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Register a new userImproved separability criteria via some classes of measurements
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The entanglement detection via local measurements can be experimentally implemented. Based on mutually unbiased measurements and general symmetric informationally complete positive-operator-valued measures, we present separability criteria for bipartite quantum states, which, by theoretical analysis, are stronger than the related existing criteria via these measurements. Two detailed examples are supplemented to show the efficiency of the presented separability criteria.
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Based on the mutually unbiased bases, the mutually unbiased measurements and the general symmetric informationally complete positive-operator-valued measures, we propose three separability criteria for $d$-dimensional bipartite quantum systems, which are more powerful than the corresponding ones introduced in [C. Spengler, M. Huber, S. Brierley, T. Adaktylos, and B.C. Hiesmayr, Phys. Rev. A textbf{86}, 022311 (2012); B. Chen, T. Ma, and S.M. Fei, Phys. Rev. A textbf{89}, 064302 (2014); B. Chen, T. Li, and S.M. Fei, arXiv:1406.7820v1 [quant-ph] (2014)]. Some states such as Werner states and Bell-diagonal states are used to further illustrate the efficiency of the presented criteria.
The correlation matrices or tensors in the Bloch representation of density matrices are encoded with entanglement properties. In this paper, based on the Bloch representation of density matrices, we give some new separability criteria for bipartite and multipartite quantum states. Theoretical analysis and some examples show that the proposed criteria can be more efficient than the previous related criteria.
The practically useful criteria of separable states $rho=sum_{k}w_{k}rho_{k}$ in $d=2times2$ are discussed. The equality $G({bf a},{bf b})= 4[langle psi|P({bf a})otimes P({bf b})|psirangle-langle psi|P({bf a})otimes{bf 1}|psiranglelangle psi|{bf 1}otimes P({bf b})|psirangle]=0$ for any two projection operators $P({bf a})$ and $P({bf b})$ provides a necessary and sufficient separability criterion in the case of a separable pure state $rho=|psiranglelanglepsi|$. We propose the separability criteria of mixed states, which are given by ${rm Tr}rho{{bf a}cdot {bf sigma}otimes {bf b}cdot {bf sigma}}=(1/3)Ccosvarphi$ for two spin $1/2$ systems and $4{rm Tr}rho {P({bf a})otimes P({bf b})}=1+(1/2)Ccos2varphi$ for two photon systems, respectively, after taking a geometrical angular average of ${bf a}$ and ${bf b}$ with fixed $cosvarphi={bf a}cdot{bf b}$. Here $-1leq Cleq 1$, and the difference in the numerical coefficients $1/2$ and $1/3$ arises from the different rotational properties of the spinor and the transverse photon. If one instead takes an average over the states in the $d=2$ Hilbert space, the criterion for two photon systems is replaced by $4{rm Tr}rho {P({bf a})otimes P({bf b})}=1+(1/3)Ccos2varphi$. Those separability criteria are shown to be very efficient using the existing experimental data of Aspect et al. in 1981 and Sakai et al. in 2006. When the Werner state is applied to two photon systems, it is shown that the Hilbert space average can judge its inseparability but not the geometrical angular average.
Separability is an important problem in theory of quantum entanglement. By using the Bloch representation of quantum states in terms of the Heisenberg-Weyl observable basis, we present a new separability criterion for bipartite quantum systems. It is shown that this criterion can be better than the previous ones in detecting entanglement. The results are generalized to multipartite quantum states.
Inspired by the realignment or computable cross norm criterion, we present a new result about the characterization of quantum entanglement. Precisely, an interesting class of inequalities satisfied by all separable states of a bipartite quantum system is derived. These inequalities induce new separability criteria that generalize the realignment criterion.
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