Operational Interpretation of Weight-Based Resource Quantifiers in Convex Quantum Resource Theories

Ducuara, Andrés F.; Skrzypczyk, Paul

doi:10.1103/physrevlett.125.110401

Cited by 51 publications

(45 citation statements)

References 51 publications

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“…Another application of the projective robustness Ω F can be obtained by connecting it with the advantage that the given resource provides in a class of channel discrimination tasks. This is essentially an extension of similar properties that were recently shown to hold for the robustness [42] and weight [44,45] measures. Since this is not related to our main discussion concerned with the uses of Ω F in constraining resource manipulation, we include the details in Appendix A.…”

Section: Projective Robustness In Channel Discriminationsupporting

confidence: 54%

“…It can also be used to study resource advantages in a different type of channel discrimination problems [44,45], and has recently been applied to establish strong bounds on deterministic resource distillation overheads [28,29]. The similarity between the two measures is made precise by noticing that they can be both expressed in terms of the max-relative entropy max [41], the non-logarithmic variant of which we define as max ( )…”

Section: B Resource Monotonesmentioning

confidence: 99%

“…(A1) as the average probability of guessing incorrectly, and we aim to minimise this quantity. In channel discrimination, the robustness F ( ) is known to quantify the advantage that a given input state can provide over all free states [42], while in channel exclusion, it is the weight F ( ) which quantifies the advantage [44,45]. Combining the two, we can show that Ω F ( ) quantifies the advantage when channel discrimination and channel exclusion tasks are considered at the same time.…”

Section: General Resource Theoriesmentioning

confidence: 99%

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Tight constraints on probabilistic convertibility of quantum states

Regula¹

2021

Preprint

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We develop two general approaches to characterising the manipulation of quantum states by means of probabilistic protocols constrained by the limitations of some quantum resource theory.First, we give a general necessary condition for the existence of a physical transformation between quantum states, obtained using a new resource monotone based on the Hilbert projective metric. In all affine quantum resource theories (e.g. coherence, asymmetry, imaginarity) as well as in entanglement distillation, we show that the monotone provides a necessary and sufficient condition for resource convertibility, and hence no better restrictions on all probabilistic protocols are possible. We use the monotone to establish improved bounds on the performance of both one-shot and many-copy probabilistic resource distillation protocols.Complementing this approach, we introduce a general method for bounding achievable probabilities in resource transformations through a family of convex optimisation problems. We show it to tightly characterise single-shot probabilistic distillation in broad types of resource theories, allowing an exact analysis of the trade-offs between the probabilities and errors in distilling maximally resourceful states. We demonstrate the usefulness of both of our approaches in the study of quantum entanglement distillation. CONTENTSI. Introduction II. Preliminaries A. Resource transformations B. Resource monotones III. Projective robustness A. Properties B. Necessary condition for probabilistic transformations C. Sufficient condition for probabilistic transformations IV. Probabilistic resource distillation A. Improved bounds on probabilistic distillation errors and overheads B. Comparison with the eigenvalue bound C. Achievable fidelity V. Bounding probability and error trade-offs A. General bounds on achievable probability B. Trade-offs in probabilistic resource distillation VI. Discussion References A. Projective robustness in channel discrimination *

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Section: Projective Robustness In Channel Discriminationsupporting

confidence: 54%

Section: B Resource Monotonesmentioning

confidence: 99%

Section: General Resource Theoriesmentioning

confidence: 99%

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Tight constraints on probabilistic convertibility of quantum states

Regula¹

2021

Preprint

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“…[ 3 ] Coherence quantification, and in particular the development of coherence quantifiers which have an operational meaning in experiments, have seen steady active progress within the resource‐theoretic framework. [ 6–19 ] Other important questions concern state transformation, that is, the possibility to transform a quantum state into another one by using quantum operations which do not create coherence. [ 16,20–33 ] Coherence theory in multipartite system has also been investigated, allowing to provide powerful links between the theories of entanglement and coherence.…”

Section: Introductionmentioning

confidence: 99%

Experimental Progress on Quantum Coherence: Detection, Quantification, and Manipulation

Streltsov

Regula

et al. 2021

Adv Quantum Tech

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Quantum coherence is a fundamental property of quantum systems, separating quantum from classical physics. Recently, there has been significant interest in the characterization of quantum coherence as a resource, investigating how coherence can be extracted and used for quantum technological applications. In this work, the progress of this research is reviewed, focusing in particular on recent experimental efforts. After a brief review of the underlying theory, the main platforms for realizing the experiments are discussed: linear optics, nuclear magnetic resonance, and superconducting systems. Experimental detection and quantification of coherence, experimental state conversion and coherence distillation, and experiments investigating the dynamics of quantum coherence are then considered. Experiments exploring the connections between coherence and uncertainty relations, path information, and coherence of operations and measurements are also reviewed. Experimental efforts on multipartite and multilevel coherence are also discussed.

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“…This has led to the discovery of physical tasks and operational quantities that are relevant in not just one particular resource theory, but also in general settings. This motivates us to consider quantities that are universally applicable in the sense that they maintain a physically meaningful interpretation while being able to identify every state which is considered "nonclassical" or "resourceful" within the physical constraints of the given resource theory [32][33][34][35][36][37][38][39][40]. An example of such quantities would be the class of robustness measures [41], which are well-defined quantifiers of any quantum resource that find use in quantifying the operational advantages of resources in channel discrimination tasks [35,37,42].…”

mentioning

confidence: 99%