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- Michal Horodecki
- 1996

We provide necessary and sufficient conditions for the separability of mixed states. As a result we obtain a simple criterion of the separability for 2 x 2 and 2 x 3 systems. Here, the positivity of the partial transposition of a state is necessary and sufficient for its separability. However, this is not the case in general. Some examples of mixtures which… (More)

- Michal Horodecki
- Quantum Information & Computation
- 2001

- Patrick M. Hayden, Michal Horodecki, Andreas J. Winter, Jon T. Yard
- Open Syst. Inform. Dynam.
- 2008

We give a short proof that the coherent information is an achievable rate for the transmission of quantum information through a noisy quantum channel. Our method is to produce random codes by performing a unitarily covariant projective measurement on a typical subspace of a tensor power state. We show that, provided the rank of each measurement operator is… (More)

- Fernando G. S. L. Brandão, Michal Horodecki, Nelly Huei Ying Ng, Jonathan Oppenheim, Stephanie Wehner
- Proceedings of the National Academy of Sciences…
- 2015

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)

- Karol Horodecki, Michal Horodecki, Pawel Horodecki, Jonathan Oppenheim
- IEEE Transactions on Information Theory
- 2009

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… (More)

- Lukasz Pankowski, Marco Piani, Michal Horodecki, Pawel Horodecki
- IEEE Transactions on Information Theory
- 2010

In this paper, existence of bound entangled states with nonpositive partial transpose (NPT) is considered. As one knows, existence of such states would in particular imply nonadditivity of distillable entanglement. Moreover, it would rule out a simple mathematical description of the set of distillable states. The particular state, known to be 1-copy… (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)

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)

- Michal Horodecki, Pawel Horodecki, Ryszard Horodecki, Debbie W. Leung, Barbara M. Terhal
- Quantum Information & Computation
- 2001

Received (received date) Revised (revised date) We derive the general formula for the capacity of a noiseless quantum channel assisted by an arbitrary amount of noisy entanglement. In the capacity formula, the role of mutual information is played by the ratio of the quantum mutual information and the von Neumann entropy of the sender's part of the noisy… (More)

- Jonathan Oppenheim, Michal Horodecki
- ArXiv
- 2003

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)