Entangled coherent states versus entangled photon pairs for practical quantum information processing

We compare effects of decoherence and detection inefficiency on entangled coherent states (ECSs) and entangled photon pairs (EPPs), both of which are known to be particularly useful for quantum information processing (QIP). When decoherence effects caused by photon losses are heavy, the ECSs outperform the EPPs as quantum channels for teleportation both in fidelities and in success probabilities. On the other hand, when inefficient detectors are used, the teleportation scheme using the ECSs suffers undetected errors that result in the degradation of fidelity, while this is not the case for the teleportation scheme using the EPPs. Our study reveals the merits and demerits of the two types of entangled states in realizing practical QIP under realistic conditions.Comment: 9 pages, 6 figures, substantially revised version, to be published in Phys. Rev.

Dropping cold quantum gases on Earth over long times and large distances

We describe the non-relativistic time evolution of an ultra-cold degenerate quantum gas (bosons/fermions) falling in Earth's gravity during long times (10 sec) and over large distances (100 m). This models a drop tower experiment that is currently performed by the QUANTUS collaboration at ZARM (Bremen, Germany). Starting from the classical mechanics of the drop capsule and a single particle trapped within, we develop the quantum field theoretical description for this experimental situation in an inertial frame, the corotating frame of the Earth, as well as the comoving frame of the drop capsule. Suitable transformations eliminate non-inertial forces, provided all external potentials (trap, gravity) can be approximated with a second order Taylor expansion around the instantaneous trap center. This is an excellent assumption and the harmonic potential theorem applies. As an application, we study the quantum dynamics of a cigar-shaped Bose-Einstein condensate in the Gross-Pitaevskii mean-field approximation. Due to the instantaneous transformation to the rest-frame of the superfluid wave packet, the long-distance drop (100m) can be studied easily on a numerical grid.Comment: 18 pages latex, 5 eps figures, submitte

NMR experiment factors numbers with Gauss sums

We factor the number 157573 using an NMR implementation of Gauss sums.Comment: 4 pages 5 figure

Exact decoherence to pointer states in free open quantum systems is universal

In this paper it is shown that exact decoherence to minimal uncertainty Gaussian pointer states is generic for free quantum particles coupled to a heat bath. More specifically, the paper is concerned with damped free particles linearly coupled under product initial conditions to a heat bath at arbitrary temperature, with arbitrary coupling strength and spectral densities covering the Ohmic, subohmic, and supraohmic regime. Then it is true that there exists a time t_c such that for times t>t_c the state can always be exactly represented as a mixture (convex combination) of particular minimal uncertainty Gaussian states, regardless of and independent from the initial state. This exact `localisation' is hence not a feature specific to high temperatures and weak damping limit, but is rather a generic property of damped free particles.Comment: 4 pages, 1 figur

Exact number conserving phase-space dynamics of the M-site Bose-Hubbard model

The dynamics of M-site, N-particle Bose-Hubbard systems is described in quantum phase space constructed in terms of generalized SU(M) coherent states. These states have a special significance for these systems as they describe fully condensed states. Based on the differential algebra developed by Gilmore, we derive an explicit evolution equation for the (generalized) Husimi-(Q)- and Glauber-Sudarshan-(P)-distributions. Most remarkably, these evolution equations turn out to be second order differential equations where the second order terms scale as 1/N with the particle number. For large N the evolution reduces to a (classical) Liouvillian dynamics. The phase space approach thus provides a distinguished instrument to explore the mean-field many-particle crossover. In addition, the thermodynamic Bloch equation is analyzed using similar techniques.Comment: 11 pages, Revtex

Generation of a superposition of multiple mesoscopic states of radiation in a resonant cavity

Using resonant interaction between atoms and the field in a high quality cavity, we show how to generate a superposition of many mesoscopic states of the field. We study the quasi-probability distributions and demonstrate the nonclassicality of the superposition in terms of the zeroes of the Q-function as well as the negativity of the Wigner function. We discuss the decoherence of the generated superposition state. We propose homodyne techniques of the type developed by Auffeves et al [Phys. Rev. Lett. 91, 230405 (2003)] to monitor the superposition of many mesoscopic states.Comment: submitted to Phys. Rev.

Quantum bit commitment under Gaussian constraints

Quantum bit commitment has long been known to be impossible. Nevertheless, just as in the classical case, imposing certain constraints on the power of the parties may enable the construction of asymptotically secure protocols. Here, we introduce a quantum bit commitment protocol and prove that it is asymptotically secure if cheating is restricted to Gaussian operations. This protocol exploits continuous-variable quantum optical carriers, for which such a Gaussian constraint is experimentally relevant as the high optical nonlinearity needed to effect deterministic non-Gaussian cheating is inaccessible.Comment: 9 pages, 6 figure

Quantum Repeaters using Coherent-State Communication

We investigate quantum repeater protocols based upon atomic qubit-entanglement distribution through optical coherent-state communication. Various measurement schemes for an optical mode entangled with two spatially separated atomic qubits are considered in order to nonlocally prepare conditional two-qubit entangled states. In particular, generalized measurements for unambiguous state discrimination enable one to completely eliminate spin-flip errors in the resulting qubit states, as they would occur in a homodyne-based scheme due to the finite overlap of the optical states in phase space. As a result, by using weaker coherent states, high initial fidelities can still be achieved for larger repeater spacing, at the expense of lower entanglement generation rates. In this regime, the coherent-state-based protocols start resembling single-photon-based repeater schemes.Comment: 11 pages, 8 figure

Complementarity in generic open quantum systems

We develop a unified, information theoretic interpretation of the number-phase complementarity that is applicable both to finite-dimensional (atomic) and infinite-dimensional (oscillator) systems, with number treated as a discrete Hermitian observable and phase as a continuous positive operator valued measure (POVM). The relevant uncertainty principle is obtained as a lower bound on {\it entropy excess}, $X$, the difference between the entropy of one variable, typically the number, and the knowledge of its complementary variable, typically the phase, where knowledge of a variable is defined as its relative entropy with respect to the uniform distribution. In the case of finite dimensional systems, a weighting of phase knowledge by a factor $\mu$ ($> 1$) is necessary in order to make the bound tight, essentially on account of the POVM nature of phase as defined here. Numerical and analytical evidence suggests that $\mu$ tends to 1 as system dimension becomes infinite. We study the effect of non-dissipative and dissipative noise on these complementary variables for oscillator as well as atomic systems.Comment: 18 pages, 15 figures; accepted for publication in Modern Physics Letters