Optimal N-to-M Cloning of Quantum Coherent States

The cloning of continuous quantum variables is analyzed based on the concept of Gaussian cloning machines, i.e., transformations that yield copies that are Gaussian mixtures centered on the state to be copied. The optimality of Gaussian cloning machines that transform N identical input states into M output states is investigated, and bounds on the fidelity of the process are derived via a connection with quantum estimation theory. In particular, the optimal N-to-M cloning fidelity for coherent states is found to be equal to MN/(MN+M-N).Comment: 3 pages, RevTe

Universal Quantum Cloning in Cavity QED

We propose an implementation of an universal quantum cloning machine [UQCM, Hillery and Buzek, Phys. Rev. A {\bf 56}, 3446 (1997)] in a Cavity Quantum Electrodynamics (CQED) experiment. This UQCM acts on the electronic states of atoms that interact with the electromagnetic field of a high $Q$ cavity. We discuss here the specific case of the $1 \to 2$ cloning process using either a one- or a two-cavity configuration

Advancement of estimation fidelity in continuous quantum measurement

We estimate an unknown qubit from the long sequence of n random polarization measurements of precision Delta. Using the standard Ito-stochastic equations of the aposteriori state in the continuous measurement limit we calculate the advancement of fidelity. We show that the standard optimum value 2/3 is achieved asymptotically for n >> Delta^2 / 96 >> 1. We append a brief derivation of novel Ito-equations for the estimate state.Comment: 12 pp LaTe

Reversibility of continuous-variable quantum cloning

We analyze a reversibility of optimal Gaussian $1\to 2$ quantum cloning of a coherent state using only local operations on the clones and classical communication between them and propose a feasible experimental test of this feature. Performing Bell-type homodyne measurement on one clone and anti-clone, an arbitrary unknown input state (not only a coherent state) can be restored in the other clone by applying appropriate local unitary displacement operation. We generalize this concept to a partial LOCC reversal of the cloning and we show that this procedure converts the symmetric cloner to an asymmetric cloner. Further, we discuss a distributed LOCC reversal in optimal $1\to M$ Gaussian cloning of coherent states which transforms it to optimal $1\to M'$ cloning for $M'<M$. Assuming the quantum cloning as a possible eavesdropping attack on quantum communication link, the reversibility can be utilized to improve the security of the link even after the attack.Comment: 7 pages, 5 figure

Experimental detection of entanglement via witness operators and local measurements

In this paper we address the problem of detection of entanglement using only few local measurements when some knowledge about the state is given. The idea is based on an optimized decomposition of witness operators into local operators. We discuss two possible ways of optimizing this local decomposition. We present several analytical results and estimates for optimized detection strategies for NPT states of 2x2 and NxM systems, entangled states in 3 qubit systems, and bound entangled states in 3x3 and 2x4 systems.Comment: 24 pages, 2 figures. Contribution to the proceedings of the International Conference on Quantum Information in Oviedo, Spain (July 13-18, 2002). Error in W_W1-witness Eq. (35) corrected as well as minor typos. Reference adde

Optimal purification of single qubits

We introduce a new decomposition of the multiqubit states of the form $\rho^{\otimes N}$ and employ it to construct the optimal single qubit purification procedure. The same decomposition allows us to study optimal quantum cloning and state estimation of mixed states.Comment: 4 pages, 1 figur

Quantum cloning and the capacity of the Pauli channel

A family of quantum cloning machines is introduced that produce two approximate copies from a single quantum bit, while the overall input-to-output operation for each copy is a Pauli channel. A no-cloning inequality is derived, describing the balance between the quality of the two copies. This also provides an upper bound on the quantum capacity of the Pauli channel with probabilities $p_x$, $p_y$ and $p_z$. The capacity is shown to be vanishing if $(\sqrt{p_x},\sqrt{p_y},\sqrt{p_z})$ lies outside an ellipsoid whose pole coincides with the depolarizing channel that underlies the universal cloning machine.Comment: 5 pages RevTeX, 3 Postscript figure

Nonlinear dynamics of two coupled nano-electromechanical resonators

As a model of coupled nano-electromechanical resonantors we study two nonlinear driven oscillators with an arbitrary coupling strength between them. Analytical expressions are derived for the oscillation amplitudes as a function of the driving frequency and for the energy transfer rate between the two oscillators. The nonlinear restoring forces induce the expected nonlinear resonance structures in the amplitude-frequency characteristics with asymmetric resonance peaks. The corresponding multistable behavior is shown to be an efficient tool to control the energy transfer arising from the sensitive response to small changes in the driving frequency. Our results imply that the nonlinear response can be exploited to design precise sensors for mass or force detection experiments based on nano-electromechanical resonators.Comment: 19 pages, 2 figure

Distributed phase-covariant cloning with atomic ensembles via quantum Zeno dynamics

We propose an interesting scheme for distributed orbital state quantum cloning with atomic ensembles based on the quantum Zeno dynamics. These atomic ensembles which consist of identical three-level atoms are trapped in distant cavities connected by a single-mode integrated optical star coupler. These qubits can be manipulated through appropriate modulation of the coupling constants between atomic ensemble and classical field, and the cavity decay can be largely suppressed as the number of atoms in the ensemble qubits increases. The fidelity of each cloned qubit can be obtained with analytic result. The present scheme provides a new way to construct the quantum communication network.Comment: 5 pages, 4 figure

Optimal minimal measurements of mixed states

The optimal and minimal measuring strategy is obtained for a two-state system prepared in a mixed state with a probability given by any isotropic a priori distribution. We explicitly construct the specific optimal and minimal generalized measurements, which turn out to be independent of the a priori probability distribution, obtaining the best guesses for the unknown state as well as a closed expression for the maximal mean averaged fidelity. We do this for up to three copies of the unknown state in a way which leads to the generalization to any number of copies, which we then present and prove.Comment: 20 pages, no figure