2019
DOI: 10.1103/physrevlett.122.050402
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Quantifying Measurement Incompatibility of Mutually Unbiased Bases

Abstract: Quantum measurements based on mutually unbiased bases are commonly used in quantum information processing, as they are generally viewed as being maximally incompatible and complementary. Here we quantify precisely the degree of incompatibility of mutually unbiased bases (MUB) using the notion of noise robustness. Specifically, for sets of k MUB in dimension d, we provide upper and lower bounds on this quantity. Notably, we get a tight bound in several cases, in particular for complete sets of k = d + 1 MUB (us… Show more

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Cited by 74 publications
(93 citation statements)
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“…This is because joint measurability is intimately linked to this notion [6,7], as the depolarising map in d h can be equivalently applied to the state we wish to steer, due to its self-duality. We refer to [36], appendix F for details on this connection and only mention here that our results show that in a steering scenario with two (respectively three) measurements and an isotropic state of local dimension two, POVMs do not provide any advantage over projective measurements.…”
Section: Qubit Casementioning
confidence: 92%
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“…This is because joint measurability is intimately linked to this notion [6,7], as the depolarising map in d h can be equivalently applied to the state we wish to steer, due to its self-duality. We refer to [36], appendix F for details on this connection and only mention here that our results show that in a steering scenario with two (respectively three) measurements and an isotropic state of local dimension two, POVMs do not provide any advantage over projective measurements.…”
Section: Qubit Casementioning
confidence: 92%
“…The noise set depends on the specific measurements, which makes this measure different than all the other measures considered in this work. It has been investigated in many works [12,28,30,[32][33][34][35][36], often in relation with Einstein-Podolsky-Rosen steering. This specific type of noise has also been considered in scenarios different from incompatibility [37].…”
Section: Incompatibility Depolarising Robustness 311 Definition Anmentioning
confidence: 99%
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