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arXiv:1808.03757 · Physical Review A

Unification of quantum resources in distributed scenarios

Hongyi Zhou, Xiao Yuan, Xiongfeng Ma

Published Feb 22, 2019• 10 citations
arXivHTMLPDF

Abstract

Quantum resources, such as coherence, discord, and entanglement, play a key role for demonstrating an advantage in many computation and communication tasks. In order to find the nature behind these resources, tremendous efforts have been made to explore the connections between them. In this work, we extend the single party coherence resource framework to the distributed scenario and relate it to basis-dependent discord. We show the operational meaning of basis-dependent discord in quantum key distribution and propose its resource measures. With any basis-dependent discord measure, we show how to extend it to measure coherence, discord, and entanglement by considering the relation of the resource free states. Our results lead to a unification of measures of quantum resources.

DOI
10.1103/physreva.99.022326

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Quantum resources, such as coherence, discord, and entanglement, play a key role for demonstrating an advantage in many computation and communication tasks. In order to find the nature behind these resources, tremendous efforts have been made to explore the connections between them. In this work, we extend the single party coherence resource framework to the distributed scenario and relate it to basis-dependent discord. We show the operational meaning of basis-dependent discord in quantum key distribution and propose its resource measures. With any basis-dependent discord measure, we show how to extend it to measure coherence, discord, and entanglement by considering the relation of the resource free states. Our results lead to a unification of measures of quantum resources.
In this work (multipartite) entanglement, discord, and coherence are unified as different aspects of a single underlying resource theory defined through simple and operationally meaningful elemental operations. This is achieved by revisiting the resource theory defining entanglement, local operations, and classical communication (LOCC), placing the focus on the underlying quantum nature of the communication channels. Taking the natural elemental operations in the resulting generalization of LOCC yields a resource theory that singles out coherence in the wire connecting the spatially separated systems as an operationally useful resource. The approach naturally allows us to consider a reduced setting as well, namely, the one with only the wire connected to a single quantum system, which leads to discordlike resources. The general form of free operations in this latter setting is derived and presented as a closed form. We discuss in what sense the present approach defines a resource theory of quantum discord and in which situations such an interpretation is sound—and why in general discord is not a resource. This unified and operationally meaningful approach makes transparent many features of entanglement that in LOCC might seem surprising, such as the possibility to use a particle to entangle two parties, without it ever being entangled with either of them, or that there exist different forms of multipartite entanglement.
One of the fundamental features that separates quantum physics from classical physics is the idea of quantum superposition, also known as coherence. This thesis concentrates on understanding quantum coherence in the mathematical framework of resource theories, viewing it both as a resource to be harnessed and as a way to quantitatively characterise quantum states in contrast to classical states. We first examine the type of coherence resource theory which has emerged recently to cope with general settings where the physical nature of the medium encoding information is not crucial, such as computation. We identify the set of quantum processes in which coherence is neither created nor used, and use these to provide a physically motivated resource theory pictured in terms of interferometry. Using the same concepts, we then find connections between coherence and discord, a type of quantum correlation. In particular, we show how coherence can be used to generate discord, and explore basis-dependent discord as an intermediate quantity. The second part of the thesis applies the resource theory framework to quantify quantum macroscopicity, taken here to mean the extent to which coherence exists in a system on a macroscopic scale. We find the appropriate type of resource theory for this purpose, giving criteria for good measures of macroscopic coherence. We use these criteria to evaluate some previously proposed measures and highlight the role of the quantum Fisher information. Next, we build up measures based on the concept of macroscopic distinguishability and use them to show that macroscopic quantum states are fragile to noise induced by interaction with an environment. Finally, we apply measures based on the Fisher information to a range of experiments involving mechanical degrees of freedom, in order to compare their macroscopicity.
Deviations from classical physics when distant quantum systems become correlated are interesting both fundamentally and operationally. There exist situations where the correlations enable collaborative tasks that are impossible within the classical formalism. Here, we consider the efficiency of quantum computation protocols compared to classical ones as a benchmark for separating quantum and classical resources and argue that the computational advantage of collaborative quantum protocols in the discrete variable domain implies the nonclassicality of correlations. By analyzing a toy model, it turns out that this argument implies the existence of quantum correlations distinct from entanglement and discord. We characterize such quantum correlations in terms of the net global coherence resources inherent within quantum states and show that entanglement and discord can be understood as special cases of our general framework. Finally, we provide an operational interpretation of such correlations as those allowing two distant parties to increase their respective local quantum computational resources only using locally incoherent operations and classical communication.
Discordant states appear in a large number of quantum phenomena and seem to be a good indicator of divergence from classicality. While there is evidence that they are essential for a quantum algorithm to have an advantage over a classical one, their precise role is unclear. We examine the role of discord in quantum algorithms using the paradigmatic framework of restricted distributed quantum gates and show that manipulating discordant states using local operations has an associated cost in terms of entanglement and communication resources. Changing discord reduces the total correlations and reversible operations on discordant states usually require nonlocal resources. Discord alone is, however, not enough to determine the need for entanglement. A more general type of similar quantities, which we call KKK discord, is introduced as a further constraint on the kinds of operations that can be performed without entanglement resources.
Abstract Quantum discord captures nonclassical correlations beyond entanglement and plays a piv-otal role in quantum communication, computation, and thermodynamics. Traditionally defined via entropy-based asymmetries in mutual information, discord remains conceptually rich but operationally opaque particularly in noisy or mixed-state regimes where entanglement vanishes yet quantum advantage persists. In this work, we introduce a novel formulation of discord based on Measurement-Induced Coherence Transfer (MICT). Rather than quantifying information imbalance, MICT discord measures the coherence gained in subsystem A when a projective measurement is performed on subsystem B. This directional, coherence-centric perspective reframes discord as a physically observable transfer process, firmly grounded in the resource theory of quantum coherence. Numerical simulations on Werner states validate the framework and reveal strong basis sensitivity: computational-basis measurements yield vanishing discord, whereas Hadamard-basis measurements consistently produce maximal coherence. This sharp divergence from standard discord measures underscores the operational significance of measurement choice in coherence-aware protocols. Finally, we discuss experimental feasibility, showing that MICT discord can be estimated via standard quantum state tomography and coherence monotones. Our results position MICT discord as a practical diagnostic and a new lens for interpreting quantum correlations, with potential applications in coherence-based benchmarking, quantum thermodynamics, and noise-resilient communication protocols.
From an operational perspective, nonclassicality characterizes the exotic behavior in a physical process which cannot be explained with Newtonian physics. There are several widely used measures of nonclassicality, including coherence, discord, and entanglement, each proven to be essential resources in particular situations. There exists evidence of fundamental connections among the three measures. However, the sources of nonclassicality are still regarded differently and such connections are yet to be elucidated. Here, we introduce a general framework of defining a unified nonclassicality with an operational motivation founded on the capability of interferometry. Nonclassicality appears differently as coherence, discord, and entanglement in different scenarios with local measurement, weak basis-independent measurement, and strong basis-independent measurement, respectively. Our results elaborate how these three measures are related and how they can be transformed from each other. Experimental schemes are proposed to test the results.