Witness-based quantification of non-Markovianity without complete Choi state reconstruction
Abstract
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.
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BibTeX
@misc{roy2026witnessbased,
title = {{Witness-based quantification of non-Markovianity without complete Choi state reconstruction}},
author = {Pritam Roy and Saheli Mukherjee and Bivas Mallick},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36080},
eprint = {2609.36080},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36080},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Witness-based quantification of non-Markovianity without complete Choi state reconstruction
AU - Pritam Roy
AU - Saheli Mukherjee
AU - Bivas Mallick
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36080
UR - https://arxiv.org/abs/2609.36080
AB - 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.
ER -