Realization of the quantum Toffoli gate with trapped ions

Algorithms for quantum information processing are usually decomposed into sequences of quantum gate operations, most often realized with single- and two- qubit gates[1]. While such operations constitute a universal set for quantum computation, gates acting on more than two qubits can simplify the implementation of complex quantum algorithms[2]. Thus, a single three-qubit operation can replace a complex sequence of two-qubit gates, which in turn promises faster execution with potentially higher Fidelity. One important three-qubit operation is the quantum Toffoli gate which performs a NOT operation on a target qubit depending on the state of two control qubits. Here we present the first experimental realization of the quantum Toffoli gate in an ion trap quantum computer. Our implementation is particular effcient as we directly encode the relevant logic information in the motion of the ion string. [1] DiVincenzo, D. P. Two-bit gates are universal for quantum computation. cond-mat/9407022, Phys.Rev. A 51, 1015-1022 (1995). [2] Chiaverini, J. et al. Realization of quantum error correction. Nature 432, 602-605 (2004).Comment: 11 pages, 2 figure

Low-dimensional quite noisy bound entanglement with cryptographic key

We provide a class of bound entangled states that have positive distillable secure key rate. The smallest state of this kind is 4 \bigotimes 4. Our class is a generalization of the class presented in [1] (IEEE Trans. Inf. Theory 54, 2621 (2008); arXiv:quant-ph/0506203). It is much wider, containing, in particular, states from the boundary of PPT entangled states (all of the states in the class in [1] were of this kind) but also states inside the set of PPT entangled states, even, approaching the separable states. This generalization comes with a price: for the wider class a positive key rate requires, in general, apart from the one-way Devetak-Winter protocol (used in [1]) also the recurrence preprocessing and thus effectively is a two-way protocol. We also analyze the amount of noise that can be admixtured to the states of our class without losing key distillability property which may be crucial for experimental realization. The wider class contains key-distillable states with higher entropy (up to 3.524, as opposed to 2.564 for the class in [1]).Comment: 10 pages, final version for J. Phys. A: Math. Theo

Design and construction of an optical test bed for LISA imaging systems and tilt-to-length coupling

The laser interferometer space antenna (LISA) is a future space-based interferometric gravitational-wave detector consisting of three spacecraft in a triangular configuration. The interferometric measurements of path length changes between satellites will be performed on optical benches in the satellites. Angular misalignments of the interfering beams couple into the length measurement and represent a significant noise source. Imaging systems will be used to reduce this tilt-to-length coupling. We designed and constructed an optical test bed to experimentally investigate tilt-to-length coupling. It consists of two separate structures, a minimal optical bench and a telescope simulator. The minimal optical bench comprises the science interferometer where the local laser is interfered with light from a remote spacecraft. In our experiment, a simulated version of this received beam is generated on the telescope simulator. The telescope simulator provides a tilting beam, a reference interferometer and an additional static beam as a phase reference. The tilting beam can either be a flat-top beam or a Gaussian beam. We avoid tilt-to-length coupling in the reference interferometer by using a small photo diode placed at an image of the beam rotation point. We show that the test bed is operational with an initial measurement of tilt-to-length coupling without imaging systems. Furthermore, we show the design of two different imaging systems whose performance will be investigated in future experiments

Robust entanglement

It is common belief among physicists that entangled states of quantum systems loose their coherence rather quickly. The reason is that any interaction with the environment which distinguishes between the entangled sub-systems collapses the quantum state. Here we investigate entangled states of two trapped Ca$^+$ ions and observe robust entanglement lasting for more than 20 seconds

Precision spectroscopy with two correlated atoms

We discuss techniques that allow for long coherence times in laser spectroscopy experiments with two trapped ions. We show that for this purpose not only entangled ions prepared in decoherence-free subspaces can be used but also a pair of ions that are not entangled but subject to the same kind of phase noise. We apply this technique to a measurement of the electric quadrupole moment of the 3d D5/2 state of 40Ca+ and to a measurement of the linewidth of an ultrastable laser exciting a pair of 40Ca+ ions

'Designer atoms' for quantum metrology

Entanglement is recognized as a key resource for quantum computation and quantum cryptography. For quantum metrology, the use of entangled states has been discussed and demonstrated as a means of improving the signal-to-noise ratio. In addition, entangled states have been used in experiments for efficient quantum state detection and for the measurement of scattering lengths. In quantum information processing, manipulation of individual quantum bits allows for the tailored design of specific states that are insensitive to the detrimental influences of an environment. Such 'decoherence-free subspaces' protect quantum information and yield significantly enhanced coherence times. Here we use a decoherence-free subspace with specifically designed entangled states to demonstrate precision spectroscopy of a pair of trapped Ca+ ions; we obtain the electric quadrupole moment, which is of use for frequency standard applications. We find that entangled states are not only useful for enhancing the signal-to-noise ratio in frequency measurements - a suitably designed pair of atoms also allows clock measurements in the presence of strong technical noise. Our technique makes explicit use of non-locality as an entanglement property and provides an approach for 'designed' quantum metrology

Experimental Demonstration of Reduced Tilt-to-length Coupling by Using Imaging Systems in Precision Interferometers

Angular misalignment of one of the interfering beams in laser interferometers can couple into the interferometric length measurement and is called tilt-to-length (TTL) coupling in the following. In the noise budget of the planned space-based gravitational-wave detector evolved Laser Interferometer Space Antenna (eLISA) [1, 2] TTL coupling is the second largest noise source after shot noise [3

Optical suppression of tilt-to-length coupling in the LISA long-arm interferometer

The arm length and the isolation in space enable the Laser Interferometer Space Antenna (LISA) to probe for signals unattainable on the ground, opening a window to the subhertz gravitational-wave universe. The coupling of unavoidable angular spacecraft jitter into the longitudinal displacement measurement, an effect known as tilt-to-length (TTL) coupling, is critical for realizing the required sensitivity of picometer / √ Hz . An ultrastable interferometer test bed has been developed in order to investigate this issue and validate mitigation strategies in a setup representative of LISA and in this paper it is operated in the long-arm interferometer configuration. The test bed is fitted with a flat-top beam generator to simulate the beam received by a LISA spacecraft. We demonstrate a reduction of TTL coupling between this flat-top beam and a Gaussian reference beam via the introduction of two- and four-lens imaging systems. TTL coupling factors below ± 25 μ m / rad for beam tilts within ± 300 μ rad are obtained by careful optimization of the system. Moreover, we show that the additional TTL coupling due to lateral-alignment errors of elements of the imaging system can be compensated by introducing lateral shifts of the detector and vice versa. These findings help validate the suitability of this noise-reduction technique for the LISA long-arm interferometer