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Physica Scripta

Improving bidirectional controlled remote preparation of arbitrary number of qudits in noisy environment

Si Jin, Song-Ya Ma, Siyi Li

Published Sep 3, 2024• 6 citations
Publisher

Abstract

Abstract By elaborately selecting entangled channel, we put forward a universal scheme to achieve bidirectional remote preparation of qudit states with arbitrary numbers of particles under the control of the supervisor. Each sender needs to perform a positive-operator-value measurement and a projective measurement, while the supervisor requires to execute a projective measurement. Based on their measurement outcomes, the receivers can recover the desired states concurrently by carrying out single-qudit generalized Pauli operations which are given by general formulas. A point to highlight is that classical communication cost is greatly reduced at the supervisor’s broadcast channel by taking advantage of network coding. In addition, we analyze the influence of amplitude-damping and phase-damping noises, and utilize weak measurement and environment-assisted measurement to suppress noise.

DOI
10.1088/1402-4896/ad76e9

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Abstract By elaborately selecting entangled channel, we put forward a universal scheme to achieve bidirectional remote preparation of qudit states with arbitrary numbers of particles under the control of the supervisor. Each sender needs to perform a positive-operator-value measurement and a projective measurement, while the supervisor requires to execute a projective measurement. Based on their measurement outcomes, the receivers can recover the desired states concurrently by carrying out single-qudit generalized Pauli operations which are given by general formulas. A point to highlight is that classical communication cost is greatly reduced at the supervisor’s broadcast channel by taking advantage of network coding. In addition, we analyze the influence of amplitude-damping and phase-damping noises, and utilize weak measurement and environment-assisted measurement to suppress noise.
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We present a scheme for symmetric controlled remote preparation of an arbitrary 2-qudit state form a sender to either of the two receivers via positive operator-valued measurement and pure entangled two-particle states. The first sender transforms the quantum channel shared by all the agents via POVM according to her knowledge of prepared state. All the senders perform single- or two-particle projective measurements on their entangled particles and the receiver can probabilisticaly reconstruct the original state on her entangled particles via unitary transformation and auxiliary qubit. The scheme is optimal as the probability which the receiver prepares the original state equals to the entanglement of the quantum channel. Moreover, it is more convenience in application than others as it requires only two-particle entanglements for preparing an arbitrary two-qudit state.
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We present a general scheme for multiparty joint remote preparation of an arbitrary m -qudit state with a pure entangled quantum channel via positive operator-valued measurement (POVM). The n senders share the information of the prepared state. The first sender performs POVM on his particles according to his knowledge of the original state, the other n − 1 senders perform m -particle projective measurement and the receiver can probabilistically reconstruct the original state by performing unitary operations on his particles according to the senders' measurement results. The scheme has the advantage of having high success probability for multiparty joint remote preparation of an arbitrary m -qudit state via pure entangled quantum states. Moreover, it discusses the relationship between the coefficients of the pure entangled states and the success probability.