Transformations between symmetric sets of quantum states

We investigate probabilistic transformations of quantum states from a `source' set to a `target' set of states. Such transforms have many applications. They can be used for tasks which include state-dependent cloning or quantum state discrimination, and as interfaces between systems whose information encodings are not related by a unitary transform, such as continuous-variable systems and finite-dimensional systems. In a probabilistic transform, information may be lost or leaked, and we explain the concepts of leak and redundancy. Following this, we show how the analysis of probabilistic transforms significantly simplifies for symmetric source and target sets of states. In particular, we give a simple linear program which solves the task of finding optimal transforms, and a method of characterizing the introduced leak and redundancy in information-theoretic terms. Using the developed techniques, we analyse a class of transforms which convert coherent states with information encoded in their relative phase to symmetric qubit states. Each of these sets of states on their own appears in many well studied quantum information protocols. Finally, we suggest an asymptotic realization based on quantum scissors.Comment: 10 pages; 5 figure

Ideal quantum protocols in the non-ideal physical world

The development of quantum protocols from conception to experimental realizations is one of the main sources of the stimulating exchange between fundamental and experimental research characteristic to quantum information processing. In this thesis we contribute to the development of two recent quantum protocols, Universal Blind Quantum Computation (UBQC) and Quantum Digital Signatures (QDS). UBQC allows a client to delegate a quantum computation to a more powerful quantum server while keeping the input and computation private. We analyse the resilience of the privacy of UBQC under imperfections. Then, we introduce approximate blindness quantifying any compromise to privacy, and propose a protocol which enables arbitrary levels of security despite imperfections. Subsequently, we investigate the adaptability of UBQC to alternative implementations with practical advantages. QDS allow a party to send a message to other parties which cannot be forged, modified or repudiated. We analyse the security properties of a first proof-of-principle experiment of QDS, implemented in an optical system. We estimate the security failure probabilities of our system as a function of protocol parameters, under all but the most general types of attacks. Additionally, we develop new techniques for analysing transformations between symmetric sets of states, utilized not only in the security proofs of QDS but in other applications as well

Combinatorial Optimization

This report summarizes the meeting on Combinatorial Optimization where new and promising developments in the field were discussed. Th

Finiteness of circulant weighing matrices of fixed weight

10.1016/j.jcta.2010.10.004Journal of Combinatorial Theory. Series A1183908-919JCBT