Complete Resource Theory of Quantum Incompatibility as Quantum Programmability

Buscemi, Francesco; Chitambar, Eric; Zhou, Wenbin

doi:10.1103/physrevlett.124.120401

Cited by 59 publications

(44 citation statements)

References 31 publications

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“…Although being an abstract concept on the mathematical level, measurement incompatibility is important also from an experimental perspective. It gives rise to the non-classical behaviour in various quantum protocols such as quantum steering [2-5], contextuality [6,7], tests of macroreal-ism [8,9], quantum communication [10][11][12][13][14][15][16][17][18], and non-locality [19,20]. Crucially, any set of incompatible measurements results in genuinely quantum behavior given that one possesses a properly chosen catalyst state.…”

Section: Introductionmentioning

confidence: 99%

Quantum marginal problem and incompatibility

Haapasalo

Kraft

Miklin

et al. 2021

Quantum

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One of the basic distinctions between classical and quantum mechanics is the existence of fundamentally incompatible quantities. Such quantities are present on all levels of quantum objects: states, measurements, quantum channels, and even higher order dynamics. In this manuscript, we show that two seemingly different aspects of quantum incompatibility: the quantum marginal problem of states and the incompatibility on the level of quantum channels are in many-to-one correspondence. Importantly, as incompatibility of measurements is a special case of the latter, it also forms an instance of the quantum marginal problem. The generality of the connection is harnessed by solving the marginal problem for Gaussian and Bell diagonal states, as well as for pure states under depolarizing noise. Furthermore, we derive entropic criteria for channel compatibility, and develop a converging hierarchy of semi-definite programs for quantifying the strength of quantum memories.

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Section: Introductionmentioning

confidence: 99%

Quantum marginal problem and incompatibility

Haapasalo

Kraft

Miklin

et al. 2021

Quantum

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“…More broadly, the study of incompatibility as a resource for quantum information protocols has been a very active area of research in recent years [14,49,50]. Investigating the role that realizability of particular joint measurability structures can play in quantum information could lead to insights on previously under-appreciated aspects of incompatibility as well as their relevance for the foundations and applications of quantum theory.…”

Section: Discussion and Outlookmentioning

confidence: 99%

Joint measurability structures realizable with qubit measurements: Incompatibility via marginal surgery

Nikola

Kunjwal

2020

Phys. Rev. Research

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Measurements in quantum theory exhibit incompatibility, i.e., they can fail to be jointly measurable. An intuitive way to represent the (in)compatibility relations among a set of measurements is via a hypergraph representing their joint measurability structure: its vertices represent measurements and its hyperedges represent (all and only) subsets of compatible measurements. Projective measurements in quantum theory realize (all and only) joint measurability structures that are graphs. On the other hand, general measurements represented by positive operator-valued measures (POVMs) can realize arbitrary joint measurability structures. Here we explore the scope of joint measurability structures realizable with qubit POVMs. We develop a technique that we term marginal surgery to obtain nontrivial joint measurability structures starting from a set of compatible measurements. We show explicit examples of marginal surgery on a special set of qubit POVMs to construct joint measurability structures such as N-cycle and N-Specker scenarios for any integer N 3. We also show the realizability of various joint measurability structures with N ∈ {4, 5, 6} vertices. In particular, we show that all possible joint measurability structures with N = 4 vertices are realizable. We conjecture that all joint measurability structures are realizable with qubit POVMs. This contrasts with the unbounded dimension required in R. Kunjwal et al. [Phys. Rev. A 89, 052126 (2014)]. Our results also render this previous construction maximally efficient in terms of the required Hilbert space dimension. We also obtain a sufficient condition for the joint measurability of any set of binary qubit POVMs which powers many of our results and should be of independent interest.

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“…A variety of other QRTs have been studied in the past few years that characterize a wide range of quantum phenomena [6][7][8][9][10][11][12][13][14][15][16][17][18]. Despite their physical differences, these phenomena have a remarkably similar structure when viewed through the lens of a resource theory.…”

Section: Introductionmentioning

confidence: 99%

“…Unfortunately, in almost all physically-motivated QRTs, the natural choice for free operations does not coincide with the maximal set. In this case, conditions for free convertibility become more complicated, generally consisting of an infinitude of monotonicity conditions [12,14,20,26,32,[43][44][45][46][47][48][49][50]. All of these complete convertibility results depend, in way or the other, on the Hyperplane Separation Theorem for convex sets.…”

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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Complete Resource Theory of Quantum Incompatibility as Quantum Programmability

Cited by 59 publications

References 31 publications

Quantum marginal problem and incompatibility

Quantum marginal problem and incompatibility

Joint measurability structures realizable with qubit measurements: Incompatibility via marginal surgery

Convertibility and Guessing Games in Dynamic Resource Theories

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