Exploiting quantum parallelism of entanglement for a complete experimental quantum characterization of a single qubit device

We present the first full experimental quantum tomographic characterization of a single-qubit device achieved with a single entangled input state. The entangled input state plays the role of all possible input states in quantum parallel on the tested device. The method can be trivially extended to any n-qubits device by just replicating the whole experimental setup n times.Comment: 4 pages in revtex4 with 4 eps figure

Adaptive Quantum Homodyne Tomography

An adaptive optimization technique to improve precision of quantum homodyne tomography is presented. The method is based on the existence of so-called null functions, which have zero average for arbitrary state of radiation. Addition of null functions to the tomographic kernels does not affect their mean values, but changes statistical errors, which can then be reduced by an optimization method that "adapts" kernels to homodyne data. Applications to tomography of the density matrix and other relevant field-observables are studied in detail.Comment: Latex (RevTex class + psfig), 9 Figs, Submitted to PR

Quantum information becomes classical when distributed to many users

Any physical transformation that equally distributes quantum information over a large number M of users can be approximated by a classical broadcasting of measurement outcomes. The accuracy of the approximation is at least of the order 1/M. In particular, quantum cloning of pure and mixed states can be approximated via quantum state estimation. As an example, for optimal qubit cloning with 10 output copies, a single user has error probability p > 0.45 in distinguishing classical from quantum output--a value close to the error probability of the random guess.Comment: 4 pages, no figures, published versio

Efficient universal programmable quantum measurements

A universal programmable detector is a device that can be tuned to perform any desired measurement on a given quantum system, by changing the state of an ancilla. With a finite dimension d for the ancilla only approximate universal programmability is possible, with "size" d=f(1/e) increasing function of the "accuracy" 1/e. In this letter we show that, much better than the exponential size known in the literature, one can achieve polynomial size. An explicit example with linear size is also presented. Finally, we show that for covariant measurements exact programmability is feasible.Comment: 4 pages, RevTex

Superbroadcasting of mixed states

We derive the optimal universal broadcasting for mixed states of qubits. We show that the nobroadcasting theorem cannot be generalized to more than a single input copy. Moreover, for four or more input copies it is even possible to purify the input states while broadcasting. We name such purifying broadcasting superbroadcasting.Comment: 4 pages, 4 figures, to appear on Phys. Rev. Let

Optimal Time-Reversal of Multi-phase Equatorial States

Even though the time-reversal is unphysical (it corresponds to the complex conjugation of the density matrix), for some restricted set of states it can be achieved unitarily, typically when there is a common de-phasing in a n-level system. However, in the presence of multiple phases (i. e. a different de-phasing for each element of an orthogonal basis occurs) the time reversal is no longer physically possible. In this paper we derive the channel which optimally approaches in fidelity the time-reversal of multi-phase equatorial states in arbitrary (finite) dimension. We show that, in contrast to the customary case of the Universal-NOT on qubits (or the universal conjugation in arbitrary dimension), the optimal phase covariant time-reversal for equatorial states is a nonclassical channel, which cannot be achieved via a measurement/preparation procedure. Unitary realizations of the optimal time-reversal channel are given with minimal ancillary dimension, exploiting the simplex structure of the optimal maps.Comment: 7 pages, minor change

Superbroadcasting and classical information

We address the problem of broadcasting N copies of a generic qubit state to M>N copies by estimating its direction and preparing a suitable output state according to the outcome of the estimate. This semiclassical broadcasting protocol is more restrictive than a general one, since it requires an intermediate step where classical information is extracted and processed. However, we prove that a suboptimal superbroadcasting, namely broadcasting with simultaneous purification of the local output states with respect to the input ones, is possible. We show that in the asymptotic limit of $M \to \infty$ the purification rate converges to the optimal one, proving the conjecture that optimal broadcasting and state estimation are asymptotically equivalent. We also show that it is possible to achieve superbroadcasting with simultaneous inversion of the Bloch vector direction (universal NOT). We prove that in this case the semiclassical procedure of state estimation and preparation turns out to be optimal. We finally analyse semiclassical superbroadcasting in the phase-covariant case.Comment: 9 pages, 2 figure

Covariant quantum measurements which maximize the likelihood

We derive the class of covariant measurements which are optimal according to the maximum likelihood criterion. The optimization problem is fully resolved in the case of pure input states, under the physically meaningful hypotheses of unimodularity of the covariance group and measurability of the stability subgroup. The general result is applied to the case of covariant state estimation for finite dimension, and to the Weyl-Heisenberg displacement estimation in infinite dimension. We also consider estimation with multiple copies, and compare collective measurements on identical copies with the scheme of independent measurements on each copy. A "continuous-variables" analogue of the measurement of direction of the angular momentum with two anti-parallel spins by Gisin and Popescu is given.Comment: 8 pages, RevTex style, submitted to Phys. Rev.

Generation of phase-coherent states

An interaction scheme involving nonlinear $\chi^{(2)}$ media is suggested for the generation of phase-coherent states (PCS). The setup is based on parametric amplification of vacuum followed by up-conversion of the resulting twin-beam. The involved nonlinear interactions are studied by the exact numerical diagonalization. An experimentally achievable working regime to approximate PCS with high conversion rate is given, and the validity of parametric approximation is discussed.Comment: To appear in PRA -- More info at http://enterprise.pv.infn.it

Operational distance and fidelity for quantum channels

We define and study a fidelity criterion for quantum channels, which we term the minimax fidelity, through a noncommutative generalization of maximal Hellinger distance between two positive kernels in classical probability theory. Like other known fidelities for quantum channels, the minimax fidelity is well-defined for channels between finite-dimensional algebras, but it also applies to a certain class of channels between infinite-dimensional algebras (explicitly, those channels that possess an operator-valued Radon--Nikodym density with respect to the trace in the sense of Belavkin--Staszewski) and induces a metric on the set of quantum channels which is topologically equivalent to the CB-norm distance between channels, precisely in the same way as the Bures metric on the density operators associated with statistical states of quantum-mechanical systems, derived from the well-known fidelity (`generalized transition probability') of Uhlmann, is topologically equivalent to the trace-norm distance.Comment: 26 pages, amsart.cls; improved intro, fixed typos, added a reference; accepted by J. Math. Phy