论文标题
两点能量测量方案的自洽
Self-consistency of the two-point energy measurement protocol
论文作者
论文摘要
热隔离的量子系统通过与外部工作来源相互作用而经历统一进化。两点能量测量（TPM）协议可以通过在单一演变之前和之后对系统进行理想的能量测量来定义系统和工作源之间交换的工作。但是，TPM协议中使用的理想能量测量最终是由与测量设备的单一耦合导致的，这需要与外部工作源进行相互作用。为了使TPM协议具有自洽，我们必须能够在System Plus Plus设备上执行TPM协议，从而揭示总工作分布，以便在忽略自由度的设备时，我们恢复了利息系统的原始TPM工作分布。在当前的手稿中，我们表明，只要设备最初是在能量本征态准备的，就可以满足这种自洽性。此外，我们证明，如果哈密顿仪式等同于“可观察到的指针”，那么：（i）总工作分布将满足所有系统状态和仅系统单一过程的“未衡量”的热力学第一定律； （ii）当所有系统状态与系统状态之间的单一耦合所引起的统一耦合时，所有系统状态的工作状态和仅系统状态均为唯一的系统状态，对于所有系统状态和仅系统的统一过程，总工作分布将与仅系统的工作分布相同。
A thermally isolated quantum system undergoes unitary evolution by interacting with an external work source. The two-point energy measurement (TPM) protocol defines the work exchanged between the system and the work source by performing ideal energy measurements on the system before, and after, the unitary evolution. However, the ideal energy measurements used in the TPM protocol ultimately result from a unitary coupling with a measurement apparatus, which requires an interaction with an external work source. For the TPM protocol to be self-consistent, we must be able to perform the TPM protocol on the compound of system plus apparatus, thus revealing the total work distribution, such that when ignoring the apparatus degrees of freedom, we recover the original TPM work distribution for the system of interest. In the present manuscript, we show that such self-consistency is satisfied so long as the apparatus is initially prepared in an energy eigenstate. Moreover, we demonstrate that if the apparatus Hamiltonian is equivalent to the "pointer observable", then: (i) the total work distribution will satisfy the "unmeasured" first law of thermodynamics for all system states and system-only unitary processes; and (ii) the total work distribution will be identical to the system-only work distribution, for all system states and system-only unitary processes, if and only if the unmeasured work due to the unitary coupling between system and apparatus is zero for all system states.
