore, this reversal channel can be constructed explicitly and is now called the {\it Petz recovery map}. Recent developments have shown that a variation of the Petz recovery map works well for recovery in the case of approximate equality of the data processing inequality. Our main contribution here is a proof that bosonic Gaussian states and channels possess a particular closure property, namely, that the Petz recovery map associated to a bosonic Gaussian state $\sigma$ and a bosonic Gaussian channel $\mathcal{N}$ is itself a bosonic Gaussian channel. We furthermore give an explicit construction of the Petz recovery map in this case, in terms of the mean vector and covariance matrix of the state $\sigma$ and the Gaussian specification of the channel $\mathcal{N}$. [Preview Abstract] |
Monday, March 13, 2017 9:24AM - 9:36AM |
A52.00008: Low-dimensional Manifolds for Efficient Representation of Open Quantum Systems Nikolas Tezak, Nina Amini, Hideo Mabuchi Weakly nonlinear degrees of freedom in dissipative quantum systems tend to localize near manifolds of quasi-classical states. We present a family of methods for deriving optimal unitary model transformations based on representations of finite dimensionally generated Lie groups. The transformations are optimal in that they minimize the quantum relative entropy distance between a given state and the quasi-classical manifold. This naturally splits the description of quantum states into quasi-classical coordinates that specify the nearest quasi-classical state and a transformed quantum state that can be represented in fewer basis levels. We derive coupled equations of motion for the coordinates and the transformed state and demonstrate how this can be exploited for efficient numerical simulation. Our optimization objective naturally quantifies the non-classicality of states occurring in some given open system dynamics. This allows us to compare the intrinsic complexity of different open quantum systems. [Preview Abstract] |
Monday, March 13, 2017 9:36AM - 9:48AM |
A52.00009: Constructing the Bloch sphere without quantum mechanics Michael Mazurek, Matthew Pusey, Robert Spekkens, Kevin Resch Quantum state and measurement tomography are standard analysis methods which find the quantum states and measurement operators that explain a set of experimental data. Once the quantum description of an experiment is found, it is often used to draw conclusions about the experiment, or to make predictions about future ones. However, these techniques cannot be used to identify possible deviations from quantum theory, as they assume the correctness of quantum mechanics. Here, we develop a quantum-free tomography technique that finds the generalized probability theory (GPT) that best fits our data. This GPT tomography technique is able to characterize the dimension and shape of the GPT state and effect spaces in an experiment, providing a predictive theory explaining the specific preparation and measurement procedures performed. We demonstrate our technique with an experiment manipulating the polarization degree-of-freedom of single photons. The GPT state and effect spaces we construct closely resemble the corresponding spaces for a qubit, and we place small upper bounds on the maximum amount our experiment may deviate from quantum theory. [Preview Abstract] |
Monday, March 13, 2017 9:48AM - 10:00AM |
A52.00010: Quantum information theory of the Bell-state quantum eraser Jennifer Glick, Christoph Adami Wave-particle duality has long been recognized as a phenomenon that is unique to quantum systems and one that is prominently manifested in the quantum eraser experiment. The Bell-state quantum eraser brings this duality to the forefront, as one can retroactively choose to observe particle-like or wave-like properties, or anything in between. We present a unitary information-theoretic description of the Bell-state quantum eraser and show that a relationship between the coherence of the quantum state, and the classical information obtained from it, naturally emerges. The trade-off that we derive between coherence and path information does not rely on any chosen measure of coherence, as it simply follows from the chain rule for quantum entropies. We conclude that a full information-theoretic analysis of the quantum eraser and other quantum protocols can offer new insights into the origins of complementarity. [Preview Abstract] |
Monday, March 13, 2017 10:00AM - 10:12AM |
A52.00011: Resource reflecting functor and its application to non-uniformity Priyaa Varshinee Srinivasan, Barry C. Sanders, Robin Cockett In this work, we formulate an abstract approach to translate one resource theory to another. We adopt the notion of resource theories as partitioned symmetric monoidal categories and extend this notion by considering resource-reflecting functors between resource theories. A functor $F$ is a structure preserving map and $F$ is said to be resource-reflecting if $F(g)$ being a free transformation implies that the transformation $g$ is also free. Thus, a resource-reflecting functor demonstrates that the existence of a free transformation between two resources in the domain resource theory can be inferred from the existence of a free transformation in the codomain theory. As an example, we construct one such functor from the resource theory of non-uniformity to a resource theory of majorization. Thus, our work lays a foundation for expressing similarities between resource theories and for applying results achieved in one resource theory to another. An abstract approach to the translation between theories enables common patterns to be identified between resource theories thereby reducing the effort of solving the same problem for different theories. [Preview Abstract] |
Monday, March 13, 2017 10:12AM - 10:24AM |
A52.00012: Any Ontological Model of the Single Qubit Stabilizer Formalism must be Contextual Piers Lillystone, Joel J. Wallman Quantum computers allow us to easily solve some problems classical computers find hard. Non-classical improvements in computational power should be due to some non-classical property of quantum theory. Contextuality, a more general notion of non-locality, is a necessary, but not sufficient, resource for quantum speed-up. Proofs of contextuality can be constructed for the classically simulable stabilizer formalism. Previous proofs of stabilizer contextuality are known for 2 or more qubits, for example the Mermin-Peres magic square. In the work presented we extend these results and prove that any ontological model of the single qubit stabilizer theory must be contextual, as defined by R. Spekkens, and give a relation between our result and the Mermin-Peres square. By demonstrating that contextuality is present in the qubit stabilizer formalism we provide further insight into the contextuality present in quantum theory. Understanding the contextuality of classical sub-theories will allow us to better identify the physical properties of quantum theory required for computational speed up. [Preview Abstract] |
Monday, March 13, 2017 10:24AM - 10:36AM |
A52.00013: Single-photon Kerr nonlinearities help quantum computation Joshua Combes, Brod Daniel There is still much debate over whether it is actually possible to build a CPHASE gate using fully realistic models for cross-Kerr nonlinearities. The main contention is that the multimode nature of traveling photons precluded a high-fidelity CPHASE gate. This was pointed in two well-known results, due to Shapiro and Gea-Banacloche. In this talk, I will describe our proposal [1] for a high-fidelity CPHASE gate built out of networks of cross-Kerr interaction sites and counter-propagating photons. In the limit of infinitely many interaction sites and spectrally narrow wave packets, this network implements a perfect CPHASE gate [2]. Our proposal is fully passive - there is no need for active switching, error correction, gradient echo memories, wave packet reshaping, etc. Further, it is less resource- intensive than previous proposals. [1] D. J. Brod and J. Combes, Phys. Rev. Lett. 117, 080502 (2016). [2] D. J. Brod, J. Combes, and J. Gea-Banacloche, Phys. Rev. A 94, 023833 (2016). [Preview Abstract] |
Monday, March 13, 2017 10:36AM - 10:48AM |
A52.00014: Experimental investigation of the no-signalling principle in parity-time symmetric theory using an open quantum system. Jian-Shun Tang, Yi-Tao Wang, Yong-Jian Han, Chuan-Feng Li, Guang-Can Guo The experimental progress achieved in parity-time (PT) symmetry in classical optics is the most important accomplishment in the past decade and stimulates many new applications, such as unidirectional light transport and single-mode lasers. However, in the quantum regime, some controversial effects are proposed for PT-symmetric theory, for example, the potential violation of the no-signalling principle. It is therefore important to understand whether PT-symmetric theory is consistent with well-established principles. Here, we experimentally study this no-signalling problem related to the PT-symmetric theory using two space-like separated entangled photons, with one of them passing through a post-selected quantum gate, which effectively simulates a PT-symmetric evolution. Our results suggest that the superluminal information transmission can be simulated when the successfully PT-symmetrically evolved subspace is solely considered. However, considering this subspace is only a part of the full Hermitian system, additional information regarding whether the PT-symmetric evolution is successful is necessary, which transmits to the receiver at maximally light speed, maintaining the no-signalling principle. [Preview Abstract] |
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