Deconstruction and conditional erasure of quantum correlations

Abstract

We define the deconstruction cost of a tripartite quantum state on systems $ABE$ as the minimum rate of noise needed to apply to the $AE$ systems, such that there is negligible disturbance to the marginal state on the $BE$ systems, while the system $A$ of the resulting state is locally recoverable from the $E$ system alone. We refer to such actions as deconstruction operations and protocols implementing them as state deconstruction protocols. State deconstruction generalizes Landauer erasure of a single-party quantum state as well the erasure of correlations of a two-party quantum state. We find that the deconstruction cost of a tripartite quantum state on systems $ABE$ is equal to its conditional quantum mutual information (CQMI) $I(A;B|E)$, thus giving the CQMI an operational interpretation in terms of a state deconstruction protocol. We also define a related task called conditional erasure, in which the goal is to apply noise to systems $AE$ in order to decouple system $A$ from systems $BE$, while causing negligible disturbance to the marginal state of systems $BE$. We find that the optimal rate of noise for conditional erasure is also equal to the CQMI $I(A;B|E)$. State deconstruction and conditional erasure lead to operational interpretations of the quantum discord and squashed entanglement, which are quantum correlation measures based on the CQMI. We find that the quantum discord is equal to the cost of simulating einselection, the process by which a quantum system interacts with an environment, resulting in selective loss of information in the system. The squashed entanglement is equal to half the minimum rate of noise needed for deconstruction/conditional erasure if Alice has available the best possible system $E$ to help in the deconstruction/conditional erasure task.

21 pages, 3 figures, accepted for publication in Physical Review A

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• Disentanglement Cost of Quantum States
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• Conditional quantum one-time pad
• Landauer Principle and Thermodynamics of Computation
• Thermodynamic Constraints on Quantum Information Gain and Error Correction: A Triple Trade-Off
• Communication Cost for Non-Markovianity of Tripartite Quantum States: A Resource Theoretic Approach
• One-shot quantum state redistribution and quantum Markov chains
• Censorship of Quantum Resources in Quantum Networks
• Quantum State Merging for Arbitrarily Small-Dimensional Systems
• Correlation measures of a quantum state and information characteristics of a quantum channel
• Entropy in Quantum Information Theory -- Communication and Cryptography
• Necessary conditions on effective quantum entanglement catalysts
• Operational Resource Theory of Non-Markovianity
• Quantum conditional mutual information of W state in non-inertial frames
• Classical and quantum parts of conditional mutual information for open quantum systems
• Squashed quantum non-Markovianity: a measure of genuine quantum non-Markovianity in states
• Cooperation and dependencies in multipartite systems
• The entangling power of non-entangling channels
• New monotonicity property of the quantum relative entropy
• Lower semicontinuity of the relative entropy disturbance and its corollaries