arXiv quant-ph/02030302002-03-06quant-phcond-mat.mes-hallgr-qchep-th

时空中的量子信息理论

Towards Quantum Information Theory in Space and Time

Igor V. Volovich

备注：: 16 pages

摘要：

现代量子信息理论处理的是一种理想化的情况，即量子现象的时空依赖性被忽略。然而，（量子）信息的传输和处理是时空中的物理过程。因此，量子信息理论中的基本概念，如量子比特、信道、复合系统、纠缠态等，都应该在时空中表述。特别地，我们认为相对论性量子信息理论的基本概念应该是基本量子系统的概念，即在庞加莱群的不可约表示下的无穷维希尔伯特空间$H$不变量，用$[m,s]$标记，其中$m\geq 0$是质量，$s=0,1/2,1,...$是自旋。我们强调从量子场论的观点考虑量子信息理论的重要性。指出并讨论了一个基本事实：在量子场论中，时空中的两个区域即使是类空分离的，它们之间也存在统计相关性。得到了量子场论中一类关联函数的经典概率表示。在空间和时间的纠缠态被认为是。结果表明，相对论性量子场论中的任何合理态在大的类空距离上都是可分解的。因此，只有当探测器之间的距离相当小时，才能观察到贝尔不等式的违反，而不与相对论量子理论的原理相矛盾。我们建议通过研究关联函数对探测器之间距离的依赖关系，对时空中的纠缠态进行进一步的实验研究。

英文摘要：

Modern quantum information theory deals with an idealized situation when the spacetime dependence of quantum phenomena is neglected. However the transmission and processing of (quantum) information is a physical process in spacetime. Therefore such basic notions in quantum information theory as qubit, channel, composite systems and entangled states should be formulated in space and time. In particlular we suggest that instead of a two level system (qubit) the basic notion in a relativistic quantum information theory should be a notion of an elementary quantum system, i.e. an infinite dimensional Hilbert space $H$ invariant under an irreducible representation of the Poincare group labeled by $[m,s]$ where $m\geq 0$ is mass and $s=0,1/2,1,...$ is spin. We emphasize an importance of consideration of quantum information theory from the point of view of quantum field theory. We point out and discuss a fundamental fact that in quantum field theory there is a statistical dependence between two regions in spacetime even if they are spacelike separated. A classical probabilistic representation for a family of correlation functions in quantum field theory is obtained. Entangled states in space and time are considered. It is shown that any reasonable state in relativistic quantum field theory becomes disentangled (factorizable) at large spacelike distances if one makes local observations. As a result a violation of Bell`s inequalities can be observed without inconsistency with principles of relativistic quantum theory only if the distance between detectors is rather small. We suggest a further experimental study of entangled states in spacetime by studying the dependence of the correlation functions on the distance between detectors.

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