Commutative POVMs and Fuzzy Observables

Ali, S. Twareque; Carmeli, Claudio; Heinosaari, Teiko; Toigo, Alessandro

doi:10.1007/s10701-009-9292-y

Cited by 62 publications

(55 citation statements)

References 22 publications

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“…The dimension of the space is d, D(a|x, λ) are deterministic post-processings [21],G λ = (1 + t)G λ and G λ is a joint POVM of O a|x a,x . As strong duality holds [20], the solutions of the primal and dual problems coincide.…”

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confidence: 99%

Quantifying Quantum Resources with Conic Programming

et al. 2019

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Resource theories can be used to formalize the quantification and manipulation of resources in quantum information processing such as entanglement, asymmetry and coherence of quantum states, and incompatibility of quantum measurements. Given a certain state or measurement, one can ask whether there is a task in which it performs better than any resourceless state or measurement. Using conic programming, we prove that any general robustness measure (with respect to a convex set of free states or measurements) can be seen as a quantifier of such outperformance in some discrimination task. We apply the technique to various examples, e.g. joint measurability, POVMs simulable by projective measurements, and state assemblages preparable with a given Schmidt number.arXiv:1812.09216v2 [quant-ph]

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confidence: 99%

Quantifying Quantum Resources with Conic Programming

et al. 2019

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“…A heuristic approach to the problem of state discrimination with post-measurement information relies on (13) and goes as follows. We form a noisy version N of each optimal measurement N related to E , and we add enough noise to make the measurements N 1 , .…”

Section: B Incompatible Measurementsmentioning

confidence: 99%

“…From this point of view, the approximative cloning strategy is just a particular instance of the noisy joint measurement strategy described in Sec. III B; the lower bound (20) then follows just by inserting (21) into the right hand side of (13). The bound (20) is useful as it is universal, in the sense that it does not depend on any details of the optimal measurements N 1 , .…”

Section: Approximate Cloning Strategymentioning

confidence: 99%

State discrimination with postmeasurement information and incompatibility of quantum measurements

2018

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We discuss the following variant of the standard minimum error state discrimination problem: Alice picks the state she sends to Bob among one of several disjoint state ensembles, and she communicates him the chosen ensemble only at a later time. Two different scenarios then arise: either Bob is allowed to arrange his measurement set-up after Alice has announced him the chosen ensemble, or he is forced to perform the measurement before of Alice's announcement. In the latter case, he can only post-process his measurement outcome when Alice's extra information becomes available. We compare the optimal guessing probabilities in the two scenarios, and we prove that they are the same if and only if there exist compatible optimal measurements for all of Alice's state ensembles. When this is the case, post-processing any of the corresponding joint measurements is Bob's optimal strategy in the post-measurement information scenario. Furthermore, we establish a connection between discrimination with post-measurement information and the standard state discrimination. By means of this connection and exploiting the presence of symmetries, we are able to compute the various guessing probabilities in many concrete examples. arXiv:1804.09693v1 [quant-ph]

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“…with λ G(λ) = 1 1 and where D λ (x|k) are positive constants with x D λ (x|k) = 1 [18]. In practice, this means that the probabilities of the results E k (x) can be determined by measuring the G(λ) and classically postprocessing the data.…”

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Joint Measurability of Generalized Measurements Implies Classicality

2014

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The fact that not all measurements can be carried out simultaneously is a peculiar feature of quantum mechanics and responsible for many key phenomena in the theory, such as complementarity or uncertainty relations. For the special case of projective measurements quantum behavior can be characterized by the commutator but for generalized measurements it is not easy to decide whether two measurements can still be understood in classical terms or whether they show already quantum features. We prove that generalized measurements which do not fulfill the notion of joint measurability are nonclassical, as they can be used for the task of quantum steering. This shows that the notion of joint measurability is, among several definitions, the proper one to characterize quantum behavior. Moreover, the equivalence allows to derive novel steering inequalities from known results on joint measurability and new criteria for joint measurability from known results on the steerability of states.

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Commutative POVMs and Fuzzy Observables

Cited by 62 publications

References 22 publications

Quantifying Quantum Resources with Conic Programming

Quantifying Quantum Resources with Conic Programming

State discrimination with postmeasurement information and incompatibility of quantum measurements

Joint Measurability of Generalized Measurements Implies Classicality

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