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arXiv 1004.0865quant-ph
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瞬时非定域量子测量的纠缠消耗

Entanglement consumption of instantaneous nonlocal quantum measurements

S. R. Clark, A. J. Connor, D. Jaksch, S. Popescu

摘要:

相对论因果关系对非局部变量的可测性有着戏剧性的影响,并提出了一个基本问题,即谈论非局部变量在特定时间的值是否有物理意义。最近的工作表明,通过削弱测量在制备变量本征态中的作用,实际上可以通过利用纠缠来瞬时测量所有非局域可观测量。然而,为了使这些测量方案能够成功,最初必须分配无限数量的纠缠,并且所有这些纠缠都必须被消耗掉。在这项工作中,我们锐化的瞬时非本地测量的特性明确设计方案,其中只有有限数量的最初分布的纠缠是以往任何时候都利用。这使我们能够确定一个上限的平均消耗最一般的情况下,非本地测量。这包括状态验证的任务,其中测量验证系统是否处于给定状态,以及可观测的一般本征态集的验证测量。尽管它的有限性,纠缠消耗的增长被发现显示出一个非常不利的指数的指数标度与包含施密特秩的目标状态所需的量子位的数量或在系统中的量子位的总数的操作员测量。这种缩放被认为是一个后果的组合的通用指数缩放的酉分解结合高度递归的结构,我们的计划需要克服相对论因果关系的无信号约束。

英文摘要:

Relativistic causality has dramatic consequences on the measurability of nonlocal variables and poses the fundamental question of whether it is physically meaningful to speak about the value of nonlocal variables at a particular time. Recent work has shown that by weakening the role of the measurement in preparing eigenstates of the variable it is in fact possible to measure all nonlocal observables instantaneously by exploiting entanglement. However, for these measurement schemes to succeed with certainty an infinite amount of entanglement must be distributed initially and all this entanglement is necessarily consumed. In this work we sharpen the characterisation of instantaneous nonlocal measurements by explicitly devising schemes in which only a finite amount of the initially distributed entanglement is ever utilised. This enables us to determine an upper bound to the average consumption for the most general cases of nonlocal measurements. This includes the tasks of state verification, where the measurement verifies if the system is in a given state, and verification measurements of a general set of eigenstates of an observable. Despite its finiteness the growth of entanglement consumption is found to display an extremely unfavourable exponential of an exponential scaling with either the number of qubits needed to contain the Schmidt rank of the target state or total number of qubits in the system for an operator measurement. This scaling is seen to be a consequence of the combination of the generic exponential scaling of unitary decompositions combined with the highly recursive structure of our scheme required to overcome the no-signalling constraint of relativistic causality.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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