Uncertainty, Monogamy, and Locking of Quantum Correlations

Abstract

Squashed entanglement and entanglement of purification are quantum mechanical correlation measures and defined as certain minimisations of entropic quantities. We present the first non-trivial calculations of both quantities. Our results lead to the conclusion that both measures can drop by an arbitrary amount when only a single qubit of a local system is lost. This property is known as "locking" and has previously been observed for other correlation measures, such as the accessible information, entanglement cost and the logarithmic negativity. In the case of squashed entanglement, the results are obtained with the help of an inequality that can be understood as a quantum channel analogue of well-known entropic uncertainty relations. This inequality may prove a useful tool in quantum information theory. The regularised entanglement of purification is known to equal the entanglement needed to prepare a many copies of quantum state by local operations and a sublinear amount of communication. Here, monogamy of quantum entanglement (i.e., the impossibility of a system being maximally entangled with two others at the same time) leads to an exact calculation for all quantum states that are supported either on the symmetric or on the antisymmetric subspace of a dxd-dimensional system.

7 pages revtex4, no figures. v2 has improved presentation and a couple of references added

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Cited by in corpus (54)

• Quantum entanglement
• The Uncertainty Principle in the Presence of Quantum Memory
• Entropic Uncertainty Relations and their Applications
• Holographic Entanglement of Purification
• Conjectured Strong Complementary Information Tradeoff
• Quantum Reverse Shannon Theorem
• Quantum private queries
• Improved entropic uncertainty relations and information exclusion relations
• The Structure of Bipartite Quantum States - Insights from Group Theory and Cryptography
• Entropic uncertainty relations and locking: tight bounds for mutually unbiased bases
• Robustness of quantum Markov chains
• Squashed entanglement for multipartite states and entanglement measures based on the mixed convex roof
• Information theoretic treatment of tripartite systems and quantum channels
• Entropic uncertainty and measurement reversibility
• Possibility, Impossibility and Cheat-Sensitivity of Quantum Bit String Commitment
• Polygamy of Distributed Entanglement
• Approximate reversibility in the context of entropy gain, information gain, and complete positivity
• Relative entropy and squashed entanglement
• Entanglement of Purification in Many Body Systems and Symmetry Breaking
• Quantum and Classical Correlations Inside the Entanglement Wedge
• The connection between holographic entanglement and complexity of purification
• Security of quantum bit string commitment depends on the information measure
• Monogamy, polygamy, and other properties of entanglement of purification
• Complementary sequential measurements generate entanglement
• Versatile relative entropy bounds for quantum networks
• Nonvanishing of Kronecker coefficients for rectangular shapes
• On the equivalence between sharing quantum and classical secrets, and error correction
• Weak Decoupling Duality and Quantum Identification
• Exact Universal Chaos, Speed Limit, Acceleration, Planckian Transport Coefficient, "Collapse" to equilibrium, and Other Bounds in Thermal Quantum Systems
• Capacity estimation and verification of quantum channels with arbitrarily correlated errors
• Random quantum codes from Gaussian ensembles and an uncertainty relation
• Towards a unified approach to information-disturbance tradeoffs in quantum measurements
• Uncertainty relations and approximate quantum error correction
• Information-Disturbance Theorem for Mutually Unbiased Observables
• The Physics of Quantum Information: Complementarity, Uncertainty, and Entanglement
• Non-Additivity of the Entanglement of Purification (Beyond Reasonable Doubt)
• Optimized Measures of Bipartite Quantum Correlation
• Quantum preparation uncertainty and lack of information
• Uncertainty Relation for Mutual Information
• Optimized Correlation Measures in Holography
• Public Quantum Communication and Superactivation
• Symmetric extendibility of quantum states
• Loss of Information in Quantum Guessing Game
• Gaussian intrinsic entanglement for states with partial minimum uncertainty
• Operational Resource Theory of Non-Markovianity
• Fundamental limitations to key distillation from Gaussian states with Gaussian operations
• Fate of multiparticle entanglement when one particle becomes classical
• How many ebits can be unlocked with one classical bit?
• Upper bounds on the leakage of private data and operational approach to markovianity
• Quantum Versus Classical Advantages in Secret Key Distillation (and Their Links to Quantum Entanglement)
• Quantum Uncertainty and Entropy
• Polaractivation of Hidden Private Classical Capacity Region of Quantum Channels
• Topological squashed entanglement: nonlocal order parameter for one-dimensional topological superconductors
• Quantum dimension test using the uncertainty principle