Resource Preservability

Hsieh, Cheng-Ta

doi:10.22331/q-2020-03-19-244

Cited by 27 publications

(22 citation statements)

References 92 publications

(184 reference statements)

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“…For example, the identity channel perfectly preserves resources, while it is a resource-nongenerating channel belonging to O. Similar arguments have been made in recent studies of channel resource theories [47,48]. Particularly, Ref.…”

Section: Resource Preservability Of Quantum Channelssupporting

confidence: 72%

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Fundamental limits on concentrating and preserving tensorized quantum resources

Lee¹,

Baek²,

Park³

et al. 2021

Preprint

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Quantum technology offers great advantages in many applications by exploiting quantum resources like nonclassicality, coherence, and entanglement. In practice, an environmental noise unavoidably affects a quantum system and it is thus an important issue to protect quantum resources from noise. In this work, we investigate the manipulation of quantum resources possessing the so-called tensorization property and identify the fundamental limitations on concentrating and preserving those quantum resources. We show that if a resource measure satisfies the tensorization property as well as the monotonicity, it is impossible to concentrate multiple noisy copies into a single better resource by free operations. Furthermore, we show that quantum resources cannot be better protected from channel noises by employing correlated input states on joint channels if the channel output resource exhibits the tensorization property. We address several practical resource measures where our theorems apply and manifest their physical meanings in quantum resource manipulation.

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Section: Resource Preservability Of Quantum Channelssupporting

confidence: 72%

“…Particularly, Ref. [47] investigated the axiomatic properties of resource preservability measures. In this sense, our measure R is appropriate to study resources preserved by noisy channels.…”

Section: Resource Preservability Of Quantum Channelsmentioning

confidence: 99%

Fundamental limits on concentrating and preserving tensorized quantum resources

Lee¹,

Baek²,

Park³

et al. 2021

Preprint

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“…An important part of such toolsets are resource monotones, which can be used to establish restrictions on feasible conversion schemes. Although this avenue has lately seen significant attention in the context of general resource theories [11,13,14,16,[20][21][22][23][24][25][26][27], a major downside to many of such approaches is that they can only characterize deterministic transformations, i.e., ones which succeed with certainty. Due to the difficulty in realizing such exact transformations, practical protocols for the utilization and conversion of resources typically exploit measurement-based schemes that are inherently probabilistic in nature [28,29].…”

Section: Introductionmentioning

confidence: 99%

Probabilistic transformations of quantum resources

Regula

2021

Preprint

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The difficulty in manipulating quantum resources deterministically often necessitates the use of probabilistic protocols, but the characterization of their capabilities and limitations has been lacking. Here, we develop two general approaches to this problem.First, we introduce a new resource monotone based on the Hilbert projective metric and we show that it obeys a very strong type of monotonicity: it can rule out all transformations, probabilistic or deterministic, between states in any quantum resource theory. This allows us to place fundamental limitations on state transformations and restrict the advantages that probabilistic protocols can provide over deterministic ones, significantly strengthening previous findings and extending recent no-go theorems. We apply our results to obtain a substantial improvement in lower bounds for the errors and overheads of probabilistic distillation protocols, directly applicable to tasks such as entanglement or magic state distillation, and computable through convex optimization. In broad classes of resources, we show that no better restrictions on probabilistic protocols are possible -our monotone can provide a necessary and sufficient condition for probabilistic resource transformations, thus allowing us to quantify exactly the highest fidelity achievable in resource distillation tasks by means of any probabilistic manipulation protocol.Complementing this approach, we introduce a general method for bounding achievable probabilities in resource transformations through a family of convex optimization problems. We show it to tightly characterize 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.

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“…Many problems of this type can be understood as instances of the question of resource convertibility within the formalism of quantum resource theories [20,21]. However, most works that dealt with resource transformations, in particular in the context of general quantum resources, focused only on deterministic transformations [12,14,15,18,19,[22][23][24][25][26][27][28][29]. This limits the practical utility of such approaches, and in particular means that most previous results cannot be used to understand the ultimate limits of resource conversion -it is known that probabilistic transformations can be significantly more powerful than deterministic ones [4,[30][31][32], so constraining only deterministic protocols does not provide complete information about our capability to manipulate a given resource.…”

Section: Introductionmentioning

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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Resource Preservability

Cited by 27 publications

References 92 publications

Fundamental limits on concentrating and preserving tensorized quantum resources

Fundamental limits on concentrating and preserving tensorized quantum resources

Probabilistic transformations of quantum resources

Tight constraints on probabilistic convertibility of quantum states

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