scholarly journals On the partially symmetric rank of tensor products of $W$-states and other symmetric tensors

2019 ◽  
Vol 30 (1) ◽  
pp. 93-124 ◽  
Author(s):  
Edoardo Ballico ◽  
Alessandra Bernardi ◽  
Matthias Christandl ◽  
Fulvio Gesmundo
Keyword(s):  
Tensor Products ◽  
Symmetric Tensors ◽  
W States ◽  
Partially Symmetric

Entanglement criteria for the three-qubit states

2017 ◽  
Vol 15 (07) ◽  
pp. 1750049 ◽  
Author(s):  
Y. Akbari-Kourbolagh
Keyword(s):  
White Noise ◽  
Tensor Products ◽  
W State ◽  
Entangled States ◽  
Mean Values ◽  
W States ◽  
Pauli Matrices ◽  
The Mean ◽  
Simple Sets ◽  
Qubit States

We present sufficient criteria for the entanglement of three-qubit states. For some special families of states, the criteria are also necessary for the entanglement. They are formulated as simple sets of inequalities for the mean values of certain observables defined as tensor products of Pauli matrices. The criteria are good indicators of the entanglement in the vicinity of three-qubit GHZ and W states and enjoy the capability of detecting the entangled states with positive partial transpositions. Furthermore, they improve the best known result for the case of W state mixed with the white noise. The efficiency of the criteria is illustrated through several examples.

scholarly journals M-Eigenvalues-Based Sufficient Conditions for the Positive Definiteness of Fourth-Order Partially Symmetric Tensors

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8 ◽  
Author(s):  
Gang Wang ◽  
Linxuan Sun ◽  
Lixia Liu
Keyword(s):  
Spectral Radius ◽  
Fourth Order ◽  
Quantum Physics ◽  
Sufficient Conditions ◽  
Positive Definiteness ◽  
Symmetric Tensors ◽  
Nonlinear Elastic Material ◽  
Numerical Examples ◽  
Nonlinear Elastic ◽  
Partially Symmetric

M-eigenvalues of fourth-order partially symmetric tensors play important roles in the nonlinear elastic material analysis and the entanglement problem of quantum physics. In this paper, we introduce M-identity tensor and establish two M-eigenvalue inclusion intervals with n parameters for fourth-order partially symmetric tensors, which are sharper than some existing results. Numerical examples are proposed to verify the efficiency of the obtained results. As applications, we provide some checkable sufficient conditions for the positive definiteness and establish bound estimations for the M-spectral radius of fourth-order partially symmetric nonnegative tensors.

scholarly journals On the M-eigenvalue estimation of fourth-order partially symmetric tensors

2020 ◽  
Vol 16 (1) ◽  
pp. 309-324 ◽  
Author(s):  
Haitao Che ◽  
◽  
Haibin Chen ◽  
Yiju Wang ◽  
Keyword(s):  
Fourth Order ◽  
Symmetric Tensors ◽  
Eigenvalue Estimation ◽  
Partially Symmetric

scholarly journals An SDP Method for Copositivity of Partially Symmetric Tensors

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Chunyan Wang ◽  
Haibin Chen ◽  
Haitao Che
Keyword(s):  
Numerical Results ◽  
Semidefinite Relaxation ◽  
Symmetric Tensors ◽  
Relaxation Algorithm ◽  
Rectangular Tensors ◽  
Partially Symmetric

In this paper, we consider the problem of detecting the copositivity of partially symmetric rectangular tensors. We first propose a semidefinite relaxation algorithm for detecting the copositivity of partially symmetric rectangular tensors. Then, the convergence of the proposed algorithm is given, and it shows that we can always catch the copositivity of given partially symmetric tensors. Several preliminary numerical results confirm our theoretical findings.

Sign in / Sign up

Export Citation Format

Share Document