Rényi formulation of uncertainty relations for POVMs assigned to a quantum design

Rastegin, Alexey E.

doi:10.1088/1751-8121/aba8d0

Cited by 16 publications

(16 citation statements)

References 81 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Uncertainty relations in terms of Rényi entropies also produce steering criteria as explained in [38]. The papers [44,45] presented Rényi-entropy uncertainty relations and respective steering inequalities for POVMs assigned to quantum designs. A similar treatment can be developed on the base of (42).…”

Section: Some Applicationsmentioning

confidence: 99%

Entropic uncertainty relations from equiangular tight frames and their applications

Rastegin¹

2021

Preprint

View full text Add to dashboard Cite

Finite tight frames are interesting in various respects, including potential applications in quantum information science. Indeed, each complex tight frame leads to a non-orthogonal resolution of the identity in the Hilbert space. In a certain sense, equiangular tight frames are very similar to the maximal sets that provide symmetric informationally complete measurements. Hence, applications of equiangular tight frames in quantum physics deserve more attention than they have obtained. We derive entropic uncertainty relations for a quantum measurement built of the states of an equiangular tight frame. First, the corresponding index of coincidence is estimated from above, whence desired results follow. State-dependent and state-independent formulations are both presented. We also discuss applications of the corresponding measurements to detect entanglement and steerability.

show abstract

Section: Some Applicationsmentioning

confidence: 99%

Entropic uncertainty relations from equiangular tight frames and their applications

Rastegin¹

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…When α > 2, Eq. ( 20) is improved than Rastegin's lower bounds L Ras1 [20] and L Ras2 [24], and when α = 2 they are all equivalent to H 2 (P x [c]).…”

Section: B Rényi Entropy With α ≥mentioning

confidence: 99%

“…Since then entropic uncertainty relations (EURs) for multiple mutually unbiased bases have been largely investigated [11][12][13][14][15][16], and generalizations to mutually unbiased measurements (MUM) [17] as well as symmetric informationally complete positive operator-valued measures (SIC-POVM) [18] in terms of Rényi entropy [19] are also explored [20][21][22]. In two recent works entropic uncertainty relations are constructed from quantum designs for the first time [23,24].…”

Section: Introductionmentioning

confidence: 99%

Entropic uncertainty relations for SIC-POVMs and MUMs

Huang,

Chen,

2020

Preprint

View full text Add to dashboard Cite

We construct inequalities between Rényi-α entropy and the indexes of coincidence of probability distributions, based on which we obtain improved state-dependent entropic uncertainty relations for general symmetric informationally complete positive operator-valued measures (SIC-POVM) and mutually unbiased measurements (MUM) on finite dimensional systems. We show that our uncertainty relations for general SIC-POVMs and MUMs can be tight for sufficiently mixed states, moreover, comparisons to the numerically optimal results are made via information diagrams.

show abstract

“…In fact, the EUR can be further improved with the assistance of a quantum memory, so that the outcomes of two incompatible measurements can be predicted precisely by an observer with access to the quantum memory if the initial states are maximally entangled [5,6]. At present, the EUR has received a great deal of attention [7][8][9][10][11][12][13][14][15][16][17][18] due to potential applications in quantum information processing tasks such as quantum entanglement witnessing [19][20][21][22], and quantum key distribution [23,24].…”

Section: Introductionmentioning

confidence: 99%

Witnessing criticality in non-Hermitian systems via entropic uncertainty relation

Guo¹,

Wang²

2021

Preprint

View full text Add to dashboard Cite

Non-Hermitian systems with exceptional points lead to many intriguing phenomena due to the coalescence of both eigenvalues and corresponding eigenvectors, in comparison to Hermitian systems where only eigenvalues degenerate. In this paper, we have investigated entropic uncertainty relation (EUR) in a non-Hermitian system and revealed a general connection between the EUR and the exceptional points of non-Hermitian system. Compared to the unitary dynamics determined by a Hermitian Hamiltonian, the behaviors of EUR can be well defined in two different ways depending on whether the system is located in unbroken or broken phase regimes. In unbroken phase regime, EUR undergoes an oscillatory behavior while in broken phase regime where the oscillation of EUR breaks down. The exceptional points mark the oscillatory and non-oscillatory behaviors of the EUR. In the dynamical limit, we have identified the witness of critical behavior of non-Hermitian systems in terms of the EUR. Our results reveal that the EUR witness can exactly detect the critical points of non-Hermitian systems beyond (anti-) PT-symmetric systems. Our results may have potential applications to witness and detect phase transition in non-Hermitian systems.

show abstract

Rényi formulation of uncertainty relations for POVMs assigned to a quantum design

Cited by 16 publications

References 81 publications

Entropic uncertainty relations from equiangular tight frames and their applications

Entropic uncertainty relations from equiangular tight frames and their applications

Entropic uncertainty relations for SIC-POVMs and MUMs

Witnessing criticality in non-Hermitian systems via entropic uncertainty relation

Contact Info

Product

Resources

About