Entanglement and Geometrical Distances in Quantum Information and Quantum Cryptography

Rotem Liss, M.Sc. Thesis Seminar
Tuesday, 18.4.2017, 15:00
Taub 601
Prof. T. Mor

The counter-intuitive features of Quantum Mechanics make it possible to solve problems and perform tasks that are beyond the abilities of classical computers and classical communication devices. Entanglement is an important feature of quantum states, and it is important in quantum information, quantum communication, and quantum computing. In the main part of this talk, we provide a geometrical analysis of entanglement and separability for all the quantum mixed states that are of rank 2. For each rank-2 mixed state, we define its unique Bloch sphere (a geometrical representation of its "neighboring" states); we characterize those Bloch spheres into exactly five classes of entanglement and separability, give examples for each class, and prove that those are the only classes. Quantum Key Distribution (QKD) protocols make it possible for two parties to share a secret random key (an impossible task in classical communication). Several important QKD protocols, including the first protocol of Bennett and Brassard (BB84), have their unconditional security proved against very powerful adversaries. In this talk, we discuss a slightly different protocol, named "BB84-INFO-z", and prove it secure against a broad class of attacks (the collective attacks). Moreover, we make use of a quantum geometrical distance (the "trace distance") to make our security proof more composable than similar security proofs of BB84. The talk is self-contained and requires no prior knowledge of quantum information. The talk will be given in English.

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