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Results in Physics

Quantum coherence of Fermionic Gaussian states

Yangyang Wang, Xiaofei Qi, Jinchuan Hou, Bing Xu

Published Jan 7, 2025• 1 citation
Publisher

Abstract

In the present paper, quantum coherence of fermionic Gaussian states is investigated from the point of quantum resource theory. Some characterizations of m-mode (m≥1) incoherent fermionic Gaussian states and incoherent fermionic Gaussian channels are obtained, two quantification measures of fermionic Gaussian quantum coherence based on respectively the relative entropy and the Hellinger distance are proposed, and some formulas to calculate the value of these measures are established. It is shown that the m-mode fermionic Gaussian coherence is a quantum resource.

DOI
10.1016/j.rinp.2025.108107

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In the present paper, quantum coherence of fermionic Gaussian states is investigated from the point of quantum resource theory. Some characterizations of m-mode (m≥1) incoherent fermionic Gaussian states and incoherent fermionic Gaussian channels are obtained, two quantification measures of fermionic Gaussian quantum coherence based on respectively the relative entropy and the Hellinger distance are proposed, and some formulas to calculate the value of these measures are established. It is shown that the m-mode fermionic Gaussian coherence is a quantum resource.
Quantum coherence and nonclassical correlation are key features of a quantum world. Quantifying coherence and nonclassical correlation are two key tasks in quantum information theory. First, we present a bona fide measure of quantum coherence by utilizing the Hellinger distance. This coherence measure is proven to fulfill all the criteria of a well-defined coherence measure, including the strong monotonicity in the resource theories of quantum coherence. In terms of this coherence measure, the distribution of quantum coherence in multipartite systems is studied and a corresponding polygamy relation is proposed. Its operational meanings and the relations between the generation of quantum correlations and the coherence are also investigated. Moreover, we present the Hellinger distance-based measure of nonclassical correlation, which not only inherits the nice properties of the Hellinger distance including contractivity, but also shows a powerful analytic computability for a large class of quantum states. We show that there is an explicit tradeoff relation satisfied by the quantum coherence and this nonclassical correlation.
Abstract In this work we investigate how to quantify the coherence of quantum measurements. First, we establish a resource theoretical framework to address the coherence of measurement and show that any statistical distance can be adopted to define a coherence monotone of measurement. For instance, the relative entropy fulfills all the required properties as a proper monotone. We specifically introduce a coherence monotone of measurement in terms of off-diagonal elements of positive-operator-valued measure components. This quantification provides a lower bound on the robustness of measurement-coherence that has an operational meaning as the maximal advantage over all incoherent measurements in state discrimination tasks. Finally, we propose an experimental scheme to assess our quantification of measurement-coherence and demonstrate it by performing an experiment using a single qubit on IBM Q processor.
A resource theory of quantum coherence attempts to characterize the quantum coherence that exists in a given quantum system. Many different approaches to a resource theory of coherence have recently been proposed, with their differences lying primarily in the identification of ``free'' or ``incoherent'' operations. In this article, we compare a number of these operational classes. In particular, the recently introduced class of dephasing-covariant operations is analyzed, and we characterize the Kraus operators of such maps. A number of coherence measures are introduced based on relative R\'enyi entropies, and we study incoherent state transformations under different operational classes. In particular, we show that the incoherent Schmidt rank can be increased arbitrarily large by certain noncoherence generating operations. The distinction between asymmetry-based versus basis-dependent notions of coherence theory is clarified, and we further develop the resource theory of NNN asymmetry, where NNN is the group of all diagonal incoherent unitaries.
We present an approach for the quantification of quantumness of correlations in fermionic systems. We study the multipartite relative entropy of quantumness in such systems and show how the symmetries in the states can be used to obtain analytical solutions. Numerical evidence of the uniqueness of such solutions is also presented. Supported by these results, we show that the minimization of the multipartite relative entropy of quantumness, over certain choices of its mode multipartitions, reduces to the notion of quantumness of indistinguishable particles. By means of an activation protocol, we characterize the class of states without quantumness of correlations. As an example, we calculate the dynamics of quantumness of correlations for a purely dissipative system, whose stationary states exhibit interesting topological nonlocal correlations.
We investigate (k_{1},k_{2}) extendibility of fermionic Gaussian states, a property central to quantum correlations and approximations of separability. We show that these states are (k_{1},k_{2})-extendible if and only if they admit a fermionic Gaussian extension, yielding a complete covariance-matrix characterization and a simple semidefinite program (SDP) whose size scales linearly with the number of modes. This provides necessary conditions for arbitrary fermionic states and is sufficient within the Gaussian setting. Our main result is a finite de Finetti-type theorem: we derive trace-norm bounds between (k_{1},k_{2})-extendible fermionic Gaussian states and separable states, improving previous exponential scaling to linear in the number of modes, with complementary relative entropy and squashed entanglement bounds. For two modes, upper and lower bounds match at order 1/sqrt[k_{1}k_{2}]. Extendibility also provides operational support for one of the different notions of separability in fermionic systems. Finally, for fermionic Gaussian channels, we provide a simple semidefinite program criterion for antidegradability and show that entanglement-breaking channels coincide with replacement channels, implying no nontrivial entanglement-breaking fermionic Gaussian channels exist.