[论文解读] No Broadcasting of Quantum Correlation

Sourav Chatterjee, Sk Sazim+1 more|arXiv (Cornell University)|Nov 17, 2014

Quantum Information and Cryptography被引用 1

一句话总结

本文研究了使用通用对称Buzek-Hillery克隆机对量子关联（包括纠缠和非纠缠量子关联）进行广播的问题。文中分析证明，即使对纠缠以外的量子关联实现部分广播，在局部和非局部克隆机下也从根本上不可能，揭示了基于纠缠的关联与更广泛关联度量之间的关键区别。

ABSTRACT

In this work, we extensively study the problem of broadcasting of quantum correlations. This includes broadcasting of quantum entanglement as well as correlations that go beyond the notion of entanglement. It is quite well known from the No-Broadcasting theorem that perfect broadcasting of quantum correlation is not possible. However it does not rule out the possibility of partial broadcasting of correlations where we can get lesser correlated states from a given correlated state. In order to have a holistic view of broadcasting, we investigate this problem by starting with most general representation of two qubit mixed states in terms of the Bloch vectors. As a cloning transformation we have used universal symmetric optimal Buzek-Hillery (B-H) cloner both locally and nonlocally. More specifically, we obtain a set of ranges in terms of Bloch vectors for which broadcasting of entanglement will be possible. In addition to the idea of broadcasting of entanglement for general two qubit mixed states, we explore broadcasting of quantum correlations that go beyond entanglement with the help of both local and nonlocal cloners. Remarkably, we find that it is impossible to even partially broadcast such correlations by using both local and nonlocal quantum copying machines. Taking two different types Buzek-Hillery quantum cloners (state dependent and state independent) we analytically prove the impossibility of even partial broadcasting of correlation. Lastly, we generalize this impossibility result for any symmetric or asymmetric cloning machines as well. This result brings out a fundamental difference between the correlation defined from the perspective of entanglement and the correlation measure which claims to go beyond entanglement.

研究动机与目标

• 研究是否可以使用量子克隆机对两比特混合态中的量子关联（包括纠缠和非纠缠量子关联）实现部分广播。
• 分析局部和非局部克隆操作在两比特混合态中广播量子关联时的作用。
• 基于Bloch向量表示，确定广播纠缠可能成立的条件。
• 将不可能性结果推广至任意对称与非对称克隆机。
• 阐明基于纠缠的关联与更广泛量子关联度量之间的根本性差异。

提出的方法

• 研究使用两比特混合态的Bloch向量一般参数化来表示量子态。
• 应用依赖于状态和不依赖于状态的通用对称Buzek-Hillery量子克隆机，以分析广播能力。
• 分析考虑了局部和非局部克隆操作，以评估其对关联传播的影响。
• 通过解析推导，确定了可能实现纠缠广播的Bloch向量范围。
• 将框架扩展至任意对称与非对称克隆机，以推广研究发现。
• 比较基于纠缠的关联度量与超越纠缠的关联度量，以突出其结构差异。

实验结果

研究问题

• RQ1 在两比特混合态中，是否可以使用通用对称量子克隆机对量子纠缠实现部分广播？
• RQ2 是否可以使用局部或非局部克隆操作对超越纠缠的量子关联实现广播？
• RQ3 哪些Bloch向量的特定范围允许任何形式的纠缠广播？
• RQ4 依赖于状态与不依赖于状态的Buzek-Hillery克隆机在保持或广播关联方面的能力有何不同？
• RQ5 对所有对称与非对称克隆机而言，广播非纠缠量子关联的不可能性是否成立？

主要发现

• 即使使用局部和非局部Buzek-Hillery克隆机，对纠缠以外的量子关联实现部分广播在根本上也是不可能的。
• 该不可能性对依赖于状态和不依赖于状态的通用对称克隆机均成立。
• 本研究识别出在特定严格条件下可能实现纠缠广播的Bloch向量范围。
• 揭示了基于纠缠定义的关联与基于更广泛非纠缠度量定义的关联之间存在根本性差异。
• 该结果可推广至所有对称与非对称克隆机，表明广播非纠缠量子关联存在普遍限制。