Elements of information theory
Elements of information theory
Reversibility of Local Transformations of Multiparticle Entanglement
Quantum Information Processing
Information-theoretic key agreement: from weak to strong secrecy for free
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Unifying classical and quantum key distillation
TCC'07 Proceedings of the 4th conference on Theory of cryptography
New bounds in secret-key agreement: the gap between formation and secrecy extraction
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
Quantum Information & Computation
The universal composable security of quantum key distribution
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Universally composable privacy amplification against quantum adversaries
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Cryptographic distinguishability measures for quantum-mechanical states
IEEE Transactions on Information Theory
A semidefinite program for distillable entanglement
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Proof of security of quantum key distribution with two-way classical communications
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
A few steps more towards NPT bound entanglement
IEEE Transactions on Information Theory
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In this paper, we develop a formalism for distilling a classical key from a quantum state in a systematic way, expanding on our previous work on a secure key from bound entanglement (Horodecki et. al., 2005). More detailed proofs, discussion, and examples are provided of the main results. Namely, we demonstrate that all quantum cryptographic protocols can be recast in a way which looks like entanglement theory, with the only change being that instead of distilling Einstein-Podolsky-Rosen (EPR) pairs, the parties distill private states. The form of these general private states are given, and we show that there are a number of useful ways of expressing them. Some of the private states can be approximated by certain states, which are bound entangled. Thus, distillable entanglement is not a requirement for a private key. We find that such bound entangled states are useful for a cryptographic primitive we call a controlled private quantum channel (PQC). We also find a general class of states, which have negative partial transpose (are NPT), but which appear to be bound entangled. The relative entropy distance is shown to be an upper bound on the rate of a key. This allows us to compute the exact value of a distillable key for a certain class of private states.