Quorum of observables for universal quantum estimation

Any method for estimating the ensemble average of arbitrary operator (observables or not, including the density matrix) relates the quantity of interest to a complete set of observables, i.e. a quorum}. This corresponds to an expansion on an irreducible set of operators in the Liouville space. We give two general characterizations of these sets. All the known unbiased reconstruction techniques, i.e. ``quantum tomographies'', can be described in this framework. New operatorial resolutions are given that can be used to implement novel reconstruction schemes.Comment: Latex, no figure

Tomography of Quantum Operations

Quantum operations describe any state change allowed in quantum mechanics, including the evolution of an open system or the state change due to a measurement. In this letter we present a general method based on quantum tomography for measuring experimentally the matrix elements of an arbitrary quantum operation. As input the method needs only a single entangled state. The feasibility of the technique for the electromagnetic field is shown, and the experimental setup is illustrated based on homodyne tomography of a twin-beam.Comment: Submitted to Phys. Rev. Lett. 2 eps + 1 latex figure

Measuring quantum optical Hamiltonians

We show how recent state-reconstruction techniques can be used to determine the Hamiltonian of an optical device that evolves the quantum state of radiation. A simple experimental setup is proposed for measuring the Liouvillian of phase-insensitive devices. The feasibility of the method with current technology is demonstrated on the basis of Monte Carlo simulated experiments.Comment: Accepted for publication on Phys. Rev. Lett. 8 eps figures, 4 two-column pages in REVTE

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

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

Entanglement at distance: qubits versus continuous variables

We consider the problem of obtaining maximally entangled photon states at distance in the presence of loss. We compare the efficiency of two different schemes in establishing $N$ shared ebits: i) $N$ single ebit states with the qubit encoded on polarization; ii) a single continuous variable entangled state (emode) assisted by optimal local operation and classical communication (LOCC) protocol in order to obtain a $2^N$-dimensional maximally entangled state, with qubits encoded on the photon number.Comment: 5 pages. 4 eps files. Use fortschritte.sty (included