Existence of maximally correlated states
arXiv:1808.02453 · doi:10.1103/PhysRevA.98.052306
Abstract
A measure of total correlations cannot increase under deterministic local operations. We show that, for any number of systems, this condition alone does not guarantee the existence of maximally correlated states. Namely, there is no state that simultaneously maximizes all the measures satisfying it. If, in addition, the measures do not increase with probability unity under local measurements, then such states exist for two systems. They are the maximally entangled states. For a larger number of systems, it depends on their Hilbert space dimensions.
References in corpus (30)
- Quantum entanglement
- Mixed State Entanglement and Quantum Error Correction
- A computable measure of entanglement
- Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
- Quantifying Coherence
- Bell nonlocality
- Classical, quantum and total correlations
- Quantifying Entanglement
- The classical-quantum boundary for correlations: discord and related measures
- On the volume of the set of mixed entangled states
- Conditions for a class of entanglement transformations
- Unified View of Quantum and Classical Correlations
- Entanglement monotones
- Robustness of coherence: An operational and observable measure of quantum coherence
- The Quantum Chernoff Bound
- The resource theory of informational nonequilibrium in thermodynamics
- Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions
- Robustness of asymmetry and coherence of quantum states
- Absolute Maximal Entanglement and Quantum Secret Sharing
- Max- relative entropy of coherence: an operational coherence measure
- How entangled can two couples get?
- Absolutely maximally entangled states of seven qubits do not exist
- Unifying approach to the quantification of bipartite correlations by Bures distance
- Multipartite entanglement in 2 x 2 x n quantum systems
- A new coherence measure based on fidelity
- Monogamy inequality for any local quantum resource and entanglement
- Internal entanglement and external correlations of any form limit each other
- Coherence, Asymmetry, and Quantum Macroscopicity
- Measure-independent anomaly of nonlocality
- Optimization free measures of quantum resources