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arXiv:2206.14926

Optimal deterministic remote state preparation via a non-maximally entangled channel without additional quantum resources

Xuanxuan Xin, Shiwen He, Yongxing Li, Chong Li

Published Jun 29, 2022• 0 citations
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Abstract

In this paper, we reinvestigate remote state preparation by using the prepared non-maximally entangled channel. An innovative remote state preparation protocol is developed for deterministically preparing information encoded in quantum states without additional consumption of quantum resources. We have increased the success probability of preparing a d-dimensional quantum state to 1 via a non-maximally entangled quantum channel. A feasibly experimental scheme is also designed to realize the above-mentioned deterministic scheme. This work provides a valuable method to address decoherence and environmental noises in the practicalization of quantum communication tasks.

DOI
10.48550/arxiv.2206.14926

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In this paper, we reinvestigate remote state preparation by using the prepared non-maximally entangled channel. An innovative remote state preparation protocol is developed for deterministically preparing information encoded in quantum states without additional consumption of quantum resources. We have increased the success probability of preparing a d-dimensional quantum state to 1 via a non-maximally entangled quantum channel. A feasibly experimental scheme is also designed to realize the above-mentioned deterministic scheme. This work provides a valuable method to address decoherence and environmental noises in the practicalization of quantum communication tasks.
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Abstract Ideal deterministic quantum communication tasks require maximally entangled channels. The reality is that the maximally entangled channel is inevitably degraded to a generally entangled one because of various decoherence mechanisms, seriously deteriorating the performance of quantum communication. In most cases, entanglement purification and distillation are utilized to improve the entanglement and to construct the maximally entangled channel. In this paper, we proposed an alternative scheme to realize deterministic joint remote state preparation using a non-maximally entangled channel. Instead of spending additional entanglement resources in advance for entanglement purification or distillation, only two non-entangled ancillaries are employed in this scheme. Whether the employed quantum channel is a maximally entangled channel or a generally entangled one, remote state preparation would never fail theoretically in this investigation. This protocol provides a feasible way for the construction of practical quantum networks.
We propose a new generalized remote state preparation protocol for using non-maximally entangled state as a shared resource. Different from the previous schemes, the parameters of measurement basis depend on not only the state of preparation but also the state of quantum channel. The advantage of the present protocols is that, by constructing a set of appropriate mutually orthogonal measurement basis, the success probability is improved. It is worthwhile noticing that the probability of success is determined by Alice's measurement. If Alice's measurement is appropriate, the remote preparation can be successfully realized with the maximal probability.
In a process of remote state preparation, the universality of quantum channel is an essential ingredient. That is, one quantum channel should be feasible to remotely prepare any given qubit state. This problem appears in a process where one uses non-maximally entangled state as the passage. We present a scheme in which any given qubit |ϕ⟩ = cos θ|0⟩+sin θ e i φ |1⟩ could be remotely prepared by using minimum classical bits and the previously shared non-maximally entangled state with a high fidelity, under the condition that the receiver holds the knowledge of θ. This condition is helpful to reduce the necessary amount of quantum channels, which is proven to be a low quantity to realize the universality. We also give several methods to investigate the trade-off between this amount and the achievable fidelity of the protocol.
We present two schemes for preparing remotely a three-particle entangled state by two different quantum channels. In the first scheme, two partial three-particle entangled states are used as the quantum channels, while in the second scheme, three two-particle non-maximally entangled states are employed as the quantum channels. It is shown that the remote state preparation can be successfully realized with certain probability, for both two schemes, if a sender performs some projective measurements and a receiver adopts some appropriate unitary transformations. It is shown also that the successful probabilities of these two schemes are different.
We present a scheme for remote preparing a general two-particle state by two entangled states serving as the quantum communication channel. In this scheme, it is possible for the receiver to perfectly reconstruct the initial state that the sender hopes to prepare with the method of introducing an auxiliary qubit and postselection measurements in the situation of non-maximal entangled quantum channel. Furthermore, we investigate the influence of the dissipation factors on the processing of the remote state preparation when the entangled resources are in the Markovian and non-Markovian noisy environments. It is shown that the fidelity of remote state preparation is decreasing exponentially over time in Markovian environments and attenuating oscillatorily in non-Markovian. However, when the non-Markovian and the detuning conditions are satisfied simultaneously, the fidelity can be preserved at comparative high levels, effectively.