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Open Systems & Information Dynamics

Probabilistic Telecloning with Partially Entangled States

Dechao Li, Shi Zhong-ke

Published Nov 30, 2009• 1 citation
Publisher

Abstract

We propose a scheme for probabilistic telecloning of unknown d-dimensional quantum state with non-maximally (partially) entanglement via Bell measurement. The scheme requires less entanglement between the two sides, representing a much more efficient use of entanglement than the approach where Alice first clones these states on her particle and then teleports.

DOI
10.1142/s123016120900030x

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We propose a scheme for probabilistic telecloning of unknown d-dimensional quantum state with non-maximally (partially) entanglement via Bell measurement. The scheme requires less entanglement between the two sides, representing a much more efficient use of entanglement than the approach where Alice first clones these states on her particle and then teleports.
We study the process of quantum telecloning of d -dimensional pure quantum states using partially entangled pure states as quantum channel. This process efficiently mixes optimal universal symmetric cloning with quantum teleportation. It is shown that it is possible to implement universal symmetric telecloning in a probabilistic way using unambiguous state discrimination and quantum state separation schemes. It is also shown that other strategies, such as minimum error discrimination, lead to a decrease in the fidelity of the copies and that certain partially entangled pure states with maximal Schmidt rank lead to an average telecloning fidelity which is always above the optimal fidelity of measuring and preparation of quantum states. We also discuss the case of partially entangled pure states with non-maximal Schmidt rank. The results presented here are valid for arbitrary numbers of copies of a single-input qudit state of any dimension.
We establish a scheme for probabilistically teleporting an unknown 3D(dimensional) two-particle state using non-maximally entangled states as a quantum channel.In this scheme,the probabilistic teleportation is realized by using the new orthogonal complete bases measurement instead of the traditional Bell measurement,and we also use 3D entangled state as the quantum channel.These are different from the previous schemes.This scheme is more convenient for the receiver,because users could realize communication with less operators.
We have explicitly shown a teleportation scheme which allows Alice to probabilistically teleport an unknown 2-particle entangled state to either of the two receivers,Bob or Charlie,by using a non-maximally entangled 5-particle state as quantum channel.The scheme can be generalized to teleport an unknown N-(particle) entangled state to M receivers using a(N·M+1)-particle state as quantum channel at the expense of performing one CNOT operation,N·M Hadamard operations,appropriate unitary transformation without performing Bell-state measurement.
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.
Two simple schemes for probabilistic teleportation of an arbitrary unknown two-particle state using a non-maximally entangled EPR pair and a non-maximally entangled GHZ state as quantum channels are proposed. After receiving Alice's Bell state measurement results, Bob performs a collective unitary transformation on his inherent particles without introducing the auxiliary qubit. The original state can be probabilistically teleported. Meanwhile, quantum circuits for realization of successful teleportation are also presented.