Distillation of secret key and entanglement from quantum states
arXiv:quant-ph/0306078 · doi:10.1098/rspa.2004.1372
Abstract
We study and solve the problem of distilling secret key from quantum states representing correlation between two parties (Alice and Bob) and an eavesdropper (Eve) via one-way public discussion: we prove a coding theorem to achieve the "wire-tapper" bound, the difference of the mutual information Alice-Bob and that of Alice-Eve, for so-called cqq-correlations, via one-way public communication. This result yields information--theoretic formulas for the distillable secret key, giving ``ultimate'' key rate bounds if Eve is assumed to possess a purification of Alice and Bob's joint state. Specialising our protocol somewhat and making it coherent leads us to a protocol of entanglement distillation via one-way LOCC (local operations and classical communication) which is asymptotically optimal: in fact we prove the so-called "hashing inequality" which says that the coherent information (i.e., the negative conditional von Neumann entropy) is an achievable EPR rate. This result is well--known to imply a whole set of distillation and capacity formulas which we briefly review.
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- Quantum Key Distribution with Imperfections: Recent Advances in Security Proofs
- Upper bounds on the leakage of private data and operational approach to markovianity
- Pilot-reference-free continuous-variable quantum key distribution with efficient decoy-state analysis
- Hybrid Quantum Cryptography from Communication Complexity
- Entanglement and private information in many-body thermal states
- Multi-user QKD using quotient graph states derived from continuous-variable dual-rail cluster states
- Post-measurement Quantum Monte Carlo
- Coordinately Assisted Distillation of Quantum Coherence in Multipartite System
- Device Independent Quantum Key Activation
- Upper bounds on device-independent quantum key distribution rates and a revised Peres conjecture
- Quantum Key Distribution by Quantum Energy Teleportation
- Squashed quantum non-Markovianity: a measure of genuine quantum non-Markovianity in states
- Resource Cost Results for Entanglement Distillation and State Merging under Source Uncertainties
- Efficient bounds on quantum communication rates via their reduced variants
- From top quarks to enhanced quantum key distribution: A Framework for Optimal Predictability of Quantum Observables
- Long-distance device-independent quantum key distribution with standard optics tools
- No real advantage of photon subtraction and displacement in continuous variable measurement device independent quantum key distribution
- One-Shot Distributed Source Simulation: As Quantum as it Can Get
- Noise is resource-contextual in quantum communication
- Extendibility limits quantum-secured communication and key distillation
- Security of Device-independent Quantum Key Distribution under Sequential Attack
- Realistic Threat Models for Fiber and Free-Space Continuous-Variable Quantum Key Distribution
- Entangling Quantum Memories at Channel Capacity
- Condition for the generation of the secret key in a BB84 like quantum key distribution protocol
- Power and limitations of distributed quantum state purification
- Maximal extension on converse monogamy of entanglement for tripartite pure states
- Finite-size security of QKD: comparison of three proof techniques
- Probe of Generic Quantum Contextuality and Nonlocal Resources for Qubits
- Dynamic LOCC Circuits for Automated Entanglement Manipulation
- Reduced State Embedding for Error Correction in Quantum Cryptography
- Error-mitigated inference of quantum network topology
- Practical high-dimensional quantum key distribution with decoy states
- Sharing classical secrets with continuous-variable entanglement: Composable security and network coding advantage
- High-dimensional quantum communication with scalable photonic entanglement in time and frequency
- Entropic uncertainty under indefinite causal order and input-output direction
- Optimal bound on long-range distillable entanglement
- Asymmetry effects in homodyne and heterodyne measurements: Positive operator-valued measures and asymptotic security of Gaussian-continuous-variable quantum key distribution
- Quantum Uncertainty and Entropy
- Capacity-Achieving Entanglement Purification Protocol for Pauli Dephasing Channel