Continuous-variable steering and incompatibility via state-channel duality

Kiukas, Jukka; Budroni, Costantino; Uola, Roope; Pellonpää, Juha-Pekka

doi:10.1103/physreva.96.042331

Cited by 60 publications

(64 citation statements)

References 58 publications

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“…Here we implicitly assume that f g jm ¹ , but one can show that the equality f g jm = holds if and only if all POVM elements of A and B are proportional to , in which case the pair is trivially compatible (see appendix E.3.1). The above feasible point immediately implies that = ( ) the set of all POVM pairs with n A and n B outcomes, respectively, in dimension d. To the best of our knowledge, this measure was first introduced in [21] and studied further in [7,33,40,48]. Recently, it was given an operational meaning through state discrimination tasks [13,49,50].…”

Section: Upper Boundmentioning

confidence: 99%

Incompatibility robustness of quantum measurements: a unified framework

2019

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In quantum mechanics performing a measurement is an invasive process which generally disturbs the system. Due to this phenomenon, there exist incompatible quantum measurements, i.e. measurements that cannot be simultaneously performed on a single copy of the system. It is then natural to ask what the most incompatible quantum measurements are. To answer this question, several measures have been proposed to quantify how incompatible a set of measurements is, however their properties are not well-understood. In this work, we develop a general framework that encompasses all the commonly used measures of incompatibility based on robustness to noise. Moreover, we propose several conditions that a measure of incompatibility should satisfy, and investigate whether the existing measures comply with them. We find that some of the widely used measures do not fulfil these basic requirements. We also show that when looking for the most incompatible pairs of measurements, we obtain different answers depending on the exact measure. For one of the measures, we analytically prove that projective measurements onto two mutually unbiased bases are among the most incompatible pairs in every dimension. However, for some of the remaining measures we find that some peculiar measurements turn out to be even more incompatible.performed simultaneously by performing the parent measurement. If such a parent measurement does not exist, we say that the measurements are incompatible (or not jointly measurable). We remark here that other notions of compatibility, such as commutativity, non-disturbance and coexistence, are also used in the literature [1,3]; let us for completeness briefly explain how they are related. Commutativity of a measurement pair implies nondisturbance, which in turn implies joint measurability, which then implies coexistence. Moreover, it is known that none of the converse implications hold in general, therefore these notions are strictly distinct [4]. In this work we focus solely on the notion of joint measurability, because the existence (or not) of a parent measurement has a clear operational meaning. Therefore, throughout the present paper we use the terms '(in) compatibility' and '(non-)joint measurability' interchangeably. It is important to notice that whenever two measurements are compatible, they cannot be used to produce quantum advantage in tasks like Bell nonlocality [5] or Einstein-Podolsky-Rosen steering [6,7]. Moreover, it was recently shown that joint measurability is equivalent to a specific notion of classicality, namely, preparation non-contextuality [8,9]. Hence, one may think of compatible measurements as 'classical' , and incompatible measurements as a resource for the above tasks. Therefore, it is of fundamental importance to characterise and understand the structure of incompatible measurements.What is particularly important is to go beyond the dichotomy of compatible and incompatible measurements, and quantify to what extent a pair of measurements is incompatible. A natural framework for this qua...

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Section: Upper Boundmentioning

confidence: 99%

Incompatibility robustness of quantum measurements: a unified framework

2019

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“…Our strategy might also be used to study the quantification of steerability for multi-setting scenarios, in particular, for three-setting scenarios for which the joint measurability problem of three qubit observables has already been investigated 42,43 . Our method might also be used in continuous variable steering, temporal and channel steering, for which the steerability of the state assemblages or the instrument assemblages can be connected to the incompatibility problems of the quantum measurement assemblages 44,45 . Hence, the steerability of the quantum states or the quantum channels might also be studied based on the corresponding measurement incompatibility problems.…”

Section: Discussionmentioning

confidence: 99%

Quantum steerability based on joint measurability

Chen

Fei

2017

Sci Rep

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Occupying a position between entanglement and Bell nonlocality, Einstein-Podolsky-Rosen (EPR) steering has attracted increasing attention in recent years. Many criteria have been proposed and experimentally implemented to characterize EPR-steering. Nevertheless, only a few results are available to quantify steerability using analytical results. In this work, we propose a method for quantifying the steerability in two-qubit quantum states in the two-setting EPR-steering scenario, using the connection between joint measurability and steerability. We derive an analytical formula for the steerability of a class of X-states. The sufficient and necessary conditions for two-setting EPR-steering are presented. Based on these results, a class of asymmetric states, namely, one-way steerable states, are obtained.

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“…This property is at the basis of many quantum phenomena such as uncertainty relations [34], quantum contextuality [35][36][37], Bell nonlocality [38,39] and steering [40,41]. In particular, it has been shown that a state assemblage is unsteerable if and only if a collection of measurements, called steering equivalent observables measurement assemblage (SEO) is jointly measurable [42,43]. In this work, we provide an even stronger quantitative connection: (1) the SEO defines the equivalence classes of state assemblages and their transformations via local filtering, and (2) its incompatibility is the maximal steerability over a class.…”

Section: Introductionmentioning

confidence: 99%

Complete classification of steerability under local filters and its relation with measurement incompatibility

Ku,

Hsieh,

Chen

et al. 2022

Preprint

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Quantum steering is the central resource for one-sided device-independent quantum information. It is manipulated via one-way local operations and classical communication, such as local filtering on the trusted party.Here, we provide a necessary and sufficient condition for a steering assemblage to be transformable into another one via local filtering. We characterize the equivalence classes with respect to filters in terms of the steering equivalent observables measurement assemblage (SEO), first proposed to connect the problem of steerability with measurement incompatibility. We provide an efficient method to compute the maximal extractable steerability via local filters and show that it coincides with the incompatibility of the SEO. Moreover, we show that there always exists a bipartite state that provides an assemblage with steerability equal to the incompatibility of the measurements on the untrusted party. Finally, we investigate the optimal success probability and rates for transformation protocols (distillation and dilution) in the single-shot scenario together with examples.

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Continuous-variable steering and incompatibility via state-channel duality

Cited by 60 publications

References 58 publications

Incompatibility robustness of quantum measurements: a unified framework

Incompatibility robustness of quantum measurements: a unified framework

Quantum steerability based on joint measurability

Complete classification of steerability under local filters and its relation with measurement incompatibility

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