A family of separability criteria and lower bounds of concurrence

Shi, Xian; Yashuai, Sun,

doi:10.1007/s11128-023-03875-9

Cited by 6 publications

(3 citation statements)

References 32 publications

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“…In 2022, Yan et al proposed several entanglement detection criteria using quantum designs [16]. Recently, we proposed a family of separability criteria and presented lower bounds of concurrence and the convex-roof extended negativity for arbitrary dimensional systems [17].…”

Section: Introductionmentioning

confidence: 99%

The entanglement criteria based on equiangular tight frames

Shi

2024

J. Phys. A: Math. Theor.

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Finite tight frames play an important role in miscellaneous areas, including quantum information theory. Here we apply a class of tight frames, equiangular tight frames, to address the problem of detecting the entanglement of bipartite states. Here we derive some entanglement criteria based on positive operator-valued measurements built from equiangular tight frames. We also present a class of entanglement witnesses based on the equiangular tight frames. At last, we generalize the entanglement criterion for bipartite systems to multipartite systems.

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Section: Introductionmentioning

confidence: 99%

The entanglement criteria based on equiangular tight frames

Shi

2024

J. Phys. A: Math. Theor.

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“…Since the start of quantum information theory, a lot of effort has been devoted to the problems of distinguishing whether a state is separable or entangled [6][7][8][9][10][11][12][13][14][15][16]. A commonly used method to certify the entanglement of a state is to build an effective entanglement witness.…”

Section: Introductionmentioning

confidence: 99%

Families of Schmidt-number witnesses for high dimensional quantum states

Shi

2024

Commun. Theor. Phys.

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Higher dimensional entangled states demonstrate significant advantages in quantum information processing tasks. The Schmidt number is a quantity of the entanglement dimension of a bipartite state. Here we build families of k-positive maps from the symmetric information complete positive operator-valued measurements and mutually unbiased bases, and we also present the Schmidt number witnesses, correspondingly. At last, based on the witnesses obtained from mutually unbiased bases, we show the distance between a bipartite state and the set of states with a Schmidt number less than k.

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“…[17][18][19] Hence, many analytical tools, simulation techniques and several other methods for calculating and quantifying quantum correlations have been investigated to explore the separability of bipartite quantum systems. [20,21] Importantly, recent works shed light on studying quantum correlations for qubit-qutrit and qutritqutrit states, [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] which creates a fascinating future in quantum technologies. [39] Due to the possibility of maximum control of the associated Hilbert space, hybrid qubit-qudit systems have become increasingly important in the field of quantum information.…”

Section: Introductionmentioning

confidence: 99%

Witnessing Quantum Correlations in a Hybrid Qubit‐Qutrit System Under Intrinsic Decoherence

Benabdallah

Anouz

Rahman

et al. 2023

Fortschritte der Physik

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Studying qubit‐qutrit systems is crucial to harnessing their quantum advantages, especially in quantum secure technologies. In this regard, the present work consists of considering a qubit‐qutrit system under intrinsic decoherence. For this hybrid‐spin system, the relationship between negativity, local quantum uncertainty, and local quantum Fisher information is discussed. The results show that it is possible to generate and preserve the maximally correlated states by tuning the system parameters to certain fixed values. It is also demonstrated the occurrence of the sudden death/birth phenomenon by examining the behavior of quantum correlation functions.

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A family of separability criteria and lower bounds of concurrence

Cited by 6 publications

References 32 publications

The entanglement criteria based on equiangular tight frames

The entanglement criteria based on equiangular tight frames

Families of Schmidt-number witnesses for high dimensional quantum states

Witnessing Quantum Correlations in a Hybrid Qubit‐Qutrit System Under Intrinsic Decoherence

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