Operational link between mutually unbiased bases and symmetric informationally complete positive operator-valued measures

Beneduci, Roberto; Bullock, Tom; Busch, Paul; Carmeli, Claudio; Heinosaari, Teiko; Toigo, Alessandro

doi:10.1103/physreva.88.032312

Cited by 21 publications

(16 citation statements)

References 19 publications

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“…(This terminology originates from the fact that if the observables are sharp, then the respective orthonormal bases are mutually unbiased. In the previously written form the definition makes sense also for unsharp observables [29].) The condition of mutual unbiasedness is invariant under a global unitary transformation, hence it is enough to fix the basis x = (1, 0, 0), y = (0, 1, 0), z = (0, 0, 1) in R 3 and choose two of these unit vectors.…”

Section: Mutually Unbiased Qubit Observablesmentioning

confidence: 99%

Testing incompatibility of quantum devices with few states

2021

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When observations must come from incompatible devices and cannot be produced by compatible devices? This question motivates two integer valued quantifications of incompatibility, called incompatibility dimension and compatibility dimension. The first one quantifies how many states are minimally needed to detect incompatibility if the test states are chosen carefully, whereas the second one quantifies how many states one may have to use if they are randomly chosen. With concrete examples we show that these quantities have unexpected behaviour with respect to noise.

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Section: Mutually Unbiased Qubit Observablesmentioning

confidence: 99%

Testing incompatibility of quantum devices with few states

2021

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“…Thus, the former is a relationship between two different measurements, whereas the latter is a relationship within a single measurement. Since MUBs and SICs are both conceptually natural, elegant, and (as it turns out) practically important classes of measurements, they are often studied in the same context (9)(10)(11)(12)(13)(14). Let us briefly review their importance to foundational and applied aspects of quantum theory.…”

Section: Introductionmentioning

confidence: 99%

Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments

et al. 2021

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Mutually unbiased bases (MUBs) and symmetric informationally complete projectors (SICs) are crucial to many conceptual and practical aspects of quantum theory. Here, we develop their role in quantum nonlocality by (i) introducing families of Bell inequalities that are maximally violated by d-dimensional MUBs and SICs, respectively, (ii) proving device-independent certification of natural operational notions of MUBs and SICs, and (iii) using MUBs and SICs to develop optimal-rate and nearly optimal-rate protocols for device-independent quantum key distribution and device-independent quantum random number generation, respectively. Moreover, we also present the first example of an extremal point of the quantum set of correlations that admits physically inequivalent quantum realizations. Our results elaborately demonstrate the foundational and practical relevance of the two most important discrete Hilbert space structures to the field of quantum nonlocality.

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“…Interestingly, SIC POVMs and MUBs have many common applications, including quantum state tomography [5,6], quantum key distribution [7,8], and quantum entanglement detection [9,10]. They are also often analyzed in the same context [11][12][13][14]. This indicates that the two objects are closely related.…”

Section: Introductionmentioning

confidence: 99%

All classes of informationally complete symmetric measurements in finite dimensions

Siudzińska

2021

Preprint

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A broad class of informationally complete symmetric measurements is introduced. It can be understood as a common generalization of symmetric, informationally complete POVMs and mutually unbiased bases. Additionally, it provides a natural way to define two new families of mutually unbiased symmetric measurement operators in any finite dimension. We show a general method of their construction, together with an example of an optimal measurement. Finally, we analyze the properties of symmetric measurements and provide applications in entropic relations and entanglement detection.

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Operational link between mutually unbiased bases and symmetric informationally complete positive operator-valued measures

Cited by 21 publications

References 19 publications

Testing incompatibility of quantum devices with few states

Testing incompatibility of quantum devices with few states

Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments

All classes of informationally complete symmetric measurements in finite dimensions

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