Markov Gap and Bound Entanglement in Haar Random State
arXiv:2504.04802 · doi:10.1103/7fhc-hv9x
Abstract
Bound entanglement refers to entangled states that cannot be distilled into maximally entangled states and therefore cannot directly be used in many quantum information processing protocols. We identify a relationship between bound entanglement and the Markov gap, which is introduced within holography via the entanglement wedge cross section and is related to the fidelity of the partial Markov recovery problem. We prove that a bound entangled state must have a nonzero Markov gap. Conversely, for sufficiently large systems, a state with a weakly nonzero Markov gap typically has a bound entangled or separable marginal state, where entanglement is undistillable. Furthermore, this implies that the transition from a bound entangled to a separable state originates from the properties of states with a weakly nonzero Markov gap, which may be dual to non-perturbative effects from a holographic perspective. Our results shed light on the investigation of the Markov gap and enhance interdisciplinary applications of quantum information.
References in corpus (59)
- Quantum entanglement
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- A computable measure of entanglement
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- Three qubits can be entangled in two inequivalent ways
- Topological entanglement entropy
- Detecting topological order in a ground state wave function
- Aspects of Holographic Entanglement Entropy
- Black holes and the butterfly effect
- Black holes as mirrors: quantum information in random subsystems
- Quantum Resource Theories
- Characterizing Quantum Supremacy in Near-Term Devices
- Fast Scramblers
- Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
- Quantum corrections to holographic entanglement entropy
- Robust randomized benchmarking of quantum processes
- Exact and Approximate Unitary 2-Designs: Constructions and Applications
- Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
- Holographic duality from random tensor networks
- Induced measures in the space of mixed quantum states
- Structure of states which satisfy strong subadditivity of quantum entropy with equality
- The asymptotic entanglement cost of preparing a quantum state
- Limits for entanglement measures
- Holographic Entanglement of Purification
- Holographic Mutual Information is Monogamous
- The entanglement of purification
- Quantum conditional mutual information and approximate Markov chains
- Multipartite entanglement in spin chains
- Entanglement of purification: from spin chains to holography
- The maximally entangled set of multipartite quantum states
- Statistical distribution of quantum entanglement for a random bipartite state
- Multiboundary Wormholes and Holographic Entanglement
- Spectral form factors and late time quantum chaos
- Irreversibility in asymptotic manipulations of entanglement
- On Multipartite Pure-State Entanglement
- Random matrix techniques in quantum information theory
- Entanglement Negativity at Measurement-Induced Criticality
- Entanglement Wedge Cross Sections Require Tripartite Entanglement
- Robustness of quantum Markov chains
- Random bosonic states for robust quantum metrology
- Quantum Conditional Mutual Information, Reconstructed States, and State Redistribution
- Typical entanglement of stabilizer states
- Universal tripartite entanglement in one-dimensional many-body systems
- GHZ extraction yield for multipartite stabilizer states
- Universal Spectral Correlations in the Chaotic Wave Function, and the Development of Quantum Chaos
- Entanglement negativity spectrum of random mixed states: A diagrammatic approach
- Universal recovery map for approximate Markov chains
- No second law of entanglement manipulation after all
- Entanglement thresholds for random induced states
- Entanglement of the Antisymmetric State
- Quantum Approximate Markov Chains are Thermal
- Monogamy, polygamy, and other properties of entanglement of purification
- Entanglement between two subsystems, the Wigner semicircle and extreme value statistics
- Negativity Spectra in Random Tensor Networks and Holography
- Phase transitions for random states and a semi-circle law for the partial transpose
- Reflected entropy is not a correlation measure
- Observation of entanglement negativity transition of pseudo-random mixed states
- Entanglement phase diagrams from partial transpose moments
- How not to Rényi generalize the Quantum Conditional Mutual Information