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AIP conference proceedings

An observable based approach to evaluating quantum coherence

Suman Mandal, Marek Narożniak, Chandrashekar Radhakrishnan, Manikandan Kondappan, Zhi‐Qiang Jiao, Xiamin Jin, Tim Byrnes

Published Jan 1, 2020• 0 citations
Publisher

Abstract

We introduce a procedure based on quantum expectation values of measurement observables to characterize quantum coherence. In a bipartite system, the two-point correlation function is used in combination with the Schatten-1 norm to estimate the quantum coherence. This definition of coherence allows the decomposition into contributions corresponding to the non-classical correlations between the subsystems and localized on each subsystem. We illustrate the method for several bipartite systems, showing that an incomplete basis still gives a qualitative measure of the coherence.

DOI
10.1063/5.0011394

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We introduce a procedure based on quantum expectation values of measurement observables to characterize quantum coherence. In a bipartite system, the two-point correlation function is used in combination with the Schatten-1 norm to estimate the quantum coherence. This definition of coherence allows the decomposition into contributions corresponding to the non-classical correlations between the subsystems and localized on each subsystem. We illustrate the method for several bipartite systems, showing that an incomplete basis still gives a qualitative measure of the coherence.
We introduce a procedure based on quantum expectation values of measurement observables to characterize quantum coherence.Our measure allows one to quantify coherence without having to perform tomography of the quantum state and can be directly calculated from measurement expectation values.This definition of coherence allows the decomposition into contributions corresponding to the nonclassical correlations between the subsystems and localized on each subsystem.The method can also be applied to cases where the full set of measurement operators is unavailable.An estimator using the truncated measurement operators can be used to obtain lower bound to the genuine value of coherence.We illustrate the method for several bipartite systems and show the singular behavior of the coherence measure in a spin-1 chain, characteristic of a quantum phase transition.
Abstract Quantum coherence characterizes the non-classical feature of a single party system with respect to a local basis. Based on a recently introduced resource framework, coherence can be regarded as a resource and be systematically manipulated and quantified. Operationally, coherence quantifies the intrinsic randomness of the outcome of the projective measurement in the system’s computational basis. However, such a relation is only proven when randomness is characterized by the von Neumann entropy. In this work, we consider several recently proposed coherence measures and relate them to the general uncertainties of the projective measurement outcome conditioned on all the other systems. Our work thus provides a unified framework for redefining several coherence measures via general conditional entropies. Based on the relation, we numerically calculate the coherence measures via semi-definite programming. Furthermore, we discuss the operational meaning of the unified definition. Our result highlights the close relation between single partite coherence and bipartite quantum correlation.
The distribution of quantum coherence in multipartite systems is one of the basic problems in the resource theory of coherence. While the usual coherence measures are defined on a single system and cannot capture the nonlocal correlation between subsystems, in order to deal with the distribution of coherence it is crucial to quantify the coherence in bipartite systems properly. Here, we introduce incoherent-quantum (IQ) coherence measures on bipartite systems, which can characterize the correlations between systems. According to the IQ coherence measures on bipartite systems, we find the distribution of coherence of formation and assistance in bipartite systems: the total coherence of formation is lower bounded by the sum of coherence of formation in each subsystem and the entanglement of formation between the subsystems, while the total coherence of assistance is upper bounded by the sum of coherence of assistance in each subsystem and the entanglement of assistance between subsystems. Besides, we also obtain the tradeoff relation between the coherence cost and entanglement cost, distillable coherence and distillable entanglement in bipartite systems. Thus, the IQ coherence measures introduced here truly capture the nonlocal correlation between subsystems and reveal the distribution of coherence in bipartite systems.
Abstract In this article, we study quantum coherence of bipartite state from the perspective of weak measurement, which generalizes the notion of coherence relative to measurement. This is being illustrated by computing coherence for the well-known Bell diagonal and Werner states. Further, we have expanded the notion of coherence to encompass correlations, exploring its connections with other quantifications of nonlocality. We have determined that this coherence measure can be perceived as a generalized version of the Wigner-Yanese skew information measure and several other nonlocal measures. As a natural extension, we introduce uncertainty relations within the context of weak measurements. Additionally, we propose a novel form of variance by considering the weak value of an observable within a comprehensive framework.
We introduce a measure Q of bipartite quantum correlations for arbitrary two-qubit states, expressed as a state-independent function of the density matrix elements. The amount of quantum correlations can be quantified experimentally by measuring the expectation value of a small set of observables on up to four copies of the state, without the need for a full tomography. We extend the measure to 2×d systems, providing its explicit form in terms of observables and applying it to the relevant class of multiqubit states employed in the deterministic quantum computation with one quantum bit model. The number of required measurements to determine Q in our scheme does not increase with d. Our results provide an experimentally friendly framework to estimate quantitatively the degree of general quantum correlations in composite systems.
Quantum coherence quantifies the amount of superposition a quantum state can have in a given basis. Since there is a difference in the structure of eigenstates of the ergodic and many-body localized systems, we expect them also to differ in terms of their coherences in a given basis. Here, we numerically calculate different measures of quantum coherence in the excited eigenstates of an interacting disordered Hamiltonian as a function of the disorder. We show that quantum coherence can be used as an order parameter to detect the well-studied ergodic to many-body localized phase transition. We also perform quantum quench studies to distinguish the behavior of coherence in thermalized and localized phases. We then present a protocol to calculate measurement-based localizable coherence to investigate the thermal and many-body localized phases. The protocol allows one to investigate quantum correlations experimentally in a nondestructive way, in contrast to measures that require tracing out a subsystem, which always destroys coherence and correlation.