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arXiv:quant-ph/0404172 · Physical Review A

Generalized measurement and conclusive teleportation with nonmaximal entanglement

Hyunjae Kim, Yong Wook Cheong, Hai-Woong Lee

Published Jul 19, 2004• 38 citations
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Abstract

We present linear optical schemes to perform generalized measurements for conclusive teleportation when the sender and the receiver share nonmaximal entanglement resulting from amplitude errors during propagation or generation. Three different cases are considered for which the states to be teleported are unknown superpositions of (a) single-photon and vacuum states, (b) vertically polarized and horizontally polarized photon states, and (c) two coherent states of opposite phases. The generalized measurement scheme for each case is analyzed, which indicates that the success probability is much more resistant to amplitude errors for case (c) than for case (a) or (b).

DOI
10.1103/physreva.70.012309

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We present linear optical schemes to perform generalized measurements for conclusive teleportation when the sender and the receiver share nonmaximal entanglement resulting from amplitude errors during propagation or generation. Three different cases are considered for which the states to be teleported are unknown superpositions of (a) single-photon and vacuum states, (b) vertically polarized and horizontally polarized photon states, and (c) two coherent states of opposite phases. The generalized measurement scheme for each case is analyzed, which indicates that the success probability is much more resistant to amplitude errors for case (c) than for case (a) or (b).
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We investigate multiple linear optical teleportation in the Knill-Laflamme-Milburn scheme with both maximally and nonmaximally entangled states. We show that if the qubit is teleported several times via a nonmaximally entangled state, then the errors introduced in the previous teleportations can be corrected by the errors introduced in the following teleportations. This effect is so strong that it leads to another interesting phenomenon: i.e., the total probability of successful multiple linear optical teleportation is higher for nonmaximally entangled states than maximally entangled states.
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In this paper a new scheme for teleporting an unknown entangled state of two particles is proposed. To weaken the requirement for the quantum channel, without loss of generality, two communicators only share a non-maximally entangled two-particle state. Teleportation can be probabilistically realized if sender performs Bell-state measurements and Hadamard transformation and receiver introduces two auxiliary particles, operates C -not operation, single-qubit measurements and appropriate unitary transformations. The probability of successful teleportation is determined by the smaller one among the coefficients' absolute values of the quantum channel.