Stochastic Matrix Product States

The concept of stochastic matrix product states is introduced and a natural form for the states is derived. This allows to define the analogue of Schmidt coefficients for steady states of non-equilibrium stochastic processes. We discuss a new measure for correlations which is analogous to the entanglement entropy, the entropy cost $S_C$, and show that this measure quantifies the bond dimension needed to represent a steady state as a matrix product state. We illustrate these concepts on the hand of the asymmetric exclusion process

Quantum Correlations in Large-Dimensional States of High Symmetry

In this article, we investigate how quantum correlations behave for the so-called Werner and pseudo-pure families of states. The latter refers to states formed by mixing any pure state with the totally mixed state. We derive closed expressions for the Quantum Discord (QD) and the Relative Entropy of Quantumness (REQ) for these families of states. For Werner states, the classical correlations are seen to vanish in high dimensions while the amount of quantum correlations remain bounded and become independent of whether or not the the state is entangled. For pseudo-pure states, nearly the opposite effect is observed with both the quantum and classical correlations growing without bound as the dimension increases and only as the system becomes more entangled. Finally, we verify that pseudo-pure states satisfy the conjecture of [\textit{Phys. Rev. A} \textbf{84}, 052110 (2011)] which says that the Geometric Measure of Discord (GD) always upper bounds the squared Negativity of the state

Natural Metric for Quantum Information Theory

We study in detail a very natural metric for quantum states. This new proposal has two basic ingredients: entropy and purification. The metric for two mixed states is defined as the square root of the entropy of the average of representative purifications of those states. Some basic properties are analyzed and its relation with other distances is investigated. As an illustrative application, the proposed metric is evaluated for 1-qubit mixed states.Comment: v2: enlarged; presented at ISIT 2008 (Toronto

Spotlighting quantum critical points via quantum correlations at finite temperatures

We extend the program initiated in [T. Werlang et al., Phys. Rev. Lett. 105, 095702 (2010)] in several directions. Firstly, we investigate how useful quantum correlations, such as entanglement and quantum discord, are in the detection of critical points of quantum phase transitions when the system is at finite temperatures. For that purpose we study several thermalized spin models in the thermodynamic limit, namely, the XXZ model, the XY model, and the Ising model, all of which with an external magnetic field. We compare the ability of quantum discord, entanglement, and some thermodynamic quantities to spotlight the quantum critical points for several different temperatures. Secondly, for some models we go beyond nearest-neighbors and also study the behavior of entanglement and quantum discord for second nearest-neighbors around the critical point at finite temperature. Finally, we furnish a more quantitative description of how good all these quantities are in spotlighting critical points of quantum phase transitions at finite T, bridging the gap between experimental data and those theoretical descriptions solely based on the unattainable absolute zero assumption.Comment: 11 pages, 12 figures, RevTex4-1; v2: published versio

Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation

We present a continuous-variable quantum key distribution protocol combining a discrete modulation and reverse reconciliation. This protocol is proven unconditionally secure and allows the distribution of secret keys over long distances, thanks to a reverse reconciliation scheme efficient at very low signal-to-noise ratio.Comment: 4 pages, 2 figure

Entropy measures for complex networks: Toward an information theory of complex topologies

The quantification of the complexity of networks is, today, a fundamental problem in the physics of complex systems. A possible roadmap to solve the problem is via extending key concepts of information theory to networks. In this paper we propose how to define the Shannon entropy of a network ensemble and how it relates to the Gibbs and von Neumann entropies of network ensembles. The quantities we introduce here will play a crucial role for the formulation of null models of networks through maximum-entropy arguments and will contribute to inference problems emerging in the field of complex networks.Comment: (4 pages, 1 figure

Interpreting quantum discord through quantum state merging

We present an operational interpretation of quantum discord based on the quantum state merging protocol. Quantum discord is the markup in the cost of quantum communication in the process of quantum state merging, if one discards relevant prior information. Our interpretation has an intuitive explanation based on the strong subadditivity of von Neumann entropy. We use our result to provide operational interpretations of other quantities like the local purity and quantum deficit. Finally, we discuss in brief some instances where our interpretation is valid in the single copy scenario.Comment: 5 pages, no figures. See http://arxiv.org/abs/1008.3205 for similar results. Typos fixed, references and acknowledgements updated. End note adde

Experimental achievement of the entanglement assisted capacity for the depolarizing channel

We experimentally demonstrate the achievement of the entanglement assisted capacity for classical information transmission over a depolarizing channel. The implementation is based on the generation and local manipulation of 2-qubit Bell states, which are finally measured at the receiver by a complete Bell state analysis. The depolarizing channel is realized by introducing quantum noise in a controlled way on one of the two qubits. This work demonstrates the achievement of the maximum allowed amount of information that can be shared in the presence of noise and the highest reported value in the noiseless case.Comment: 4 pages, 3 figure

Flow Ambiguity: A Path Towards Classically Driven Blind Quantum Computation

Blind quantum computation protocols allow a user to delegate a computation to a remote quantum computer in such a way that the privacy of their computation is preserved, even from the device implementing the computation. To date, such protocols are only known for settings involving at least two quantum devices: either a user with some quantum capabilities and a remote quantum server or two or more entangled but noncommunicating servers. In this work, we take the first step towards the construction of a blind quantum computing protocol with a completely classical client and single quantum server. Specifically, we show how a classical client can exploit the ambiguity in the flow of information in measurement-based quantum computing to construct a protocol for hiding critical aspects of a computation delegated to a remote quantum computer. This ambiguity arises due to the fact that, for a fixed graph, there exist multiple choices of the input and output vertex sets that result in deterministic measurement patterns consistent with the same fixed total ordering of vertices. This allows a classical user, computing only measurement angles, to drive a measurement-based computation performed on a remote device while hiding critical aspects of the computation.Comment: (v3) 14 pages, 6 figures. expands introduction and definition of flow, corrects typos to increase readability; contains a new figure to illustrate example run of CDBQC protocol; minor changes to match the published version.(v2) 12 pages, 5 figures. Corrects motivation for quantities used in blindness analysi

Fisher-information condition for enhanced signal detection via stochastic resonance

Various situations where a signal is enhanced by noise through stochastic resonance are now known. This paper contributes to determining general conditions under which improvement by noise can be a priori decided as feasible or not. We focus on the detection of a known signal in additive white noise. Under the assumptions of a weak signal and a sufficiently large sample size, it is proved, with an inequality based on the Fisher information, that improvement by adding noise is never possible, generically, in these conditions. However, under less restrictive conditions, an example of signal detection is shown with favorable action of adding noise.Fabing Duan, François Chapeau-Blondeau, Derek Abbot