Realization of optimal disentanglement by teleportation via separable channels

Abstract

We discuss here the best disentanglement processes of states of two two-level systems which belong to (i) the universal set, (ii) the set in which the states of one party lie on a single great circle of the Bloch sphere, and (iii) the set in which the states of one party commute with each other, by teleporting the states of one party (on which the disentangling machine is acting) through three particular type of separable channels, each of which is a mixture of Bell states. In the general scenario, by teleporting one party's state of an arbitrary entangled state of two two-level parties through some mixture of Bell states, we have shown that this entangled state can be made separable by using a physically realizable mapṼ , acting on one party's states, if V (I) = I,Ṽ (σ j ) = λ j σ j , where λ j ≥ 0 (for j = 1, 2, 3), and λ 1 + λ 2 + λ 3 ≤ 1.

Local cloning of Bell states and distillable entanglement

“…Let Alice(1) and Bob(1) are teleporting their qubits to Alice(2) and Bob(2) respectively, using the same teleportation protocol, namely the standard teleportation protocol of Bennett et al [8], for exactly teleporting an unknown qubit through the channel state |B 1 . This teleportation (i.e., teleportation of any two-qubit state from Alice(1) : Bob(1) cut to Alice(2) : Bob(2) cut, via the shared channel state ρ S , and using the exact protocol of Bennett et al [8] for the channel state |B 1 , for each qubit) can be represented in terms of the following maps (see [9]):…”

Entanglement teleportation via Bell mixtures

“…If one takes the teleportation protocol to be P |Ψ + [8] and takes the channel state as a mixture of four Bell states, then the mapṼ is realised through this teleportation process in the following way [9]: Let the channel state be It is clear that just nonzero entanglement of channel state ρ ch does not guarantee entanglement teleportation (see for example, ref. [3]).…”

“…Let us provide an example of a channel state and a teleportation protocol which realizes the map Ṽ . If one takes the teleportation protocol to be P |Ψ + [8] and takes the channel state as a mixture of four Bell states, then the map Ṽ is realised through this teleportation process in the following way [9]: Let the channel state be…”