Structural decomposition for quantum two-level systems

Huilong Xu, Zibo Miao, Qing Zhong Gao

The structural decomposition of two-level quantum systems has recently been established, related to various applications in quantum information science. As an extension to previous work on two-level quantum systems, this paper aims to investigate the structural properties of n-level quantum systems. We develop algebraic conditions under which the attainment of quantum back-action evading (BAE) measurements, the generation of decoherence-free (DF) subspaces and quantum non-demolition (QND) variables, as well as the existence of steadystate solutions for the Lindblad equations, can be realized. In particular, a specific coordinate transformation is explicitly constructed to facilitate the achievement of above-mentioned objectives, accompanied by an illustrative numerical example.

Ting Yu

Francisco Delgado

Quantum Information is a discipline derived from Quantum Mechanics which uses quantum systems to exploit their states as information recipients.Normally, these states are conformed by two-level systems to reproduce the binary nature underlying the classical computation structure.Quantum evolution is then controlled to reproduce convenient information processing operations.Evolution could be hard to be controlled.SU(2) decomposition procedure lets to set a binary structure of processing when a convenient basis is selected to set the dynamics description.In this work, we exploit this procedure for a generic Hamiltonian in order to set the process to reduce arbitrary states into simplest ones.For this work, we use customary SU(2) operations on local and entangled states.These operations are described in the development.They involve 1, 2 and 4-local operations meaning the number of quantum parties involved, in agreement with the decomposition procedure scope.This task is complex in spite the difficulty to set a general way to manipulate the entanglement in the system.We are particularly interested on the application of stochastic procedures based in SU(2) decomposition operations to achieve that goal.In order to have a measure of the advancement of the last task, we use the Rényi-Ingarden-Urbanik entropy to describe the whole spectrum of entanglement in the large systems through the assembling/disassembling of the state.

M. Kira, S. W. Koch

Francesca Albertini, Domenico D’Alessandro

In this paper, we consider the problem of model equivalence for quantum systems. Two models are said to be (input-output) equivalent if they give the same output for every admissible input. In the case of quantum systems, the output is the expectation value of a given observable or, more in general, a probability distribution for the result of a quantum measurement. We link the input-output equivalence of two models to the existence of a homomorphism of the underlying Lie algebra. In several cases, a Cartan decomposition of the Lie algebra su(n) is useful to find such a homomorphism and to determine the classes of equivalent models. We consider in detail the important cases of two level systems with a Cartan structure and of spin networks. In the latter case, complete results are given generalizing previous results to the case of networks of spin particles with any value of the spin. In treating this problem, we prove some instrumental results on the subalgebras of su(n) which are of independent interest.