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Chinese Physics Letters

Testing Evolution Equation for Entanglement of Two-Qubit Systems in Noisy Channels on Ensemble Quantum Computers

Zhang Han, Luo Jun, Ren Ting-Ting, Xianping Sun

Published Sep 1, 2010• 5 citations
Publisher

Abstract

We report the experimental demonstration of decoherence dynamics of entanglement for the four Bell states in two-qubit nuclear-spin systems on ensemble quantum computers. Using artificial error operators to simulate noisy channels, we experimentally investigate the effect of noises on the four Bell states, and furthermore observe the time evolution of entanglement for the four Bell states in different noisy channels by calculating concurrences. Our experimental results show that the concurrences of the different Bell states under the same artificial error operations have the same values within the experimental error, and are independent of the different Bell states. These experimental results verify the theoretical evolution equation developed by Konrad et al.[Nature Phys. 4 (2008) 99] for two-qubit entanglement.

DOI
10.1088/0256-307x/27/9/090303

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We report the experimental demonstration of decoherence dynamics of entanglement for the four Bell states in two-qubit nuclear-spin systems on ensemble quantum computers. Using artificial error operators to simulate noisy channels, we experimentally investigate the effect of noises on the four Bell states, and furthermore observe the time evolution of entanglement for the four Bell states in different noisy channels by calculating concurrences. Our experimental results show that the concurrences of the different Bell states under the same artificial error operations have the same values within the experimental error, and are independent of the different Bell states. These experimental results verify the theoretical evolution equation developed by Konrad et al.[Nature Phys. 4 (2008) 99] for two-qubit entanglement.
我们报导为四只钟的纠纷的 decoherence 动力学的试验性的示范在整体量计算机上在 two-qubit 说原子纺纱的系统。使用人工的错误操作员模仿吵闹的隧道，我们试验性地在四个贝尔状态上调查噪音的效果，并且而且观察为在由精明的同时发生的不同吵闹的隧道的四个贝尔状态的纠纷的时间进化。我们在一样的人工的错误操作下面的不同贝尔状态的同时发生举办的试验性的结果表演一样在试验性的错误以内珍视，并且独立于不同贝尔状态。这些试验性的结果证实理论进化方程由 Konrad 等发展了[自然 Phys。4 (2008 ) 99 ] 为 two-qubit 纠纷。[从作者抽象]
We explore how entanglement of a bipartite system evolves when one subsystem undergoes the action of an arbitrary noisy channel. It is found that the dynamics of entanglement of such system is determined by the channel's action on the maximally entangled state, which includes as a special case the results for two-qubit systems [Konrad et al., Nat. Phys. 4, 99 (2008)]. In particular, for multiqubit or qubit-qudit systems, we get a general factorization law for the evolution equation of entanglement, with one qubit being subject to a noisy channel.
Quantum entanglement is notorious for being a very fragile resource. Significant efforts have been put into the study of entanglement degradation in the presence of a realistic noisy environment. Here, we present a theoretical and an experimental study of the decoherence properties of entangled pairs of qubits. The entanglement dynamics of maximally entangled qubit pairs is shown to be related in a simple way to the noise representation in the Bloch sphere picture. We derive the entanglement level in the case when both qubits of a Bell state are transmitted through any arbitrary unital Pauli channel, and compare it to the case when the channel is applied only to one of the qubits. The dynamics of both cases was verified experimentally using an all-optical setup. We further investigated the evolution of partially entangled initial states. Different dynamics was observed for initial mixed and pure states of the same entanglement level.
Abstract Entanglement and decoherence are two intimately related phenomena that lie at the heart of quantum information. The EPR-Bell states are the most basic quantum systems, which form the complete entangled basis of the two-particle Hilbert space, and which are important in many quantum computation schemes. The bit flip, phase flip, and bit-phase flip noise channels represent all the possible errors in quantum computation. Thus, the quantum decoherence characteristic of maximally and partially Bell entangled states under different noisy channels is studied using the concurrence. Our work is useful for linear-optical quantum computation and quantum communication schemes whose building blocks are entangled state.
Quantum information technology is mainly based on quantum entanglement. As an important coherent superposition state, the coherence of quantum entanglement source is easily affected by environment and becomes fragile, which will lead to the failure of the quantum information processing. Thus, it is critical to reveal the evolutions of quantum entanglement source under different noisy environments and different noisy channels. Firstly, we experimentally prepare a high-fidelity two-bit entangled state by several technical methods. The fidelity observed for the state prepared in our experiment is 0.993 and the signal-to-noise ratio can reach up to 299. Then, we simulate the bit-flip noise and phase-shift noise (collective and non-collective) using the all-optical experimental setup. Finally, based on the entanglement qubit state, we experimentally study the evolutions of entanglement characteristic under different noisy environments and the single, double and mixed noisy channels. The experimental results show that for the same type of noise, the entanglement properties disappear fast when entangled qubit passes through dual channel noisy environment. The upper bounds of noise intensity to destroy the entanglement property are 0.25 and 0.26 for the single bit-flip noise and phase-shift noisy channels, respectively. The comparison between the two different kinds of noisy environments shows that the entanglement properties disappear fast when entangled bit passes through non-collective environment. The upper bounds of noise intensity are 0.08 and 0.14 for non-collective bit-flip and phase-shift noise to destroy the entanglement property, while the noise intensities are 0.14 and 0.23 for collective bit-flip and phase-shift noise, respectively. For different kinds of noises, the results show that bit-flip noise is more likely to destroy the entanglement properties than the phase-shift. Our results have great significance for the theoretical and experimental studies of entanglement decoherence and have important application value for quantum information processing technology based on the nonlinear optical system.
We study the dynamics of four-qubit W state under various noisy environments by solving analytically the master equation in the Lindblad form in which the Lindblad operators correspond to the Pauli matrices and describe the decoherence of states. Also, we investigate the dynamics of the entanglement using the lower bound to the concurrence. It is found that while the entanglement decreases monotonically for Pauli-Z noise, it decays suddenly for other three noises. Moreover, by studying the time evolution of entanglement of various maximally entangled four-qubit states, we indicate that the four-qubit W state is more robust under same-axis Pauli channels. Furthermore, three-qubit W state preserves more entanglement with respect to the four-qubit W state, except for the Pauli-Z noise.