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Modern Physics Letters B

ENTANGLEMENT SWAPPING FOR TWO PAIRS OF EPR EIGENSTATES GENERATED VIA BELL MEASUREMENT

Hong-Yi Fan

Published Feb 10, 2001• 0 citations
Publisher

Abstract

We demonstrate that a common eigenvector |η> (Einstein, Podolsky and Rosen, EPR states) of two particles' relatively coordinate and total momentum possesses a property that the projection (a Bell measurement) of two pairs of EPR states |η>1,2⊗| η'>3,4 onto the subspace spanned by 1,4<η″|, yields a EPR state |η″-η*-η′* >2,3 for particles 2 and 3. Entanglement swapping operator is also derived by virtue of the technique of integration within an ordered product of operators.

DOI
10.1142/s0217984901001446

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The Einstein–Podolsky–Rosen (EPR) wavefunction is a two-particle wavefunction that is a simultaneous eigenfunction of the relative coordinate and the centre-of-mass momentum. The Fock space representation of this function is easily obtained as a direct product of an eigenfunction of the relative coordinate and an eigenfunction of the centre-of-mass momentum. Straightforward generalization to an arbitrary number of particles is shown to be feasible, and a classification of multiparticle entangled states is outlined. The relation between entanglement and inseparability is pointed out, and the status of the EPR states within the much broader family of entangled states is emphasized.
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A scheme to teleport an unknown two qubit state from Alice (the sender) to Bob (the receiver) using two Einstein Podolsky Rosen (EPR) pairs is presented, each EPR pair being shared by both Alice and Bob. Firstly, Alice combines each of the two particles in the teleported state with an EPR particle and makes Bell state measurement on each combination. Then she transmits the outcomes of her measurements to Bob classically. According to Alice′s measurement results, Bob can perform appropriate unitary operations on his two EPR particles to retrieve the initial state.
By noticing that although single-mode Susskind–Glogower phase operator does not commute with photon number operator, two-mode nonlinear phase operator commutes with number-difference operator. We reveal that the common eigenstate <η| of two-particles' relative coordinate and total momentum involves the entanglement between phase and amplitude. We also reveal entanglement between number difference and amplitude inherent in the state |D,|η|>, where [Formula: see text] is a deductive state of |η>.