Distinguishability of Bell States

Abstract

More than two multipartite orthogonal states cannot always be discriminated if only local operations and classical communication (LOCC) are allowed. We show that four Bell states cannot be discriminated by LOCC, even probabilistically, using the separability properties of a four-party unlockable bound entangled state. Using an existing inequality among the measures of entanglement, we show that any three Bell states cannot be discriminated with certainty by LOCC. Exploiting the inequality, we calculate the distillable entanglement of a certain class of 4 multiply sign in circle 4 mixed states.

Hyperentanglement-assisted Bell-state analysis

“…However, it has been proven that a complete BSM (distinguishing between the four states with 100% efficiency) is impossible using only linear operations and classical communication [8,9,10,11]. In fact, Ghosh et.…”

“…al. [11] have proven that, if only a single copy is provided, the best one can do is discriminate between two Bell states. Calsamiglia and Lütkenhaus [10] have shown that the maximum efficiency for a linear Bell-state analyzer is 50%.…”

“…Utilizing entanglement in additional auxiliary degrees of freedom, it is possible to perform a complete BSM. Due to the enlarged Hilbert space, this type of complete BSM is not restricted to the efficiency limits presented in [8,9,10,11]. Kwiat and Weinfurter [25] have proposed a scheme using photons entangled in polarization and momentum (spatial mode).…”

Nonlocality of orthogonal product-basis quantum states

“…Some of them considered the set with maximally entangled states [5][6][7][8][9][10][11][12][13][14], while the others aimed at the set with product states [2,[15][16][17][18][19][20][21][22][23][24][25][26]. Both of these researches can lead us a better understanding the limitation of the local operations and classical communication.…”

Realization of optimal disentanglement by teleportation via separable channels

“…But any great circle of the Bloch sphere is of particular interest : (i) any great circle is the largest set of Bloch vectors that can be exactly flipped [18,19], and this fact can be used for remote (exact) state preparation [20], (ii) a product state of two parallel qubits and the corresponding product state of two antiparallel qubits contain equivalent information about the qubit, if the Bloch vectors of all these qubits lie on the same great circle [21], (iii) the optimal universal 1 → 2 (isotropic) cloning machine of the equator (on which the states |0 , |1 , (1/ √ 2)(|0 ±|1 ) lie) is the same as that of the set {|0 , |1 , (1/ √ 2)(|0 ±|1 )} [22]. We consider here the set of all entangled states, where all the Bloch vectors of the reduced density matrices of one side lie on the disc of a great circle.…”