Secure key from bound entanglement

Abstract

We characterize the set of shared quantum states which contain a cryptographically private key. This allows us to recast the theory of privacy as a paradigm closely related to that used in entanglement manipulation. It is shown that one can distill an arbitrarily secure key from bound entangled states. There are also states which have less distillable private key than the entanglement cost of the state. In general the amount of distillable key is bounded from above by the relative entropy of entanglement. Relationships between distillability and distinguishability are found for a class of states which have Bell states correlated to separable hiding states. We also describe a technique for finding states exhibiting irreversibility in entanglement distillation.

4 pages, no figures, to appear in PRL

References in corpus (13)

• Mixed State Entanglement and Quantum Error Correction
• A computable measure of entanglement
• Simple Proof of Security of the BB84 Quantum Key Distribution Protocol
• Entanglement Measures and Purification Procedures
• Quantum privacy amplification and the security of quantum cryptography over noisy channels
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Hiding classical data in multi-partite quantum states
• Unconditionally Secure Key Distribution Based on Two Nonorthogonal States
• Relating quantum privacy and quantum coherence: an operational approach
• A classical analogue of entanglement
• Quantum cryptography on noisy channels: quantum versus classical key-agreement protocols
• Unified approach to quantum capacities: towards quantum noisy coding theorem
• Entanglement Cost of Antisymmetric States and Additivity of Capacity of Some Quantum Channel

Cited by in corpus (247)

• Quantum entanglement
• The Security of Practical Quantum Key Distribution
• Entanglement detection
• Advances in Quantum Cryptography
• General Benchmarks for Quantum Repeaters
• Fundamental Limits of Repeaterless Quantum Communications
• Quantum repeaters: From quantum networks to the quantum internet
• Fundamental rate-loss tradeoff for optical quantum key distribution
• Quantum Communication With Zero-Capacity Channels
• Quantum channels and memory effects
• End-to-end capacities of a quantum communication network
• The mother of all protocols: Restructuring quantum information's family tree
• Optimal spin squeezing inequalities detect bound entanglement in spin models
• Faithful Squashed Entanglement
• Quantum channels and their entropic characteristics
• Quantum discord as a resource for quantum cryptography
• Disproving the Peres conjecture: Bell nonlocality from bipartite bound entanglement
• Entanglement and permutational symmetry
• Quantum Conference Key Agreement: A Review
• Converse bounds for private communication over quantum channels
• All entangled states are useful for channel discrimination
• General paradigm for distilling classical key from quantum states
• Theory of channel simulation and bounds for private communication
• All entangled states are useful for information processing
• Steering bound entangled states: A counterexample to the stronger Peres conjecture
• Entanglement irreversibility from quantum discord and quantum deficit
• Laser seeding attack in quantum key distribution
• Evaluation of convex roof entanglement measures
• The squashed entanglement of a quantum channel
• The private capacity of quantum channels is not additive
• General bounds for sender-receiver capacities in multipoint quantum communications
• The private classical capacity with a symmetric side channel and its application to quantum cryptography
• Gaussian bosonic synergy: quantum communication via realistic channels of zero quantum capacity
• Experimental bound entanglement in a four-photon state
• A few steps more towards NPT bound entanglement
• Tools for quantum network design
• Bound entanglement maximally violating Bell inequalities: quantum entanglement is not equivalent to quantum security
• Low dimensional bound entanglement with one-way distillable cryptographic key
• Universal Limitations on Quantum Key Distribution over a Network
• Relative Entropy Bounds on Quantum, Private and Repeater Capacities
• Principles of Quantum Communication Theory: A Modern Approach
• Structured Codes Improve the Bennett-Brassard-84 Quantum Key Rate
• Quantum key distribution based on private states: unconditional security over untrusted channels with zero quantum capacity
• Locking entanglement measures with a single qubit
• Semidefinite programming strong converse bounds for classical capacity
• Dephrasure channel and superadditivity of coherent information
• Fidelity of recovery, geometric squashed entanglement, and measurement recoverability
• Security bound of two-bases quantum key-distribution protocols using qudits
• Extensive nonadditivity of privacy
• Physical Underpinnings of Privacy
• Limitations on Quantum Key Repeaters
• Aggregating quantum repeaters for the quantum internet
• Privacy Amplification, Private States, and the Uncertainty Principle
• Bounds for multi-end communication over quantum networks
• Energy-constrained private and quantum capacities of quantum channels
• Polar codes for private and quantum communication over arbitrary channels
• Quantum and Classical Data Transmission through Completely Depolarising Channels in a Superposition of Cyclic Orders
• Capacities of repeater-assisted quantum communications
• Relative entropy and squashed entanglement
• Bound entanglement from randomized measurements
• Entanglement of the Antisymmetric State
• Quantum and private capacities of low-noise channels
• High-Dimensional Entanglement in States with Positive Partial Transposition
• Family of bound entangled states on the boundary of Peres set
• An Introduction to Quantum Entanglement: a Geometric Approach
• Noisy Preprocessing and the Distillation of Private States
• Multipartite secret key distillation and bound entanglement
• Fundamental limits on the capacities of bipartite quantum interactions
• Amortized entanglement of a quantum channel and approximately teleportation-simulable channels
• Finite-key security analysis for multilevel quantum key distribution
• Free versus Bound Entanglement: Machine learning tackling a NP-hard problem
• How to reuse a one-time pad and other notes on authentication, encryption and protection of quantum information
• Entanglement and secret-key-agreement capacities of bipartite quantum interactions and read-only memory devices
• Distillability and PPT entanglement of low-rank quantum states
• Assessing the performance of quantum repeaters for all phase-insensitive Gaussian bosonic channels
• Unconditional privacy over channels which cannot convey quantum information
• When Do Composed Maps Become Entanglement Breaking?
• Qubit-qudit states with positive partial transpose
• Upper bounds on secret key agreement over lossy thermal bosonic channels
• Versatile relative entropy bounds for quantum networks
• When does noise increase the quantum capacity?
• A class of 2^N x 2^N bound entangled states revealed by non-decomposable maps
• Amortization does not enhance the max-Rains information of a quantum channel
• Squashed entanglement and approximate private states
• Experimental generation of pseudo bound entanglement
• Complete elimination of information leakage in continuous-variable quantum communication channels
• Exact solution for the quantum and private capacities of bosonic dephasing channels
• Linear programs for entanglement and key distribution in the quantum internet
• Bound entanglement in the XY model
• Description of rank four PPT entangled states of two qutrits
• Symmetric extension in two-way quantum key distribution
• Distinguishability classes, resource sharing, and bound entanglement distribution
• Unconstrained Capacities of Quantum Key Distribution and Entanglement Distillation for Pure-Loss Bosonic Broadcast Channels
• Quantum Non-locality and Partial Transposition for Continuous-Variable Systems
• Quantum information
• Energy-constrained two-way assisted private and quantum capacities of quantum channels
• Bell-Correlated Activable Bound Entanglement in Multiqubit Systems
• Bound entangled states with a private key and their classical counterpart
• Quantum mechanical which-way experiment with an internal degree of freedom
• Experimental Activation of Bound Entanglement
• Generic nonadditivity of quantum capacity in simple channels
• For quantum information, two wrongs can make a right
• A family of nonlocal bound entangled states
• Bounds on entanglement distillation and secret key agreement for quantum broadcast channels
• Bound entangled states fit for robust experimental verification
• Upper bounds on device-independent quantum key distribution
• Channel correction via quantum erasure
• Simulation of non-Pauli Channels
• Entanglement Theory and the Quantum Simulation of Many-Body Physics
• Experimental Extraction of Secure Correlations from a Noisy Private State
• Of Local Operations and Physical Wires
• Achieving the ultimate end-to-end rates of lossy quantum communication networks
• The positive partial transpose conjecture for n=3
• Quantum states representing perfectly secure bits are always distillable
• Distributed Private Randomness Distillation
• Public and private communication with a quantum channel and a secret key
• Macroscopic bound entanglement in thermal graph states
• Highly Entangled States With Almost No Secrecy
• Construction of noisy bound entangled states and the range criterion
• Finite-resource teleportation stretching for continuous-variable systems
• Secret key capacity of the thermal-loss channel: Improving the lower bound
• Can non-private channels transmit quantum information?
• Bound entangled singlet-like states for quantum metrology
• Strong and uniform convergence in the teleportation simulation of bosonic Gaussian channels
• Multipartite unlockable bound entanglement in the stabilizer formalism
• Efficient Quantum Polar Codes Requiring No Preshared Entanglement
• Local Indistinguishability and Possibility of Hiding cbits in Activable Bound Entangled States
• Maximal Privacy Without Coherence
• Private states, quantum data hiding and the swapping of perfect secrecy
• Properties and construction of extreme bipartite states having positive partial transpose
• Work and Heat Value of Bound Entanglement
• General upper bounds for distributing conferencing keys in arbitrary quantum networks
• Perfect Quantum Privacy Implies Nonlocality
• How many mutually unbiased bases are needed to detect bound entangled states?
• Role of Bell-CHSH violation and local filtering in quantum key distribution
• Unconstrained distillation capacities of a pure-loss bosonic broadcast channel
• Upper bound on the secret key rate distillable from effective quantum correlations with imperfect detectors
• Bound entanglement in quantum phase transitions
• Five open problems in quantum information
• Quantum key distribution based on arbitrarily-weak distillable entangled states
• Nonlocal Activation of Bound Entanglement via Local Quantum Zeno Dynamics
• Entanglement properties of quantum grid states
• Collapse of the quantum correlation hierarchy links entropic uncertainty to entanglement creation
• Entanglement Distillation; A Discourse on Bound Entanglement in Quantum Information Theory
• Teleportation simulation of bosonic Gaussian channels: Strong and uniform convergence
• Efficiency in Quantum Key Distribution Protocols with Entangled Gaussian States
• Unextendible product bases, bound entangled states, and the range criterion
• Upper bounds on device-independent quantum key distribution rates in static and dynamic scenarios
• The platypus of the quantum channel zoo
• Investigating a Class of $2\otimes 2\otimes d$ Chessboard Density Matrices via Linear and Non-linear Entanglement Witnesses Constructed by Exact Convex Optimization
• Tight bounds for private communication over bosonic Gaussian channels based on teleportation simulation with optimal finite resources
• Bound entangled states with nonzero distillable key rate
• Bounds on quantum nonlocality via partial transposition
• Distillation of free entanglement from bound entangled states using weak measurements
• Non-secret correlations can be used to distribute secrecy
• Symmetric extension of bipartite quantum states and its use in quantum key distribution with two-way postprocessing
• Quantitative bound entanglement in two-qutrit states
• The Physics of Quantum Information: Complementarity, Uncertainty, and Entanglement
• Experimental determination of multipartite entanglement with incomplete information
• Bounding quantum capacities via partial orders and complementarity
• Quantum channel capacities - multiparty communication
• Family of Bell inequalities violated by higher-dimensional bound entangled states
• Relative entropy of steering: On its definition and properties
• Polar codes for private classical communication
• A class of genuinely high-dimensionally entangled states with a positive partial transpose
• Upper bounds for the secure key rate of decoy state quantum key distribution
• Quantum cryptography: theory and practice
• Bound entangled states with extremal properties
• Quantum states for perfectly secure secret sharing
• Preparation of bipartite bound entangled Gaussian states in quantum optics
• Every entangled state provides an advantage in classical communication
• Long-range multipartite quantum correlations and factorization in a one-dimensional spin-1/2 $XY$ chain
• Equivalence classes and canonical forms for two-qutrit entangled states of rank four having positive partial transpose
• Quantum privacy witness
• Entanglement of disjoint blocks in the one dimensional Spin 1 VBS
• Experimental generation of complex noisy photonic entanglement
• Is bound entanglement Lorentz invariant?
• W-like bound entangled states and secure key distillation
• Any multipartite entangled state violating Mermin-Klyshko inequality can be distilled for almost all bipartite splits
• Entanglement generation with a quantum channel and a shared state
• Increasing distillable key rate from bound entangled states by using local filtration
• Getting Something Out of Nothing
• Response in violation of Bell inequality to imperfect photon addition and subtraction in noisy squeezed states of light
• Bipartite bound entanglement in continuous variables through deGaussification
• Public Quantum Communication and Superactivation
• Introduction to quantum entanglement in many-body systems
• Improving the lower bound to the secret-key capacity of the thermal amplifier channel
• Quantum Communications Made Easy: Deterministic Models of Bosonic Channels
• Improved one-way rates for BB84 and 6-state protocols
• Performance of polar codes for quantum and private classical communication
• Characterizing generalized axisymmetric quantum states in $d\times d$ systems
• Experimental Detection of Qubit-Ququart Pseudo-Bound Entanglement using Three Nuclear Spins
• Activation of Nonmonogamous Multipartite Quantum States
• Quantifying the unextendibility of entanglement
• Symmetric extendibility of quantum states
• Maximum privacy without coherence, zero-error
• Optical fibres with memory effects and their quantum communication capacities
• Advantage Distillation for Quantum Key Distribution
• Bipartite Bound Entanglement
• Limitations on device independent key secure against non signaling adversary via the squashed non-locality
• Construction of Bound Entangled States Based on Permutation Operators
• Hybrid quantum network design against unauthorized secret-key generation, and its memory cost
• Genuine Secret-Sharing States
• Quantum cryptographic resource distillation and entanglement
• New Protocols for Conference Key and Multipartite Entanglement Distillation
• Low-dimensional quite noisy bound entanglement with cryptographic key
• Allowing leakage can increase quantum transmission
• Fully undistillable quantum states are separable
• Fundamental limitations to key distillation from Gaussian states with Gaussian operations
• Random private quantum states
• Optimal supplier of single-error-type entanglement via coherent-state transmission
• Comparative Dynamical Study of a Bound Entangled State
• Multipartite bound entanglement and multi-setting Bell inequalities
• On the geometric distance between quantum states with positive partial transposition and private states
• Creating multiphoton-polarization bound-entangled states
• Optimal allocation of quantum resources
• Seven definitions of bipartite bound entanglement
• The Role of Entanglement in Quantum Communication, and Analysis of the Detection Loophole
• Simple proof of confidentiality for private quantum channels in noisy environments
• Assisted Macroscopic Quantumness
• Quantum Wiretap Channel Coding Assisted by Noisy Correlation
• Quantum Grid States and Hybrid Graphs
• Inevitable Negativity: Additivity Commands Negative Quantum Channel Entropy
• Decomposable Pauli diagonal maps and Tensor Squares of Qubit Maps
• Quantum Information with Continuous Variable systems
• On the state space structure of tripartite quantum systems
• Entanglement Cost for Steering Assemblages
• Secret key distillation from shielded two-qubit states
• Limitations for private randomness repeaters
• Bound entanglement-assisted prepare-and-measure scenarios based on four-dimensional quantum messages
• Measurement-device-independent Schmidt number certification of all entangled states
• Effect of Quantum Information Scrambling on Bound Entangled States
• Constructing unextendible product bases from multiqubit ones
• Unextendible entanglement of quantum channels
• A non-distillability criterion for secret correlations
• Upper bounds on the leakage of private data and operational approach to markovianity
• Upper bounds on device-independent quantum key distribution rates and a revised Peres conjecture
• Geometric Discord of any arbitrary dimensional bipartite system and its application in quantum key distribution
• Additivity of quantum capacities in simple non-degradable quantum channels
• Extendibility limits quantum-secured communication and key distillation
• Quantum Versus Classical Advantages in Secret Key Distillation (and Their Links to Quantum Entanglement)
• Generation and Detection of Quantum Correlations and Entanglement on a Spin-Based Quantum Information Processor
• Information storage and transmission under Markovian noise
• Beyond pure state entanglement for atomic ensembles
• Using linear and nonlinear entanglement witnesses to generate and detect bound entangled states on an IBM quantum processor
• Unlimited quantum correlation advantage from bound entanglement
• Construction and properties of a class of private states in arbitrary dimensions