J. I. Cirac

Long-distance quantum communication with atomic ensembles and linear optics

Quantum communication holds promise for absolutely secure transmission of secret messages and the faithful transfer of unknown quantum states. Photonic channels appear to be very attractive for the physical implementation of quantum communication. However, owing to losses and decoherence in the channel, the communication fidelity decreases exponentially with the channel length. Here we describe a scheme that allows the implementation of robust quantum communication over long lossy channels. The scheme involves laser manipulation of atomic ensembles, beam splitters, and single-photon detectors with moderate efficiencies, and is therefore compatible with current experimental technology. We show that the communication efficiency scales polynomially with the channel length, and hence the scheme should be operable over very long distances.

Three qubits can be entangled in two inequivalent ways

Invertible local transformations of a multipartite system are used to define equivalence classes in the set of entangled states. This classification concerns the entanglement properties of a single copy of the state. Accordingly, we say that two states have the same kind of entanglement if both of them can be obtained from the other by means of local operations and classical communication (LOCC) with nonzero probability. When applied to pure states of a three-qubit system, this approach reveals the existence of two inequivalent kinds of genuine tripartite entanglement, for which the Greenberger-Horne-Zeilinger state and a W state appear as remarkable representatives. In particular, we show that the W state retains maximally bipartite entanglement when any one of the three qubits is traced out. We generalize our results both to the case of higher-dimensional subsystems and also to more than three subsystems, for all of which we show that, typically, two randomly chosen pure states cannot be converted into each other by means of LOCC, not even with a small probability of success.

Cold Bosonic Atoms in Optical Lattices

The dynamics of an ultracold dilute gas of bosonic atoms in an optical lattice can be described by a Bose-Hubbard model where the system parameters are controlled by laser light. We study the continuous (zero temperature) quantum phase transition from the superfluid to the Mott insulator phase induced by varying the depth of the optical potential, where the Mott insulator phase corresponds to a commensurate filling of the lattice (``optical crystal). Examples for formation of Mott structures in optical lattices with a superimposed harmonic trap and in optical superlattices are presented.

Quantum state transfer and entanglement distribution among distant nodes in a quantum network

We propose a scheme to utilize photons for ideal quantum transmission between atoms located at spatially separated nodes of a quantum network. The transmission protocol employs special laser pulses that excite an atom inside an optical cavity at the sending node so that its state is mapped into a time-symmetric photon wave packet that will enter a cavity at the receiving node and be absorbed by an atom there with unit probability. Implementation of our scheme would enable reliable transfer or sharing of entanglement among spatially distant atoms.

Inseparability Criterion for Continuous Variable Systems

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 Gaussian states, this criterion turns out to be a necessary and sufficient condition for inseparability.

Entanglement of Atoms via Cold Controlled Collisions

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.

Many-particle entanglement with Bose–Einstein condensates

The possibility of creating and manipulating entangled states of systems of many particles is of significant interest for quantum information processing; such a capability could lead to new applications that rely on the basic principles of quantum mechanics. So far, up to four atoms have been entangled in a controlled way. A crucial requirement for the production of entangled states is that they can be considered pure at the single-particle level. Bose–Einstein condensates fulfil this requirement; hence it is natural to investigate whether they can also be used in some applications of quantum information. Here we propose a method to achieve substantial entanglement of a large number of atoms in a Bose–Einstein condensate. A single resonant laser pulse is applied to all the atoms in the condensate, which is then allowed to evolve freely; in this latterxa0stage, collisional interactions produce entanglement between the atoms. The technique should be realizable with present technology.

Improvement of frequency standards with quantum entanglement

The optimal precision of frequency measurements in the presence of decoherence is discussed. We analyze different preparations of n two-level systems as well as different measurement procedures. We show that standard Ramsey spectroscopy on uncorrelated atoms and optimal measurements on maximally entangled states provide the same resolution. The best resolution is achieved using partially entangled preparations with a high degree of symmetry. [S0031-9007(97)04541-9] PACS numbers: 42.50.Ar, 03.65.Bz The rapid development of laser cooling and trapping techniques has opened up new perspectives in high precision spectroscopy. Frequency standards based on laser cooled ions are expected to achieve accuracies of the order of 1 part in 10 14 10 18 [1]. In this Letter we discuss the limits to the maximum precision achievable in the spectroscopy of n two-level atoms in the presence of decoherence. This question is particularly timely in view of current efforts to improve high precision spectroscopy by means of quantum entanglement. In the present context standard Ramsey spectroscopy refers to the situation schematically depicted in Fig. 1. An ion trap is loaded with n ions initially prepared in the same internal state j0l. A Ramsey pulse of frequency v is applied to all ions. The pulse shape and duration are carefully chosen so that it drives the atomic transition j0l

A scalable quantum computer with ions in an array of microtraps

j 1 lof natural frequency v0 and prepares an equally weighted superposition of the two internal states j0l and j1l for each ion. Next the system evolves freely for a time t followed by the second Ramsey pulse. Finally, the internal state of each particle is measured. Provided that the duration of the Ramsey pulses is much smaller than the free evolution time t, the probability that an ion is found in j1l is given by

Geometric Manipulation of Trapped Ions for Quantum Computation

Quantum computers require the storage of quantum information in a set of two-level systems (called qubits), the processing of this information using quantum gates and a means of final readout. So far, only a few systems have been identified as potentially viable quantum computer models—accurate quantum control of the coherent evolution is required in order to realize gate operations, while at the same time decoherence must be avoided. Examples include quantum optical systems (such as those utilizing trapped ions or neutral atoms, cavity quantum electrodynamics and nuclear magnetic resonance) and solid state systems (using nuclear spins, quantum dots and Josephson junctions). The most advanced candidates are the quantum optical and nuclear magnetic resonance systems, and we expect that they will allow quantum computing with about ten qubits within the next few years. This is still far from the numbers required for useful applications: for example, the factorization of a 200-digit number requires about 3,500 qubits, rising to 100,000 if error correction is implemented. Scalability of proposed quantum computer architectures to many qubits is thus of central importance. Here we propose a model for an ion trap quantum computer that combines scalability (a feature usually associated with solid state proposals) with the advantages of quantum optical systems (in particular, quantum control and long decoherence times).