基于见证者的非马尔可夫性量化：无需完整Choi态重构
Witness-based quantification of non-Markovianity without complete Choi state reconstruction
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中文总结 AI 辅助
提出基于见证者的非马尔可夫性量化框架，无需完整Choi态重构，通过正半定见证者提供RHP度量的认证下界，并在振幅阻尼和泡利动力学中简化为贝尔奇偶校验投影仪，实现高效实验量化。
中文摘要 AI 辅助
量化非马尔可夫性是开放量子系统理论中的一个基本问题，因为这对于在量子技术中利用环境记忆作为资源至关重要。然而，现有的资源理论和操作量化器通常需要中间动力学映射的完整知识，因此在实验上要求很高。在此，我们开发了一种基于见证者的非马尔可夫性量化框架，该框架绕过了与中间动力学映射相关的Choi态的完整重构。我们首先证明，每个非马尔可夫性见证者都提供了非马尔可夫性几何资源度量的可认证下界，并确定了该下界紧致的必要且充分条件。鉴于非正半定见证者在实际实验场景中通常难以测量，我们随后关注正半定见证者，它们可以自然地实现为正算子值测量（POVM）元素。我们证明，每个正见证者都产生了Rivas-Huelga-Plenio（RHP）度量的认证下界，从而建立了连接基于见证者的量化、RHP度量和几何距离度量的完整层级。将我们的框架应用于振幅阻尼和一般泡利动力学，我们发现最优正见证者简化为简单的贝尔奇偶校验投影仪。此外，我们表明，所得的见证者值可以直接从少量实验上可访问的关联测量中获得，从而消除了对完整Choi态重构的需求，并为开放量子系统中非马尔可夫性的量化提供了一种高效且实验上可行的方法。
英文摘要
Quantifying non-Markovianity is a fundamental problem in the theory of open quantum systems, as it is essential for exploiting environmental memory as a resource in quantum technologies. Existing resource-theoretic and operational quantifiers, however, generally require complete knowledge of the intermediate dynamical map and are therefore experimentally demanding. Here, we develop a witness-based framework for the quantification of non-Markovianity that bypasses complete reconstruction of the Choi state associated with the intermediate dynamical map. We first show that every non-Markovianity witness provides a certifiable lower bound on the geometric resource measure of non-Markovianity and identify the necessary and sufficient conditions under which this bound is tight. Motivated by the fact that non-positive-semidefinite witnesses are generally difficult to measure in real experimental scenario, we then focus on positive-semidefinite witnesses, which admit a natural implementation as positive operator valued measure (POVM) elements. We prove that every positive witness yields a certified lower bound on the Rivas--Huelga--Plenio (RHP) measure, thereby establishing a complete hierarchy connecting witness-based quantification, the RHP measure, and the geometric distance measure. Applying our framework to amplitude-damping and general Pauli dynamics, we find that the optimal positive witnesses reduce to simple Bell-parity projectors. Furthermore, we show that the resulting witness values can be obtained directly from a small number of experimentally accessible correlation measurements, thereby eliminating the need for complete Choi-state reconstruction and providing an efficient and experimentally feasible approach for the quantification of non-Markovianity in open quantum systems.
发表机构
- S. N. Bose National Centre for Basic Sciences（S.N. 玻色基础科学国家中心）
- Statistics and Mathematics Unit, Indian Statistical Institute（印度统计学院统计与数学单元）
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