Bound entanglement maximally violating Bell inequalities: quantum entanglement is not equivalent to quantum security

Abstract

It is shown that Smolin four-qubit bound entangled states [Phys. Rev. A, 63 032306 (2001)] can maximally violate two-setting Bell inequality similar to standard CHSH inequality. Surprisingly this entanglement does not allow for secure key distillation, so neither entanglement nor violation of Bell inequalities implies quantum security. It is also pointed out how that kind of bound entanglement can be useful in reducing communication complexity.

Slightly improved version, title changed

References in corpus (6)

• No Signalling and Quantum Key Distribution
• Secure key from bound entanglement
• Entanglement as precondition for secure quantum key distribution
• Violation of Bell's inequality: criterion for quantum communication complexity advantage
• Measures of entanglement in multipartite bound entangled states
• Non-additivity of quantum capacity for multiparty communication channels

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• Experimental bound entanglement in a four-photon state
• Geometry of two-qubit states with negative conditional entropy
• Additivity and non-additivity of multipartite entanglement measures
• Quantum metrology: Heisenberg limit with bound entanglement
• Multipartite secret key distillation and bound entanglement
• Convex optimization over classes of multiparticle entanglement
• Device-Independent Certification of Genuinely Entangled Subspaces
• Multipartite nonlocality and random measurements
• Two computable sets of multipartite entanglement measures
• Searching for extremal PPT entangled states
• Bell-Correlated Activable Bound Entanglement in Multiqubit Systems
• Entanglement in a class of multiqubit mixed states without multipartite tangles
• Macroscopic bound entanglement in thermal graph states
• Multipartite unlockable bound entanglement in the stabilizer formalism
• Bound entanglement helps to reduce communication complexity
• Quantifying mixed-state quantum entanglement by optimal entanglement witness
• Constructive Interference Between Disordered Couplings Enhances Multiparty Entanglement in Quantum Heisenberg Spin Glass Models
• Family of Bell inequalities violated by higher-dimensional bound entangled states
• A simplex of bound entangled multipartite qubit states
• Any multipartite entangled state violating Mermin-Klyshko inequality can be distilled for almost all bipartite splits
• Bell's Inequalities: Foundations and Quantum Communication
• Witness Operator Provides Better Estimate of the Lower Bound of Concurrence of Bipartite Bound Entangled States in $d_1\otimes d_2$ Dimensional System
• Quantum secret sharing based on Smolin states alone
• Creating multiphoton-polarization bound-entangled states
• Multipartite bound entanglement and multi-setting Bell inequalities
• Quantum Entanglement and Geometry
• Entanglement and distillation from symmetric positive maps
• State-witness contraction
• Cooperation and dependencies in multipartite systems
• Using linear and nonlinear entanglement witnesses to generate and detect bound entangled states on an IBM quantum processor
• Beyond pure state entanglement for atomic ensembles