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

A short impossibility proof of Quantum Bit Commitment

Bit commitment protocols, whose security is based on the laws of quantum mechanics alone, are generally held to be impossible on the basis of a concealment-bindingness tradeoff. A strengthened and explicit impossibility proof has been given in: G. M. D'Ariano, D. Kretschmann, D. Schlingemann, and R. F. Werner, Phys. Rev. A 76, 032328 (2007), in the Heisenberg picture and in a C*-algebraic framework, considering all conceivable protocols in which both classical and quantum information are exchanged. In the present paper we provide a new impossibility proof in the Schrodinger picture, greatly simplifying the classification of protocols and strategies using the mathematical formulation in terms of quantum combs, with each single-party strategy represented by a conditional comb. We prove that assuming a stronger notion of concealment--worst-case over the classical information histories--allows Alice's cheat to pass also the worst-case Bob's test. The present approach allows us to restate the concealment-bindingness tradeoff in terms of the continuity of dilations of probabilistic quantum combs with respect to the comb-discriminability distance.Comment: 15 pages, 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

Applications of the group SU(1,1) for quantum computation and tomography

This paper collects miscellaneous results about the group SU(1,1) that are helpful in applications in quantum optics. Moreover, we derive two new results, the first is about the approximability of SU(1,1) elements by a finite set of elementary gates, and the second is about the regularization of group identities for tomographic purposes.Comment: 11 pages, no figure

Universal and phase covariant superbroadcasting for mixed qubit states

We describe a general framework to study covariant symmetric broadcasting maps for mixed qubit states. We explicitly derive the optimal N to M superbroadcasting maps, achieving optimal purification of the single-site output copy, in both the universal and the phase covariant cases. We also study the bipartite entanglement properties of the superbroadcast states.Comment: 19 pages, 8 figures, strictly related to quant-ph/0506251 and quant-ph/051015

There exist non orthogonal quantum measurements that are perfectly repeatable

We show that, contrarily to the widespread belief, in quantum mechanics repeatable measurements are not necessarily described by orthogonal projectors--the customary paradigm of "observable". Nonorthogonal repeatability, however, occurs only for infinite dimensions. We also show that when a non orthogonal repeatable measurement is performed, the measured system retains some "memory" of the number of times that the measurement has been performed.Comment: 4 pages, 1 figure, revtex4, minor change

A relational quantum computer using only two-qubit total spin measurement and an initial supply of highly mixed single qubit states

We prove that universal quantum computation is possible using only (i) the physically natural measurement on two qubits which distinguishes the singlet from the triplet subspace, and (ii) qubits prepared in almost any three different (potentially highly mixed) states. In some sense this measurement is a `more universal' dynamical element than a universal 2-qubit unitary gate, since the latter must be supplemented by measurement. Because of the rotational invariance of the measurement used, our scheme is robust to collective decoherence in a manner very different to previous proposals - in effect it is only ever sensitive to the relational properties of the qubits.Comment: TR apologises for yet again finding a coauthor with a ridiculous middle name [12

Quantum universal detectors

We address the problem of estimating the expectation value of an arbitrary operator O via a universal measuring apparatus that is independent of O, and for which the expectation values for different operators are obtained by changing only the data-processing. The ``universal detector'' performs a joint measurement on the system and on a suitably prepared ancilla. We characterize such universal detectors, and show how they can be obtained either via Bell measurements or via local measurements and classical communication between system and ancilla.Comment: 4 pages, no figure

Informationally complete measurements and groups representation

Informationally complete measurements on a quantum system allow to estimate the expectation value of any arbitrary operator by just averaging functions of the experimental outcomes. We show that such kind of measurements can be achieved through positive-operator valued measures (POVM's) related to unitary irreducible representations of a group on the Hilbert space of the system. With the help of frame theory we provide a constructive way to evaluate the data-processing function for arbitrary operators.Comment: 9 pages, no figures, IOP style. Some new references adde

Superbroadcasting of harmonic oscillators mixed states

We consider the problem of broadcasting quantum information encoded in the displacement parameter for an harmonic oscillator, from N to M>N copies of a thermal state. We show the Weyl-Heisenberg covariant broadcasting map that optimally reduces the thermal photon number, and we prove that it minimizes the noise in conjugate quadratures at the output for general input states. We find that from two input copies broadcasting is feasible, with the possibility of simultaneous purification (superbroadcasting).Comment: 9 pages, 1 figure, revtex4, to appear in the Proceedings of ICQO2006, Minsk, May 200