Multiple Entropy Measures for Multi-particle Pure Quantum State

Liu, Dan; Zhao, Xiaoxue; Long, Gui Lu

doi:10.1088/0253-6102/54/5/09

Cited by 23 publications

(12 citation statements)

References 53 publications

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“…Note that the difference for the distributions of coherence between N ‐qubit GHz and N ‐qubit W states is closely related to their behaviors of entanglement. [ 68 ] In the N ‐qubit GHz state, any L ‐partite (

1 \leq L \leq N - 1

) subsystem as a whole can be regarded as a qubit, which is maximally entangled with the rest of the system, leading to the vanishing of coherence for the corresponding subsystem. In the N ‐qubit W state, however, similar entanglement is not maximal, so that every orders of subsystems may have coherence.…”

Section: Discussionmentioning

confidence: 99%

Distribution and Evolution of Quantum Coherence for Open Multi‐Qubit Systems in Non‐Inertial Frames

Zeng

Cao

2021

Annalen der Physik

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The distribution and evolution of quantum coherence for multi‐qubit W and GHz states of Dirac fields in the non‐inertial frames and under the action of local environments is studied. It is found that the N‐qubit W state has all orders of coherence (from bipartite to N‐partite subsystems), and the coherence of the whole system is equal to the sum of all the bipartite coherences in the whole time evolution. However, the evolved N‐qubit GHz state has its coherence belonged only to the whole system and no coherence resides in any subsystems. Further, it is found that the expressions of coherence for both W and GHz states are covariant with respect to the transformation of decaying rates.

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1 \leq L \leq N - 1

Section: Discussionmentioning

confidence: 99%

Distribution and Evolution of Quantum Coherence for Open Multi‐Qubit Systems in Non‐Inertial Frames

Zeng

Cao

2021

Annalen der Physik

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“…The complete entanglement measure in terms of the APE was pointed out in Ref. [36], where they named the entanglement measure multiple entropy measures (MEMS). Suppose {q 1 , q 2 , • • • , q n } is a permutation of {1, 2, • • • , n}; the MEMS for multipartite pure quantum states is defined as a vector,…”

Section: The Mape and Coefficient Matricesmentioning

confidence: 99%

Quantifying entanglement of arbitrary-dimensional multipartite pure states in terms of the singular values of coefficient matrices

Li¹,

Wang²,

Cui³

et al. 2013

Phys. Rev. A

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The entanglement quantification and classification of multipartite quantum states are two important research fields in quantum information. In this work, we study the entanglement of arbitrary-dimensional multipartite pure states by looking at the averaged partial entropies of various bipartite partitions of the system, namely, the so-called Manhattan distance (l 1 norm) of averaged partial entropies (MAPE), and it is proved to be an entanglement measure for pure states. We connected the MAPE with the coefficient matrices, which are important tools in entanglement classification and reexpressed the MAPE for arbitrary-dimensional multipartite pure states by the nonzero singular values of the coefficient matrices. The entanglement properties of the n-qubit Dicke states, arbitrary-dimensional Greenberger-Horne-Zeilinger states, and D n 3 states are investigated in terms of the MAPE, and the relation between the rank of the coefficient matrix and the degree of entanglement is demonstrated for symmetric states by two examples.

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“…The de¯nition of the multiple concurrence is given according to a newly proposed entanglement measurement named Multiple Entropy Measures (MEMS). 15,16 In MEMS, one uses the geometric average of entropies of reduced density matrix to measure the entanglement of multi-partite states.…”

Section: A New Entanglement Measure -Geometric Average Of Bipartite Cmentioning

confidence: 99%

Multiple Concurrence of Multi-Partite Quantum System

Zhao

et al. 2010

Int. J. Quantum Inform.

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We propose a new way of description of the global entanglement property of a multi-partite pure state quantum system. Based on the idea of bipartite concurrence, by dividing the multi-partite quantum system into two subsystems, a combination of all the bipartite concurrences of a multipartite quantum system is used to describe the entanglement property of the multi-partite system. We derive the analytical results for GHZ-state, W-state with arbitrary number of qubits, and cluster state with the number of particles no greater than 6.

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Multiple Entropy Measures for Multi-particle Pure Quantum State

Cited by 23 publications

References 53 publications

Distribution and Evolution of Quantum Coherence for Open Multi‐Qubit Systems in Non‐Inertial Frames

Distribution and Evolution of Quantum Coherence for Open Multi‐Qubit Systems in Non‐Inertial Frames

Quantifying entanglement of arbitrary-dimensional multipartite pure states in terms of the singular values of coefficient matrices

Multiple Concurrence of Multi-Partite Quantum System

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