Operational memory detection and compression
For a specified set of multi-time interventions, determine optimal tests for quantum memory and the minimal memory dimension or simulation cost needed to reproduce the accessible statistics within error .
Problem statement
For a specified set of multi-time interventions, determine optimal tests for quantum memory and the minimal memory dimension or simulation cost needed to reproduce the accessible statistics within error .
Lean 4
No Lean statement or proof is attached yet. Have a formalization? Share its source to add it to this problem.
Background
Different quantum memory criteria probe different data. CP-divisibility concerns a family of reduced maps; homogeneous semigroup embeddability concerns a time-independent generator; process-tensor Markovianity concerns statistics under interventions. Their inequivalence is not itself a missing definition.
What is known: The main proposals include CP-divisibility of the dynamical map (Rivas–Huelga–Plenio measure), information backflow measured by non-monotonicity of trace distance / distinguishability (Breuer–Laine–Piilo measure), negativity of decay rates in the canonical master equation, and growth of system–environment correlations. These measures disagree — a process can be non-Markovian by one and Markovian by another. A more complete, operationally grounded framework is the process tensor / quantum stochastic process formalism (Pollock–Rodríguez-Rosario–Frauenheim–Paternostro–Modi; Costa–Shrapnel), which treats multi-time statistics under interventions and gives a genuine quantum generalization of the Kolmogorov extension theorem and a clear Markov condition.
Published progress (August 2026; preprint February 2026): Kattemölle, Gulácsi and Burkard show that Pauli twirling can map divisible noise to a channel not embeddable in a Pauli semigroup. For positive nondegenerate Pauli eigenvalues, negative Pauli–Lindblad parameters diagnose failure of the specified semigroup criterion. This is not automatically a witness of multi-time memory in an implemented intervention process.
Pollock et al.'s operational Markov condition is already necessary and sufficient within its process framework. The open quantitative questions concern restricted experimental access, finite-sample witnesses, and matching upper/lower bounds on memory compression or simulation error. State whether the target norm controls all admissible interventions or only a restricted set. Related: O4, O9, C9.
Progress & source assessment
Source catalogue review: 4 September 2026. Improved indicates partial progress, including qualified preprint claims.
- [1]Breuer, Laine, Piilo, Vacchini, 'Colloquium: Non-Markovian dynamics in open quantum systems', Rev. Mod. Phys. 88, 021002 (2016) link
- [2]Pollock, Rodríguez-Rosario, Frauenheim, Paternostro, Modi, 'Non-Markovian quantum processes: complete framework and efficient characterisation', PRA 97, 012127 (2018) link
- [3]Pollock et al., 'Operational Markov condition for quantum processes', PRL 120, 040405 (2018) link
- [4]Kattemölle, Gulácsi & Burkard, 'Non-Markovianity induced by Pauli twirling', npj Quantum Information (2026) link
Recorded progress
Add yours →Nothing recorded yet. A pointer to a paper the entry is missing counts.
Machine attempts
0 recordedAttempts run against the statement below and are recorded in full, including the failures. The point is to stop the next model — and the next person — from re-walking a road that is already known to end. Each attempt costs 25 credits.
No machine attempts recorded.
Sign in to run an attempt. New accounts start with enough credits for ten.
Discussion
0 notesNotes are for clarifying the statement, flagging a missing reference, or recording why an approach fails. Claimed solutions belong in a submission, where they can be reviewed.
No notes yet.
Sign in to add a note.