Squashed quantum non-Markovianity: a measure of genuine quantum non-Markovianity in states
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| Format: | Preprint |
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2023
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| _version_ | 1866910858321330176 |
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| author | Gangwar, Rajeev Pandit, Tanmoy Goswami, Kaumudibikash Das, Siddhartha Bera, Manabendra Nath |
| author_facet | Gangwar, Rajeev Pandit, Tanmoy Goswami, Kaumudibikash Das, Siddhartha Bera, Manabendra Nath |
| contents | Quantum non-Markovianity in tripartite quantum states $ρ_{ABC}$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_18323 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Squashed quantum non-Markovianity: a measure of genuine quantum non-Markovianity in states Gangwar, Rajeev Pandit, Tanmoy Goswami, Kaumudibikash Das, Siddhartha Bera, Manabendra Nath Quantum Physics Other Condensed Matter High Energy Physics - Theory Mathematical Physics Quantum non-Markovianity in tripartite quantum states $ρ_{ABC}$ 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. |
| title | Squashed quantum non-Markovianity: a measure of genuine quantum non-Markovianity in states |
| topic | Quantum Physics Other Condensed Matter High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2311.18323 |