Generalized monogamy inequality of negativity for multi-qubit systems

Wei Chen, Gang Li, Zhu‐Jun Zheng

Published Aug 23, 2016• 0 citations

Abstract

In this paper, we present some generalized monogamy inequalities based on negativity and convex-roof extended negativity (CREN). The monogamy relations are satisfied by the negativity of $N-$qubit quantum systems $ABC_1\cdots C_{N-2},$ under the partition $AB$ and $C_1C_2\cdots C_{N-2}.$ This result can be generalized to the $N-$qubit pure states under the partition $ABC_1$ and $C_2\cdots C_{N-2}.$ Furthermore, we give some examples to test the generalized monogamy inequalities.

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OpenAlex

Abstract

In this paper, we present some generalized monogamy inequalities based on negativity and convex-roof extended negativity (CREN). The monogamy relations are satisfied by the negativity of

N-

qubit quantum systems

ABC_1\cdots C_{N-2},

under the partition

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In this paper, we present some generalized monogamy inequalities based on negativity and convex-roof extended negativity (CREN). The monogamy relations are satisfied by the negativity of

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ABC_1\cdots C_{N-2},

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C_1C_2\cdots C_{N-2}.

This result can be generalized to the

N-

qubit pure states under the partition

ABC_1

and

C_2\cdots C_{N-2}.

Furthermore, we give some examples to test the generalized monogamy inequalities.

N

-qubit quantum systems $AB{C}_{1}\ensuremath{\cdots}{C}_{N\ensuremath{-}2}$, under the partitions $AB|{C}_{1}\ensuremath{\cdots}{C}_{N\ensuremath{-}2}$ and $AB{C}_{1}|{C}_{2}\ensuremath{\cdots}{C}_{N\ensuremath{-}2}$. Furthermore, the

W

-class states are used to test these generalized monogamy inequalities.

We investigate monogamy relations related to quantum entanglement for

n-

qubit quantum systems. General monogamy inequalities are presented to the

\beta

(\beta\in(0,2))

power of concurrence, negativity and the convex-roof extended negativity, as well as the

\beta

(\beta\in(0,\sqrt{2}))

power of entanglement of formation. These monogamy relations are complementary to the existing ones with different regions of parameter

\beta

. In additions, new monogamy relations are also derived which include the existing ones as special cases.

W

-class state with the vacuum and show that the CREN version of MOE for qudits is satisfied in this case as well. The CREN version of MOE for qudits is thus a strong conjecture with no obvious counterexamples.

ν

-th (

ν\geq2

) power of the concurrence. We show that they are tighter than the existing ones by detailed example. We then establish tighter product-form monogamy inequalities based on the negativity. We show that they are valid even for high dimensional states to which the well-known CKW inequality is violated.