arXiv subjects
Publications and source records attributed to J. I. Cirac.
An inseparability criterion based on the total variance of a pair of Einstein-Podolsky-Rosen type operators is proposed for continuous variable systems. The criterion provides a sufficient condition for entanglement of any two-party continuous variable states. Furthermore, for all the Gaussian states, this criterion turns out to be a necessary and sufficient condition for inseparability.
Protocols for quantum communication between massive particles, such as atoms, are usually based on transmitting nonclassical light, and/or super-high finesse optical cavities are normally needed to enhance interaction between atoms and photons. We demonstrate a surprising result: an unknown quantum state can be teleported from one free-space atomic ensemble to the other by transmitting only coherent light. No non-classical light and no cavities are needed in the scheme, which greatly simplifies its experimental implementation.
We analyze the existence of activable bound entangled states in multi-particle systems. We first give a series of examples which illustrate some different ways in which bound entangled states can be activated by letting some of the parties to share maximally entangled states. Then, we derive necessary conditions for a state to be distillable as well as to be activable. These conditions turn out to be also sufficient for a certain family of multi-qubit states. We use these results to explicitely to construct states displaying novel properties related to bound entanglement and its activation.
We consider the case of a cubic nonlinear Schrödinger equation with an additional chaotic potential, in the sense that such a potential produces chaotic dynamics in classical mechanics. We derive and describe an appropriate semiclassical limit to such a nonlinear Schrödinger equation, using a semiclassical interpretation of the Wigner function, and relate this to the hydrodynamic limit of the Gross-Pitaevskii equation used in the context of Bose-Einstein condensation. We investigate a specific example of a Gross-Pitaevskii equation with such a chaotic potential: the one-dimensional delta-kicked harmonic oscillator, and its semiclassical limit. We explore the feasibility of experimental realization of such a system in a Bose-Einstein condensate experiment, giving a concrete proposal of how to implement such a configuration, and considering the problem of condensate depletion.
We analyze the separability properties of density operators supported on $\C^2\otimes \C^N$ whose partial transposes are positive operators. We show that if the rank of $ρ$ equals N then it is separable, and that bound entangled states have rank larger than N. We also give a separability criterion for a generic density operator such that the sum of its rank and the one of its partial transpose does not exceed 3N. If it exceeds this number we show that one can subtract product vectors until decreasing it to 3N, while keeping the positivity of $ρ$ and its partial transpose. This automatically gives us a sufficient criterion for separability for general density operators. We also prove that all density operators that remain invariant after partial transposition with respect to the first system are separable.
We present a family of 3--qubit states to which any arbitrary state can be depolarized. We fully classify those states with respect to their separability and distillability properties. This provides a sufficient condition for nonseparability and distillability for arbitrary states. We generalize our results to $N$--particle states.
We give a complete, hierarchic classification for arbitrary multi-qubit mixed states based on the separability properties of certain partitions. We introduce a family of N-qubit states to which any arbitrary state can be depolarized. This family can be viewed as the generalization of Werner states to multi-qubit systems. We fully classify those states with respect to their separability and distillability properties. This provides sufficient conditions for nonseparability and distillability for arbitrary states.
We study the distillability of a certain class of bipartite density operators which can be obtained via depolarization starting from an arbitrary one. Our results suggest that non-positivity of the partial transpose of a density operator is not a sufficient condition for distillability, when the dimension of both subsystems is higher than two.
We theoretically study specific schemes for performing a fundamental two-qubit quantum gate via controlled atomic collisions by switching microscopic potentials. In particular we calculate the fidelity of a gate operation for a configuration where a potential barrier between two atoms is instantaneously removed and restored after a certain time. Possible implementations could be based on microtraps created by magnetic and electric fields, or potentials induced by laser light.
We develop a method to entangle neutral atoms using cold controlled collisions. We analyze this method in two particular set-ups: optical lattices and magnetic micro-traps. Both offer the possibility of performing certain multi-particle operations in parallel. Using this fact, we show how to implement efficient quantum error correction and schemes for fault-tolerant computing.
We show that all density operators of 2$\times N$--dimensional quantum systems that remain invariant after partial transposition with respect to the first system are separable. Based on this criterion, we derive a sufficient separability condition for general density operators in such quantum systems. We also give a simple proof of the separability criterion in $2\times 2$--dimensional systems [A. Peres, Phys. Rev. Lett {\bf 77}, 1413 (1996)]
We analyse the use of entangled states to perform quantum computations non locally among distant nodes in a quantum network. The complexity associated with the generation of multiparticle entangled states is quantified in terms of the concept of global cost. This parameter allows us to compare the use of physical resources in different schemes. We show that for ideal channels and for a sufficiently large number of nodes, the use of maximally entangled states is advantageous over uncorrelated ones. For noisy channels, one has to use entanglement purification procedures in order to create entangled states of high fidelity. We show that under certain circumstances a quantum network supplied with a maximally entangled input still yields a smaller global cost, provided that $n$ belongs to a given interval $n\in [n_{min},n_{max}]$. The values of $n_{min}$ and $n_{max}$ crucially depend on the purification protocols used to establish the $n$-- processor entangled states, as well as on the presence of decoherence processes during the computation. The phase estimation problem has been used to illustrate this fact.
We introduce a new decomposition of the multiqubit states of the form $ρ^{\otimes N}$ 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.
We demonstrate that an appropriate sequence of laser pulses allows to condense a gas of trapped bosonic atoms into an arbitrary trap level. Such condensation is robust, can be achieved in experimentally feasible traps, and may lead to multistability and hysteresis phenomena.
We study laser cooling of two ions that are trapped in a harmonic potential and interact by Coulomb repulsion. Sideband cooling in the Lamb-Dicke regime is shown to work analogously to sideband cooling of a single ion. Outside the Lamb-Dicke regime, the incommensurable frequencies of the two vibrational modes result in a quasi-continuous energy spectrum that significantly alters the cooling dynamics. The cooling time decreases nonlinearly with the linewidth of the cooling transition, and the effect of trapping states which may slow down the cooling is considerably reduced. We show that cooling to the ground state is possible also outside the Lamb-Dicke regime. We develop the model and use Quantum Monte Carlo calculations for specific examples. We show that a rate equation treatment is a good approximation in all cases.
We study the feasibility of preparing a Bose-Einstein condensed sample of atoms in a 2D spin monopole. In this state, the atomic internal spins lie in the x-y plane, and point in the radial direction.
We show that quantum information may be transferred between atoms in different locations by using ``phantom photons'': the atoms are coupled through electromagnetic fields, but the corresponding field modes do not have to be fully populated. In the case where atoms are placed inside optical cavities, errors in quantum information processing due to photon absorption inside the cavity are diminished in this way. This effect persists up to intercavity distances of about a meter for the current levels of cavity losses, and may be useful for distributed quantum computing.
We show that by using cold controlled collisions between two atoms one can achieve conditional dynamics in moving trap potentials. We discuss implementing two qubit quantum--gates and efficient creation of highly entangled states of many atoms in optical lattices.