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arXiv:quant-ph/0102010 · Physical Review A

Realization of optimal disentanglement by teleportation via separable channels

Sibasish Ghosh A, Guruprasad Kar, Anirban Roy, Debasis Sarkar, Ujjwal Sen

Published Sep 19, 2001• 4 citations

Abstract

We discuss optimal disentanglement processes of states of two two-level systems that 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 types 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 map $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{V}$ acting on one party's states, if $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{V}(I)=I,\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{V}({\ensuremath{\sigma}}_{j})={\ensuremath{\lambda}}_{j}{\ensuremath{\sigma}}_{j},$ where ${\ensuremath{\lambda}}_{j}>~0$ (for $j=1,2,3)$ and ${\ensuremath{\lambda}}_{1}+{\ensuremath{\lambda}}_{2}+{\ensuremath{\lambda}}_{3}<~1.$

DOI: 10.1103/physreva.64.042114

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We discuss optimal disentanglement processes of states of two two-level systems that 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 types 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 map

\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{V}

acting on one party's states, if

\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{V}(I)=I,\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{V}({\ensuremath{\sigma}}_{j})={\ensuremath{\lambda}}_{j}{\ensuremath{\sigma}}_{j},

where

{\ensuremath{\lambda}}_{j}>~0

(for

j=1,2,3)

and

{\ensuremath{\lambda}}_{1}+{\ensuremath{\lambda}}_{2}+{\ensuremath{\lambda}}_{3}<~1.

We investigate two-channel scenarios of optimal quantum teleportation based on Bell measurements and GHZ measurements. The detailed protocols are presented and the general expressions of the optimal teleportation fidelities are derived, which turn out to be functions of two-channel fully entangled fractions -- invariants under local unitary transformations. We prove that the set of states which are useful for two-channel teleportation is convex and compact. Hence witness operators exist to separate states that are useful for optimal teleportation from the rest ones. Moreover, we show that our two-channel teleportation fidelity is better than the usual one channel ones. The corresponding experimental schemes for two-channel teleportation of photon states are also presented.

We provide an alternative simple proof of the necessity of entanglement in quantum teleportation by using the no-disentanglement theorem. We show that this is true even when the state to be teleported is known to be among two noncommuting qubits. We further show that to teleport any set of commuting qubits, it is sufficient to have a classically correlated channel. Using this result we provide a simple proof of the fact that any set of bipartite entangled states can be exactly disentangled if the single particle density matrices of any one party commute.

We provide an alternative simple proof of the necessity of entanglement in quantum teleportation by using the no-disentanglement theorem. We show that this is true even when the state to be teleported is known to be among two noncommuting qubits. We further show that to teleport any set of commuting qubits, it is sufficient to have a classically correlated channel. Using this result we provide a simple proof of the fact that any set of bipartite entangled states can be exactly disentangled if the single-particle density matrices of any one party commute.

I present a four-party unlockable bound entangled state, that is, a four-party quantum state which cannot be written in a separable form and from which no pure entanglement can be distilled by local quantum operations and classical communication among the parties, and yet when any two of the parties come together in the same laboratory they can perform a measurement which enables the other two parties to create a pure maximally entangled state between them without coming together. This unlocking ability can be viewed in two ways, either as a determination of which Bell state is shared in the mixture or as a kind of quantum teleportation with cancellation of Pauli operators.

An optimal scheme is presented for the quantum teleportation of an arbitrary [Formula: see text]-particle generalized Bell-type state. In this paper, we have discussed three examples of two-particle, three-particle, and four-particle generalized Bell-type state in detail. Not only that, we have also analyzed the specific optimization process of quantum teleportation. Compared with previous schemes, our scheme has less quantum cost and transmission complexity due to the optimized quantum channel and operations.