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We give a proof that the coherent information is an achievable rate for the transmission of quantum information through a noisy quantum channel. Our method is to select coding subspaces according to the unitarily invariant measure and then show that provided those subspaces are sufficiently small, any data contained within them will with high probability be… (More)

The existing unconditional security definitions of quantum key distribution (QKD) do not apply to joint attacks over QKD and the subsequent use of the resulting key. In this paper, we close this potential security gap by using a universal composability theorem for the quantum setting. We first derive a composable security definition for QKD. We then prove… (More)

The second law of thermodynamics places constraints on state transformations. It applies to systems composed of many particles, however, we are seeing that one can formulate laws of thermodynamics when only a small number of particles are interacting with a heat bath. Is there a second law of thermodynamics in this regime? Here, we find that for processes… (More)

Assume that two distant parties, Alice and Bob, as well as an adversary, Eve, have access to (quantum) systems prepared jointly according to a tripartite state ρABE. In addition, Alice and Bob can use local operations and authenticated public classical communication. Their goal is to establish a key which is unknown to Eve. We initiate the study of this… (More)

We develop a formalism of distilling classical key from quantum state in a systematic way, expanding on our previous work on secure key from bound entanglement [K. Horodecki et. al., Phys. Rev. Lett. 94 (2005)]. More detailed proofs, discussion and examples are provided for the main results. Namely, we demonstrate that all quantum cryptographic protocols… (More)

— New measures of multipartite entanglement are constructed based on two definitions of multipartite information and different methods of optimizing over extensions of the states. One is a generalization of the squashed entanglement where one takes the mutual information of parties conditioned on the state's extension and takes the infimum over such… (More)

How to reuse a one-time pad and other notes on authentication, encryption and protection of quantum information. Quantum information is a valuable resource which can be encrypted in order to protect it. We consider the size of the one-time pad that is needed to protect quantum information in a number of cases. The situation is dramatically different from… (More)