All Quantum Resources Provide an Advantage in Exclusion Tasks

Uola, Roope; Bullock, Tom; Kraft, Tristan; Pellonpää, Juha-Pekka; Brunner, Nicolás

doi:10.1103/physrevlett.125.110402

Cited by 56 publications

(71 citation statements)

References 36 publications

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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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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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“…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%

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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“…Numerous works have been devoted to characterizing resource convertibility in terms of complete sets of monotones in different types of QRTs [12,26,27,45,46,50,[52][53][54][55][56][57][58][59][60][61]. Recently, such complete characterizations for general (convex) resource theories of states and measurements in GPTs have been derived in Ref.…”

Section: Convertibility Conditions and Index-preservation Gamesmentioning

confidence: 99%

“…In the one-shot setting, resource monotones are often given operational interpretation in terms of guessing games [12,26,27,45,50,[52][53][54][55][56][57][58][59][60][61]. Typically this involves a scenario in which a player (or group of players) is trying to identify which state or channel has been prepared by a referee, among a finite ensemble of known possibilities.…”

Section: Introductionmentioning

confidence: 99%

Convertibility and Guessing Games in Dynamic Resource Theories

Ji¹,

Chitambar²

2021

Preprint

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Dynamic quantum resource theories describe the study of both states and channels in physicallyconstrained scenarios. Under the allowable operations of the theory, only certain states or channels can be transformed from one to another. In this paper we view a general resource theory from the "top-down", which starts at the level of supermaps and reduces to the level of states. Following this approach, we introduce a complete set of resource monotones for any convex resource theory based on a generalized form of the conditional min-entropy, which simplifies the ones recently presented in [Gour and Scandolo arXiv:2101.01552]. These monotones have an intuitive operational interpretation in terms of an index guessing game played between two parties.

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All Quantum Resources Provide an Advantage in Exclusion Tasks

Cited by 56 publications

References 36 publications

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

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

Tight constraints on probabilistic convertibility of quantum states

Convertibility and Guessing Games in Dynamic Resource Theories

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