Squashed quantum non-Markovianity: a measure of genuine quantum non-Markovianity in states

• URL: http://arxiv.org/abs/2311.18323v3
• Date: Thu, 20 Feb 2025 10:49:07 GMT
• Title: Squashed quantum non-Markovianity: a measure of genuine quantum non-Markovianity in states
• Authors: Rajeev Gangwar, Tanmoy Pandit, Kaumudibikash Goswami, Siddhartha Das, Manabendra Nath Bera,
• Abstract summary: We propose a faithful measure for non-Markovianity of genuine quantum origin called squashed quantum non-Markovianity (sQNM) It is based on the quantum conditional mutual information and is defined by the left-over non-Markovianity after squashing out all non-quantum contributions. We show that the sQNM is monogamous, continuous, convex, additive on tensor-product states, and generally super-additive.
• Score: 0.6597195879147555
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• Abstract: Quantum non-Markovianity in tripartite quantum states $\rho_{ABC}$ represents a correlation between systems $A$ and $C$ when conditioned on the system $B$ and is known to have both classical and quantum contributions. However, a systematic characterization of the latter is missing. To address this, we propose a faithful measure for non-Markovianity of genuine quantum origin called squashed quantum non-Markovianity (sQNM). It is based on the quantum conditional mutual information and is defined by the left-over non-Markovianity after squashing out all non-quantum contributions. It is lower bounded by the squashed entanglement between non-conditioning systems in the reduced state and is delimited by the extendibility of either of the non-conditioning systems. We show that the sQNM is monogamous, asymptotically continuous, convex, additive on tensor-product states, and generally super-additive. We characterize genuine quantum non-Markovianity as a resource via a convex resource theory after identifying free states with vanishing sQNM and free operations that do not increase sQNM in states. We use our resource-theoretic framework to bound the rate of state transformations under free operations and to study state transformation under non-free operations; in particular, we find the quantum communication cost from Bob ($B$) to Alice ($A$) or Charlie ($C$) is lower bounded by the change in sQNM in the states. The sQNM finds operational meaning; in particular, the optimal rate of private communication in a variant of conditional one-time pad protocol is twice the sQNM. Also, the minimum deconstruction cost for a variant of quantum deconstruction protocol is given twice the sQNM of the state.

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