[論文レビュー] Optimal Distillation of Non-Markovianity: Bounds, Multi-Copy Gain, and the Weak-to-Essential Transition

Gabriel M. Arantes, Bárbara Amaral+1 more|arXiv (Cornell University)|Mar 14, 2026

Quantum Information and Cryptography被引用数 0

ひとこと要約

The paper develops an algorithm to optimally distill non-Markovianity by coarse-graining multiple copies of a quantum process, showing a weakly non-Markovian channel can be converted into essentially non-Markovian via distillation.

ABSTRACT

Quantum channels generally reduce the distinguishability of quantum states, limiting information transmission and processing. Previous work introduced a protocol capable of increasing the distinguishability of states after the action of a specific quantum channel. Here we show how to systematically determine the maximal distinguishability gain achievable by this method. We develop an algorithm that identifies the optimal implementation of the protocol and applies to arbitrary quantum channels in a straightforward manner. Using this approach, we demonstrate that a weakly non-Markovian channel can effectively be converted into an essentially non-Markovian one through a distillation-like process. We further analyze the quantitative features of the optimized protocol, characterizing the conditions under which the enhancement is most pronounced. Our results provide a general framework to assess and optimize distinguishability recovery in open quantum systems.

研究の動機と目的

• Motivate and quantify the distillation of non-Markovianity in open quantum systems.
• Determine the maximal distinguishability gain achievable by a distillation protocol.
• Develop an algorithm to identify optimal coarse-graining maps for arbitrary quantum channels.
• Characterize when distillation yields a transition from weak to essential non-Markovianity.

提案手法

• Define CPTP quantum dynamics and the weak/essential non-Markovianity regimes via positivity of the intermediate map.
• Introduce a distillation protocol where n copies are processed through a coarse-graining CPTP map lambda to yield an effective single-copy dynamics.
• Derive bounds on the possible increase in distinguishability under distillation and identify saturation conditions (General Bound and Effective Bound).
• Use Stinespring-type dilations to parameterize CPTP maps and optimize over unitaries to maximize the distilled trace-distance change.
• Provide a concrete two- and three-copy analysis for a discrete-time channel model and explore the dependence on initial state pairs and ancilla dimension.

実験結果

リサーチクエスチョン

• RQ1 Can a weakly non-Markovian channel be converted into an essentially non-Markovian one through a distillation protocol?
• RQ2 What are the maximal achievable gains in state distinguishability under multi-copy coarse-graining, and when are these gains saturated?
• RQ3 How do the choice of input states and the number of copies affect the ability to distill non-Markovianity?
• RQ4 Does increasing the ancilla/dimension of the coarse-graining system improve the distilled non-Markovianity?
• RQ5 What structural conditions determine saturation of the bounds and regime transitions for general channels?

主な発見

• Optimized distillation can induce a regime change from weak to essential non-Markovianity, evidenced by positive changes in trace distance.
• The distilled change in distinguishability saturates the Effective Bound for tested cases, indicating maximal possible gain under the protocol.
• Two-copy processing can already trigger regime changes for certain initial states, while three copies can enhance effects in the weak regime.
• The choice of input states critically influences whether distillation yields significant gains; some saturating pairs show little to no improvement at two copies, while non-saturating pairs benefit notably at three copies.
• Increasing ancilla dimension beyond one qubit does not improve the distilled gain and may increase computational cost.
• Numerical optimization over the coarse-graining unitary demonstrates robustness and applicability to experimental settings.