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Chinese Physics Letters

Remote State Preparation Using Non-Maximally Entangled State: Universality and Necessary Amount of Quantum Channels

Yu-Xue Mei, Lin Chen, Yi-Xin Chen

Published Feb 24, 2006• 5 citations
Publisher

Abstract

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.

DOI
10.1088/0256-307x/23/3/007

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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 a scheme in which any pure qubit $|ϕ=\cosθ|0+\sinθe^{i\varp hi}|1$ could be remotely prepared by using minimum classical bits and the previously shared non-maximally entangled states, on condition that the receiver holds the knowledge of θθθ. Several methods are available to check the trade-off between the necessary entanglement resource and the achievable fidelity.
在遥远的州的准备的一个过程，量隧道的普遍性都是必要成分。也就是说，一条量隧道应该是可行的遥远地准备任何给定的 qubit 状态。这个问题在一使用 non-maximally 作为经过纠缠了状态的一个过程出现。我们在场在的一个计划任何给定的 qubit 垂直酒吧 phi >= cos thetavertical 酒吧 0 >+ 罪恶 theta e (i phi ) 垂直酒吧 1 > 能被与高保真度使用最小的古典位和以前分享的 non-maximally 纠缠的状态遥远地准备。在接收装置保持的条件下面 theta 的知识。这个条件是有用的减少量隧道的必要数量，它被证明是低数量认识到普遍性。我们也给几个方法调查在这数量和协议的可完成的忠实之间的交易。
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.
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.
Remote state preparation is the variant of quantum state teleportation in which the sender knows the quantum state to be communicated. The original paper introducing teleportation established minimal requirements for classical communication and entanglement but the corresponding limits for remote state preparation have remained unknown until now: previous work has shown, however, that it not only requires less classical communication but also gives rise to a tradeoff between these two resources in the appropriate setting. We discuss this problem from first principles, including the various choices one may follow in the definitions of the actual resources. Our main result is a general method of remote state preparation for arbitrary states of many qubits, at a cost of 1 bit of classical communication and 1 bit of entanglement per qubit sent. In this "universal" formulation, these ebit and cbit requirements are shown to be simultaneously optimal by exhibiting a dichotomy. Our protocol then yields the exact tradeoff curve for memoryless sources of pure states (including the case of incomplete knowledge of the ensemble probabilities), based on the recently established quantum-classical tradeoff for visible quantum data compression. A variation of that method allows us to solve the even more general problem of preparing entangled states between sender and receiver (i.e., purifications of mixed state ensembles). The paper includes an extensive discussion of our results, including the impact of the choice of model on the resources, the topic of obliviousness, and an application to private quantum channels and quantum data hiding.
Remote state preparation (RSP) is the act of preparing a quantum state at a remote location without actually transmitting the state itself. Using at most two classical bits and a single shared maximally entangled state, one can in theory remotely prepare any qubit state with certainty and with perfect fidelity. However, in any experimental implementation the average fidelity between the target and output states cannot be perfect. In order for an RSP experiment to demonstrate genuine quantum advantages, it must surpass the optimal threshold of a comparable classical protocol. Here we study the fidelity achievable by RSP protocols lacking shared entanglement and determine the optimal value for the average fidelity in several different cases. We implement an experimental scheme for deterministic remote preparation of arbitrary photon polarization qubits, preparing 178178178 different pure and mixed qubit states with an average fidelity of 0.9950.9950.995. Our experimentally achieved average fidelities surpass our derived classical thresholds whenever the classical protocol does not trivially allow for perfect RSP.