Non-Markovian quantum dynamics from symmetric measurements

Siudzińska, Katarzyna

doi:10.1103/physreva.110.012440

Cited by 3 publications

(1 citation statement)

References 57 publications

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“…for κ + ⩾ κ − > 0 and the flip operator [18]. Examples include general SIC POVMs, mutually unbiased measurements [47], (N, M)-POVMs [48,49], and a class of generalized symmetric measurements [27]. We show that some of the generalized equiangular measurements are conical two-designs, as well.…”

Section: Conical Designsmentioning

confidence: 96%

Informationally overcomplete measurements from generalized equiangular tight frames

Siudzińska

2024

J. Phys. A: Math. Theor.

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Informationally overcomplete measurements find important applications in quantum tomography and quantum state estimation. The most popular are maximal sets of mutually unbiased bases, for which trace relations between measurement operators are well known. In this paper, we introduce a more general class of informationally overcomplete POVMs that are generated by equiangular tight frames of arbitrary rank. This class provides a generalization of equiangular measurements to non-projective POVMs, which include rescaled mutually unbiased measurements and bases. We provide a method of their construction, analyze their symmetry properties, and provide examples for highly symmetric cases. In particular, we find a wide class of generalized equiangular measurements that are conical 2-designs, which allows us to derive the index of coincidence. Our results show benefits of considering a single informationally overcomplete measurement over informationally complete collections of POVMs.

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Section: Conical Designsmentioning

confidence: 96%

Informationally overcomplete measurements from generalized equiangular tight frames

Siudzińska

2024

J. Phys. A: Math. Theor.

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Decomposable dynamics on matrix algebras

Siudzińska,

Szczygielski

2025

Physics Letters A

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How much symmetry do symmetric measurements need for efficient operational applications?

Siudzińska

2024

J. Phys. A: Math. Theor.

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We introduce a generalization of symmetric measurements to collections of unequinumerous positive, operator-valued measures (POVMs). This provides a uniform description of objects that are more general than symmetric, informationally complete POVMs and mutually unbiased bases, but at the same time less destructive and more noise tolerant. For informationally complete sets, we propose construction methods from orthonormal Hermitian operator bases. The correspondence between operator bases and measurements can be as high as one-to-four, with a one-to-one correspondence following only under additional assumptions. Importantly, it turns out that some of the symmetry properties, lost in the process of generalization, can be recovered without fixing the same number of elements for all POVMs. In particular, for a wide class of unequinumerous symmetric measurements that are conical 2-designs, we derive the index of coincidence, entropic uncertainty relations, and separability criteria for bipartite quantum states.

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Non-Markovian quantum dynamics from symmetric measurements

Cited by 3 publications

References 57 publications

Informationally overcomplete measurements from generalized equiangular tight frames

Informationally overcomplete measurements from generalized equiangular tight frames

Decomposable dynamics on matrix algebras

How much symmetry do symmetric measurements need for efficient operational applications?

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