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Chinese Physics Letters

Simulating Entangling Unitary Operator Using Non-maximally Entangled States

Chun-Xian Li, Wang Cheng-Zhi, Nie Liu-Ying, Jiangfan Li

Published Feb 1, 2009• 0 citations
Publisher

Abstract

We use non-maximally entangled states (NMESs) to simulate an entangling unitary operator (EUO) with a certain probability. Given entanglement resources, the probability of the success we achieve is a decreasing function of the parameters of the EUO. Given an EUO, for certain entanglement resources the result is optimal, i.e., the probability obtains a maximal value, and for optimal result higher parameters of the EUO match more amount of entanglement resources. The probability of the success we achieve is higher than the known results under some condition.

DOI
10.1088/0256-307x/26/2/020303

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We use non-maximally entangled states (NMESs) to simulate an entangling unitary operator (EUO) with a certain probability. Given entanglement resources, the probability of the success we achieve is a decreasing function of the parameters of the EUO. Given an EUO, for certain entanglement resources the result is optimal, i.e., the probability obtains a maximal value, and for optimal result higher parameters of the EUO match more amount of entanglement resources. The probability of the success we achieve is higher than the known results under some condition.
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A scheme for teleporting an unknown two two-level atoms entangled state via four identical two-level atoms non-maximally entangled Cluster state as quantum channel is proposed.In the scheme,the receiver Bob can reconstruct the original state with a certain probability by introducing an auxiliary atom and operating unitary transformations according to the sender Alice′s measurement results,and the successful probability is determined by the smallest two coefficients′ absolute values of the Cluster state.The considerable advantage of the scheme is that a non-maximally entangled Cluster state is employed as quantum channel,thus,the scheme can greatly reduce the amount of entanglement resources and need less classical bits.If a maximally entangled Cluster state is employed as quantum channel,the probabilistic teleportation scheme becomes usual teleportation,of which the successful probability is 100%.
Quantum entanglement, a fundamental phenomenon in quantum mechanics, holds immense potential for advanced computational modeling. This research explores the use of quantum entanglement simulation to analyze non-asymptotic properties of entangled systems, aiming to overcome limitations inherent in traditional simulation techniques. We propose a novel simulation algorithm that directly leverages entanglement's unique characteristics, enhancing precision and reducing latency. This work presents a framework for high-fidelity quantum simulations based on entangled states, demonstrating the efficacy of this approach through a rigorous theoretical analysis and preliminary experimental validation. The core claim is that this method offers a significant advancement in quantum computation, particularly in scenarios requiring high accuracy and low computational cost.
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Two schemes for teleporting an unknown two-particle entangled state via a four-qubit non-maximally entangled cluster state as quantum channel are proposed.In the first scheme,a special bipartite entangled state was teleported,the receiver Bob can reconstruct the original state with a certain probability according to the sender Alice's measurement results,and the successful probability is determined by the smallest two coefficients' absolute values of the cluster state.In the latter scheme an arbitrary two-particle entangled state was teleported.Contrast to the first scheme, Bob should perform a quantum controlled phase gate operation besides the unitary transformation. The considerable advantage is that it employs a non-maximally entangled cluster state as quantum channel in these two schemes.Thus,the schemes can greatly reduce the amount of entanglement resources and need less classical bits.