Disentanglement Cost of Quantum States

Berta, Mario; Majenz, Christian

doi:10.1103/physrevlett.121.190503

Cited by 29 publications

(23 citation statements)

References 38 publications

(65 reference statements)

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“…We saw earlier that the set of free operations induces Majorization theory is a topic in matrix analysis with several textbooks written on the subject; see e.g. (Marshall et al, 2011) and(Bhatia, 1996). It has many applications in different areas of science, from mathematics to economy and statistics, and more recently quantum physics.…”

Section: A Majorization Theorymentioning

confidence: 99%

Quantum resource theories

2019

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Quantum resource theories (QRTs) offer a highly versatile and powerful framework for studying different phenomena in quantum physics. From quantum entanglement to quantum computation, resource theories can be used to quantify a desirable quantum effect, develop new protocols for its detection, and identify processes that optimize its use for a given application. Particularly, QRTs have revolutionized the way we think about familiar properties of physical systems like entanglement, elevating them from being just interesting fundamental phenomena to being useful in performing practical tasks. The basic methodology of a general QRT involves partitioning all quantum states into two groups, one consisting of free states and the other consisting of resource states. Accompanying the set of free states is a collection of free quantum operations arising from natural restrictions placed on the physical system, restrictions that force the free operations to act invariantly on the set of free states. The QRT then studies what information processing tasks become possible using the restricted operations. Despite the large degree of freedom in how one defines the free states and free operations, unexpected similarities emerge among different QRTs in terms of resource measures and resource convertibility. As a result, objects that appear quite distinct on the surface, such as entanglement and quantum reference frames, appear to have great similarity on a deeper structural level. This article reviews the general framework of a quantum resource theory, focusing on common structural features, operational tasks, and resource measures. To illustrate these concepts, an overview is provided on some of the more commonly studied QRTs in the literature.

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Section: A Majorization Theorymentioning

confidence: 99%

Quantum resource theories

2019

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“…A natural question which arises in this context is whether the given measure can be understood in an operational sense, assessing exactly the usefulness of a given object in some physical task; however, establishing such an interpretation for a given quantifier is often highly nontrivial. The family of so-called robustness measures [34,84] stands out in this context, as two prominent members of the family have found several applications in operational settings: these are the generalized robustness [33,36,[79][80][81][82][85][86][87][88][89][90][91] and the standard robustness [18,89,92]. They are not only fundamental resource quantifiers faithfully capturing the resourcefulness of given objects with clear geometric interpretations, but also significantly relevant to experiments -they are directly observable, that is, can be obtained in an experiment by measuring a single, suitably chosen observable, rather than requiring complicated and expensive methods such as state tomography, allowing for the experimental quantification of resources [93,94].…”

Section: Introductionmentioning

confidence: 99%

General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks

2019

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We establish an operational characterization of general convex resource theories -describing the resource content of not only states, but also measurements and channels, both within quantum mechanics and in general probabilistic theories (GPTs) -in the context of state and channel discrimination. We find that discrimination tasks provide a unified operational description for quantification and manipulation of resources by showing that the family of robustness measures can be understood as the maximum advantage provided by any physical resource in several different discrimination tasks, as well as establishing that such discrimination problems can fully characterize the allowed transformations within the given resource theory.Specifically, we introduce a quantifier of resourcefulness of a measurement in any GPT, the generalized robustness of measurement, and show that it admits an operational interpretation as the maximum advantage that a given measurement provides over resourceless measurements in all state discrimination tasks. In the special case of quantum mechanics, we connect discrimination problems with single-shot information theory by showing that the generalized robustness of any measurement can be alternatively understood as the maximal increase in one-shot accessible information when compared to free measurements. We introduce two different approaches to quantifying the resource content of a physical channel based on the generalized robustness measures, and show that they quantify the maximum advantage that a resourceful channel can provide in several classes of state and channel discrimination tasks. Furthermore, we endow another measure of resourcefulness of states, the standard robustness, with an operational meaning in general GPTs as the exact quantifier of the maximum advantage that a state can provide in binary channel discrimination tasks. Finally, we establish that several classes of channel and state discrimination tasks form complete families of monotones fully characterizing the transformations of states and measurements, respectively, under general classes of free operations. Our results establish a fundamental connection between the operational tasks of discrimination and core concepts of resource theories -the geometric quantification of resources and resource manipulation -valid for all physical theories beyond quantum mechanics with no additional assumptions about the structure of the GPT

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“…Similarly, the generalized robustness of entanglement corresponds to the largest fidelity achievable with a maximally entangled state under free transformations [58]. The logarithmic version of this measure, known as the max-relative entropy [59], plays an essential role in the characterization of one-shot entanglement dilution [60,61] and one-shot coherence dilution [62], and quantifies the minimal rate of noise needed to catalytically erase the resource contained in a given state for a wider class of resource theories [28,63]. However, a general operational meaning of the generalized robustness in all convex resource theories was not known.…”

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Operational Advantage of Quantum Resources in Subchannel Discrimination

et al. 2019

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One of the central problems in the study of quantum resource theories is to provide a given resource with an operational meaning, characterizing physical tasks in which the resource can give an explicit advantage over all resourceless states. We show that this can always be accomplished for all convex resource theories. We establish in particular that any resource state enables an advantage in a channel discrimination task, allowing for a strictly greater success probability than any state without the given resource. Furthermore, we find that the generalized robustness measure serves as an exact quantifier for the maximal advantage enabled by the given resource state in a class of subchannel discrimination problems, providing a universal operational interpretation to this fundamental resource quantifier. We also consider a wider range of subchannel discrimination tasks and show that the generalized robustness still serves as the operational advantage quantifier for several well-known theories such as entanglement, coherence, and magic.Introduction. -A rigorous understanding of quantum resources has been one of the ultimate goals in quantum information science. In addition to the apparent theoretical interest, it also has high relevance to burgeoning quantum information technologies such as quantum communication [1,2], quantum cryptography [3,4], and quantum computation [5,6].Quantum resource theories [7] have recently attracted much attention as powerful tools which offer formal frameworks dealing with quantification and manipulation of intrinsic resources associated with quantum systems. One could consider different theories depending on the relevant physical constraints, and indeed various resource theories have been proposed and analyzed, such as entanglement [8,9], coherence [10][11][12], asymmetry [13,14], quantum thermodynamics [15,16], non-Markovianity [17], magic [18,19], and non-Gaussianity [20][21][22]. Although these resource theories provide deeper insights into their specific physical settings,they do not tell us much about how to understand the individual properties and results in a unified fashion. In particular, despite the generality of the resource theoretical framework, only a small number of results reported in the literature are applicable to wide classes of general quantum resource theories [23][24][25][26][27][28][29]. In this work, we add a fundamental item to this list with regard to one of the central questions asked in the study of resource theories: the operational characterization of quantum states and the resources they possess.An essential building block of a resource theory is the set of free states. It is the set of states that are considered "easy to prepare" in that theory, and any state outside of this set is called a resource state. A common and intuitive assumption is that the set of free states should be convex and closed. Convexity reflects a natural attribute in many physical settings, i.e. the fact that losing information about which free state was prepared, hence resulti...

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Disentanglement Cost of Quantum States

Cited by 29 publications

References 38 publications

Quantum resource theories

Quantum resource theories

General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks

Operational Advantage of Quantum Resources in Subchannel Discrimination

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