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

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

Tomographic measurement of nonclassical radiation states

We propose to experimentally test the nonclassicality of quantum states through homodyne tomography. For single-mode states we check violations of inequalities involving the photon-number probability. For two-mode states we test the nonclassicality by reconstructing some suitable number-operator functions. The test can be performed with available quantum efficiency of homodyne detection, by measuring the pertaining quantities on the corresponding noisy states.Comment: 5 pages, two columns, 8 eps figures, RevTe

Italian translation and cross cultural comparison with the Childhood Attachment and Relational Trauma Screen (CARTS)

Background: The Childhood Attachment and Relational Trauma Screen (CARTS) is a computer-administered survey designed to assess retrospectively the socio-ecological context in which instances of child abuse may have occurred. To date, studies supporting the validity of the CARTS have only been undertaken in English-speaking North American populations. Validation projects in other countries and cross-cultural comparisons are therefore warranted. Objective: Develop and preliminarily evaluate the psychometric properties of an Italian version of the CARTS on college students and compare such observations to data acquired from Canadian students. Method: Seventy-nine undergraduate students from the University of Padua (Italy) completed an Italian translation of the CARTS as well as measures of childhood experiences, mental health and attachment, responses to which were compared to those obtained in 288 Canadian students who completed the CARTS in English. Results: Internal consistency and convergent validity with the Childhood Trauma Questionnaire and Parental Bonding Instrument were found to be acceptable for the Italian translation. Within the Italian sample, correlation analyses suggested that CARTS Mother ratings referring to attachment and abuse were associated with romantic attachment, whereas CARTS Father ratings were significantly correlated to PTSD symptoms and other symptoms of psychopathology-distress. Significant differences between Italian and Canadian students across the relationship types for the CARTS abuse and attachment scales were found, indicating that Italian students rated their mothers and fathers as simultaneously less abusive, but also less as a source of secure attachment. Conclusions: The results of this preliminary study seem to suggest convergent validity of the Italian CARTS and the association between childhood attachment-related experiences and romantic attachment. Cultural variations were identified between Canadian and Italian students in both attachment and abuse scales. Future studies to investigate cross-cultural variations in the relational context of childhood abuse and in order to boost Italian CARTS psychometric features are warranted

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

Quantum state decorrelation

We address the general problem of removing correlations from quantum states while preserving local quantum information as much as possible. We provide a complete solution in the case of two qubits, by evaluating the minimum amount of noise that is necessary to decorrelate covariant sets of bipartite states. We show that two harmonic oscillators in arbitrary Gaussian state can be decorrelated by a Gaussian covariant map. Finally, for finite-dimensional Hilbert spaces, we prove that states obtained from most cloning channels (e.g., universal and phase-covariant cloning) can be decorrelated only at the expense of a complete erasure of information about the copied state. More generally, in finite dimension, cloning without correlations is impossible for continuous sets of states. On the contrary, for continuos variables cloning, a slight modification of the customary set-up for cloning coherent states allows one to obtain clones without correlations.Comment: 11 pages, 2 figures, RevTex

Bell Measurements and Observables

A general matrix approach to study entangled states is presented, based on operator completeness relations. Bases of unitary operators are considered, with focus on irreducible representations of groups. Bell measurements for teleportation are considered, and robustness of teleportation to various kinds of non idealities is shown.Comment: 11 pages. Elsart styl