Transforming quantum operations: quantum supermaps

We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and measurements, quantum supermaps describe all possible transformations between elementary quantum objects (quantum systems as well as quantum devices). After giving the axiomatic definition of supermap, we prove a realization theorem, which shows that any supermap can be physically implemented as a simple quantum circuit. Applications to quantum programming, cloning, discrimination, estimation, information-disturbance trade-off, and tomography of channels are outlined.Comment: 6 pages, 1 figure, published versio

Optimization of quantum universal detectors

The expectation value of an arbitrary operator O can be obtained via a universal measuring apparatus that is independent of O, by changing only the data-processing of the outcomes. Such a ``universal detector'' performs a joint measurement on the system and on a suitable ancilla prepared in a fixed state, and is equivalent to a positive operator valued measure (POVM) for the system that is ``informationally complete''. The data processing functions generally are not unique, and we pose the problem of their optimization, providing some examples for covariant POVM's, in particular for SU(d) covariance group.Comment: 8 pages, no figures. Proceedingsof the 8th International Conference on Squeezed States and Uncertainty Relations ICSSUR' 2003, Puebla, Mexico - June 9-13, 200

Informationally complete measurements on bipartite quantum systems: comparing local with global measurements

Informationally complete measurements allow the estimation of expectation values of any operator on a quantum system, by changing only the data-processing of the measurement outcomes. In particular, an informationally complete measurement can be used to perform quantum tomography, namely to estimate the density matrix of the quantum state. The data-processing is generally nonunique, and can be optimized according to a given criterion. In this paper we provide the solution of the optimization problem which minimizes the variance in the estimation. We then consider informationally complete measurements performed over bipartite quantum systems focusing attention on universally covariant measurements, and compare their statistical efficiency when performed either locally or globally on the two systems. Among global measurements we consider the special case of Bell measurements, which allow to estimate the expectation of a restricted class of operators. We compare the variance in the three cases: local, Bell, and unrestricted global--and derive conditions for the operators to be estimated such that one type of measurement is more efficient than the other. In particular, we find that for factorized operators and Bell projectors the Bell measurement always performs better than the unrestricted global measurement, which in turn outperforms the local one. For estimation of the matrix elements of the density operator, the relative performances depend on the basis on which the state is represented, and on the matrix element being diagonal or off-diagonal, however, with the global unrestricted measurement generally performing better than the local one.Comment: 8 pages, no figure

Quantum Circuits Architecture

We present a method for optimizing quantum circuits architecture. The method is based on the notion of "quantum comb", which describes a circuit board in which one can insert variable subcircuits. The method allows one to efficiently address novel kinds of quantum information processing tasks, such as storing-retrieving, and cloning of channels.Comment: 10 eps figures + Qcircuit.te

The Thirring quantum cellular automaton

We analytically diagonalize a discrete-time on-site interacting fermionic cellular automaton in the two-particle sector. Important features of the solutions sensibly differ from those of analogous Hamiltonian models. In particular, we found a wider variety of scattering processes, we have bound states for every value of the total momentum, and there exist bound states also in the free case, where the coupling constant is null.Comment: 4 pages+references, Revtex style, 2 figures, supplemental material included as appendi

About the use of entanglement in the optical implementation of quantum information processing

We review some applications of entanglement to improve quantum measurements and communication, with the main focus on the optical implementation of quantum information processing. The evolution of continuos variable entangled states in active optical fibers is also analyzed.Comment: 8pages, invited contribution to Quant. Interf. IV (ICTP Trieste 2002

Efficient use of quantum resources for the transmission of a reference frame

We propose a covariant protocol for transmitting reference frames encoded on $N$ spins, achieving sensitivity $N^{-2}$ without the need of a pre-established reference frame and without using entanglement between sender and receiver. The protocol exploits the use of equivalent representations, which were overlooked in the previous literature.Comment: 4 pages, no figures; added new references and improved introduction. Accepted for publication on PR

The Quantum Cocktail Party

We consider the problem of decorrelating states of coupled quantum systems. The decorrelation can be seen as separation of quantum signals, in analogy to the classical problem of signal-separation rising in the so-called cocktail-party context. The separation of signals cannot be achieved perfectly, and we analyse the optimal decorrelation map in terms of added noise in the local separated states. Analytical results can be obtained both in the case of two-level quantum systems and for Gaussian states of harmonic oscillators.Comment: 4 pages, 2figures, revtex