Measurement contextuality and Planck’s constant
Measurement contextuality and Planck’s constant
复制标题
测量背景和普朗克常数
DOI：
10.1088/1367-2630/aacef2
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发表时间：
2018
影响因子：
3.3
通讯作者：
Love, Peter
中科院分区：
文献类型：
--
作者：
Kocia, Lucas;Love, Peter
上下文是通用量子计算的必要资源，在许多情况下，经典计算机可以有效地模拟非上下文量子力学。普朗克常数 ℏ 的阶数也可用于通过扩展 ℏ 幂的感兴趣量来表征经典量子鸿沟——所有高于 ℏ 0 的阶数都可以解释为对 ℏ 0 阶项的量子修正。我们证明，有限维系统中的上下文测量具有 Wigner–Weyl–Moyal (WWM) 形式主义中的公式，需要包含高于 ℏ 0 阶的项，才能违反其期望值的经典界限。结果，我们表明，上下文作为一种资源与 WWM 形式体系中作为资源的 ℏ 的顺序密切相关。这解释了为什么量子位只能在泡利可观测量下表现出状态无关的上下文，如佩雷斯-梅明广场，而奇数维量子位也可以表现出状态依赖的上下文。特别是，当用量子位泡利可观测量测量时，无论测量的状态如何，量子位状态都会表现出上下文关系，因此这些可观测量的 Weyl 符号完全缺乏 ℏ 0 阶贡献。另一方面，奇数维 qudit 状态在由 qudit 可观测量测量时表现出上下文关系，具体取决于所测量的状态，因此奇维 qudit 可观测量通常在其 WWM 公式中拥有非零阶 ℏ 0 项及更高阶：表现出测量上下文性的奇数维 qudit 状态在其期望值中具有 ℏ 1 阶贡献，可观测量允许违反经典边界，而具有不够大的顺序 ℏ 1 贡献不表现出测量上下文。
Contextuality is a necessary resource for universal quantum computation and non-contextual quantum mechanics can be simulated efficiently by classical computers in many cases. Orders of Planck's constant, ℏ, can also be used to characterize the classical-quantum divide by expanding quantities of interest in powers of ℏ—all orders higher than ℏ 0 can be interpreted as quantum corrections to the order ℏ 0 term. We show that contextual measurements in finite-dimensional systems have formulations within the Wigner–Weyl–Moyal (WWM) formalism that require higher than order ℏ 0 terms to be included in order to violate the classical bounds on their expectation values. As a result, we show that contextuality as a resource is closely related to orders of ℏ as a resource within the WWM formalism. This offers an explanation for why qubits can only exhibit state-independent contextuality under Pauli observables as in the Peres–Mermin square while odd-dimensional qudits can also exhibit state-dependent contextuality. In particular, qubit states exhibit contextuality when measured by qubit Pauli observables regardless of the state being measured and so the Weyl symbol of these observables lack an order ℏ 0 contribution altogether. On the other hand, odd-dimensional qudit states exhibit contextuality when measured by qudit observables depending on the state measured and so odd-dimensional qudit observables generally possess non-zero order ℏ 0 terms, and higher, in their WWM formulation: odd-dimensional qudit states that exhibit measurement contextuality have an order ℏ 1 contribution in their expectation values with the observable that allows for the violation of classical bounds while states that have insufficiently large order ℏ 1 contributions do not exhibit measurement contextuality.
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DOI：
--
发表时间：
2012
期刊：
影响因子：
--
作者：
Joel J. Wallman;S. Bartlett
通讯作者：
S. Bartlett
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DOI：
--
发表时间：
2016
期刊：
影响因子：
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作者：
S. Weinberg
通讯作者：
S. Weinberg
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DOI：
--
发表时间：
1977
期刊：
影响因子：
--
作者：
F. Berezin;M. Marinov
通讯作者：
M. Marinov
影响因子：
1.7
作者：
A. Rivas;M. Saraceno;A. O. D. Almeida
通讯作者：
A. O. D. Almeida
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影响因子：
2.9
作者：
Kocia, Lucas;Huang, Yifei;Love, Peter
通讯作者：
Love, Peter