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International Journal of Quantum Information

QUANTUM CIRCUITS FOR PROBABILISTIC ENTANGLEMENT TELEPORTATION VIA A PARTIALLY ENTANGLED PAIR

Xiu‐Bo Chen, Qiaoyan Wen, Fu-Chen Zhu

Published Oct 1, 2007• 19 citations
Publisher

Abstract

It deserves mentioning that the quantum circuit, i.e. quantum logic network, is essential to the practical realization of teleportation in experiment. Using only one partially entangled pair, we first propose two novel strategies for probabilistically teleporting any partially entangled state of a bipartite system. The feature of the present protocol is to weaken the requirement for the quantum channel, and also to cut down the number of entangled particles initially shared by the sender and receiver. On the other hand, we explicitly construct the generalized measurement described by the positive operator-valued measure (POVM). Two kinds of efficient quantum circuits for implementing the teleportation are offered. In addition, we generalize the two-particle probabilistic teleportation to the system of many particles.

DOI
10.1142/s021974990700316x

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It deserves mentioning that the quantum circuit, i.e. quantum logic network, is essential to the practical realization of teleportation in experiment. Using only one partially entangled pair, we first propose two novel strategies for probabilistically teleporting any partially entangled state of a bipartite system. The feature of the present protocol is to weaken the requirement for the quantum channel, and also to cut down the number of entangled particles initially shared by the sender and receiver. On the other hand, we explicitly construct the generalized measurement described by the positive operator-valued measure (POVM). Two kinds of efficient quantum circuits for implementing the teleportation are offered. In addition, we generalize the two-particle probabilistic teleportation to the system of many particles.
Utilizing the generalized measurement described by positive operator-valued measure, this paper comes up with a protocol for teleportation of an unknown multi-particle entangled (GHZ) state with a certain probability. The feature of the present protocol is to weaken requirement for the quantum channel initially shared by sender and receiver. All unitary transformations performed by receiver are summarized into a formula. On the other hand, this paper explicitly constructs the efficient quantum circuits for implementing the proposed teleportation by means of universal quantum logic operations in quantum computation.
Deterministic and exact teleportation can be achieved via two partially entangled pairs of particles [Gu Y J 2005 Opt. Comm. ]. The key point of the protocol is a generalized measurement described by a positive operator-valued measure, which can be realized by performing a unitary operation in the extended space and a conventional Von Neumann orthogonal measurement. By decomposing the evolution process from the initial state to the final state, we construct the quantum circuits for realizing the unitary operation with quantum Toffoli gates and thus provide a physical means to realize the teleportation. Our method for constructing quantum circuits differs from the usual methods based on decomposition of unitary matrices and is convenient for a large class of quantum processes involving generalized measurements.
Teleportation of an arbitrary single-qubit state using two partially entangled states is considered.Firstly,we present a method for realizing probabilistically two-destination teleportation by using two partially entangled pairs as quantum channel.Then,we put forward a scheme for realizing deterministic and exact teleportation by using same quantum channel.In these schemes,the sender's local generalized measurement described by a positive operator valued measurement(POVM) lies at the heart.We construct the required POVM.The methods are applicable to any two partially entangled pairs satisfying the condition that their smaller Schmidt coefficients μ and v are 2μ+2μv-2v-1≥0.
By means of the primitive operations consisting of single-qubit gates, two-qubit controlled-not gates, Von Neuman measurement and classically controlled operations, we construct efficient quantum logic networks for implementing probabilistic teleportation of a single qubit, a two-particle entangled state and an N -particle entanglement. Based on the quantum networks, we show that after the partially entangled states are concentrated into maximal entanglement, the above three kinds of probabilistic teleportation are the same as the standard teleportation using the corresponding maximally entangled states as the quantum channels.
By eans of the primitive operations consisting of single-qubit gates.two-qubit controlled-not gates,Von Neuman measurement and classically controlled operations.,we construct efficient quantum logic networks for implementing probabilistic teleportation of a single qubit,a two-particle entangled state,and an N-particle entanglement.Based on the quantum networks,we show that after the partially entangled states are concentrated into maximal entanglement,the above three kinds of probabilistic teleportation are the same as the standard teleportation using the corresponding maximally entangled states as the quantum channels.
Very recently, Lee et al. proposed a secure quantum teleportation protocol to transfer shared quantum secret between multiple parties in a network [Phys. Rev. Lett. 124 060501 (2020)]. This quantum network is encoded with a maximally entangled GHZ state. In this paper, we consider a partially entangled GHZ state as the entanglement channel, where it can achieve, probabilistically, unity fidelity transfer of the state. Two kinds of strategies are given. One arises when an auxiliary particle is introduced and a general evolution at any receiver’s location is then adopted. The other one involves performing a single generalized Bell-state measurement at the location of any sender. This could allow the receivers to recover the transmitted state with a certain probability, in which only the local Pauli operators are performed, instead of introducing an auxiliary particle. In addition, the successful probability is provided, which is determined by the degree of entanglement of the partially multipartite entangled state. Moreover, the proposed protocol is robust against the bit and phase flip noise.