Transformations between quantum states

Kin Man Lai, Xin Wang

Finding ways to transform a quantum state to another is fundamental to quantum information processing. In this paper, we apply the sparse matrix approach to the quantum state transformation problem. In particular, we present an approach for searching for unitary matrices for quantum state transformation by directly optimizing the objective problem using the alternating direction method of multipliers. Moreover, we consider the use of group sparsity as an alternative sparsity choice in quantum state transformation problems. Our approach incorporates sparsity constraints into quantum state transformation by formulating it as a nonconvex problem. It establishes a useful framework for efficiently handling complex quantum systems and achieving precise state transformations.

Jun Song, Fan Hong‐Yi

In the context of quantum mechanics we employ the technique of integration within an ordered product of operators to recast the classical wavelet transform to a squeezing-displacing transform between the mother wavelet vector and the state vector to be transformed. In this way we propose the wavelet-transform spectrum for quantum optical states. For some typical states we obtain numerical results which imply that the spectrum can be used to recognize a variety of quantum optical states, and the inverse wavelet transform has the possibility to play a role in quantum state engineering.

Sarah Croke, Stephen Mark Barnett, Stig Stenholm

Alon E. Faraggi, Marco Matone

Vedran Dunjko, Erika Andersson

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.