Flag additivity in quantum resource theories

Liu, C. L.; Yu, Xiao-Dong; Tong, D. M.

doi:10.1103/physreva.99.042322

Cited by 24 publications

(13 citation statements)

References 37 publications

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“…QRTs have covered numerous aspects of quantum properties such as entanglement [2][3][4], coherence [5][6][7][8][9][10][11], athermality [12][13][14][15][16], magic states [17,18], asymmetry [19][20][21][22][23], purity [24], non-Gaussianity [25][26][27][28], and non-Markovianity [29,30]. Recently, QRTs for a general resource have been studied to figure out common structures shared among known QRTs and to understand the quantum properties systematically [31][32][33][34][35][36][37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

General Quantum Resource Theories: Distillation, Formation and Consistent Resource Measures

Kuroiwa

Yamasaki

2020

Quantum

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Quantum resource theories (QRTs) provide a unified theoretical framework for understanding inherent quantum-mechanical properties that serve as resources in quantum information processing, but resources motivated by physics may possess structure whose analysis is mathematically intractable, such as non-uniqueness of maximally resourceful states, lack of convexity, and infinite dimension. We investigate state conversion and resource measures in general QRTs under minimal assumptions to figure out universal properties of physically motivated quantum resources that may have such mathematical structure whose analysis is intractable. In the general setting, we prove the existence of maximally resourceful states in one-shot state conversion. Also analyzing asymptotic state conversion, we discover catalytic replication of quantum resources, where a resource state is infinitely replicable by free operations. In QRTs without assuming the uniqueness of maximally resourceful states, we formulate the tasks of distillation and formation of quantum resources, and introduce distillable resource and resource cost based on the distillation and the formation, respectively. Furthermore, we introduce consistent resource measures that quantify the amount of quantum resources without contradicting the rate of state conversion even in QRTs with non-unique maximally resourceful states. Progressing beyond the previous work showing a uniqueness theorem for additive resource measures, we prove the corresponding uniqueness inequality for the consistent resource measures; that is, consistent resource measures of a quantum state take values between the distillable resource and the resource cost of the state. These formulations and results establish a foundation of QRTs applicable in a unified way to physically motivated quantum resources whose analysis can be mathematically intractable.

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Section: Introductionmentioning

confidence: 99%

General Quantum Resource Theories: Distillation, Formation and Consistent Resource Measures

Kuroiwa

Yamasaki

2020

Quantum

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“…In order to describe different quantum phenomena in a unified manner and establish methods that can apply to a broad variety of physical settings, we will employ the formalism of quantum resource theories 21 . The recent years have seen an active development of general resource-theoretic approaches to state manipulation and distillation problems, but the study of quantum channel manipulation in this setting is still in its infancy 3,[22][23][24][25] . In particular, not much is known about constraining one-shot transformations of channels beyond specific settings, and questions such as transformation rates have previously only been addressed under specific assumptions on the structure of the involved resources and protocols.…”

Section: Resultsmentioning

confidence: 99%

“…Our methods allow us to establish two general bounds on the transformation rates. We can use the robustness R O to provide a general bound for the rate of any manipulation protocol, as well as obtain an improved bound for parallel protocols by suitably 'smoothing' the definition of the robustness over channels within a small distance of the original input E 15,24,25,30 .…”

Section: Resultsmentioning

confidence: 99%

Fundamental limitations on distillation of quantum channel resources

Regula

Takagi

2021

Nat Commun

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Quantum channels underlie the dynamics of quantum systems, but in many practical settings it is the channels themselves that require processing. We establish universal limitations on the processing of both quantum states and channels, expressed in the form of no-go theorems and quantitative bounds for the manipulation of general quantum channel resources under the most general transformation protocols. Focusing on the class of distillation tasks — which can be understood either as the purification of noisy channels into unitary ones, or the extraction of state-based resources from channels — we develop fundamental restrictions on the error incurred in such transformations, and comprehensive lower bounds for the overhead of any distillation protocol. In the asymptotic setting, our results yield broadly applicable bounds for rates of distillation. We demonstrate our results through applications to fault-tolerant quantum computation, where we obtain state-of-the-art lower bounds for the overhead cost of magic state distillation, as well as to quantum communication, where we recover a number of strong converse bounds for quantum channel capacity.

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“…where M = A , B is a flag system and {|i } are the local orthogonal basic vectors. In addition, (3) is just the flag additivity which is equivalent to the average monotonicity and the convexity, i.e., the conditions (iii) and (iv) [51]. In this case, any entanglement monotone defined in [30] is an entanglement measure.…”

Section: Bound On Q-concurrencementioning

confidence: 99%

Estimating parameterized entanglement measure

Wei

Luo

Fei

2022

Quantum Inf Process

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The parameterized entanglement monotone, the q-concurrence, is also a reasonable parameterized entanglement measure. By exploring the properties of the q-concurrence with respect to the positive partial transposition and realignment of density matrices, we present tight lower bounds of the q-concurrence for arbitrary q 2. Detailed examples are given to show that the bounds are better than the previous ones.

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Flag additivity in quantum resource theories

Cited by 24 publications

References 37 publications

General Quantum Resource Theories: Distillation, Formation and Consistent Resource Measures

General Quantum Resource Theories: Distillation, Formation and Consistent Resource Measures

Fundamental limitations on distillation of quantum channel resources

Estimating parameterized entanglement measure

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