Towards quantum superpositions of a mirror: an exact open systems analysis

We analyze the recently proposed mirror superposition experiment of Marshall, Simon, Penrose, and Bouwmeester, assuming that the mirror's dynamics contains a nonunitary term of the Lindblad-type proportional to -[q,[q,rho]], with q the position operator for the center of mass of the mirror, and rho the statistical operator. We derive an exact formula for the fringe visibility for this system. We discuss the consequences of our result for tests of environmental decoherence and of collapse models. In particular, we find that with the conventional parameters for the continuous spontaneous localization model of state vector collapse, maintenance of coherence is expected to within an accuracy of at least 1 part in 10(8). Increasing the apparatus coupling to environmental decoherence may lead to observable modifications of the fringe visibility, with time dependence given by our exact result.     

Quest for quantum superpositions of a mirror: High and moderately low temperatures

The Born-Markov master equation analysis of the vibrating mirror and photon experiment proposed by Marshall, Simon, Penrose, and Bouwmeester is completed by including the important issues of temperature and friction. We find that at the level of cooling available to date, visibility revivals are purely classical, and no quantum effect can be detected by the setup, no matter how strong the photon-mirror coupling is. Checking proposals of universal nonenvironmental decoherence is ruled out by dominating thermal decoherence; a conjectured coordinate-diffusion contribution to decoherence may become observable on reaching moderately low temperatures.     

Stable macroscopic quantum superpositions

We study the stability of superpositions of macroscopically distinct quantum states under decoherence. We introduce a class of quantum states with entanglement features similar to Greenberger-Horne-Zeilinger (GHZ) states, but with an inherent stability against noise and decoherence. We show that in contrast to GHZ states, these so-called concatenated GHZ states remain multipartite entangled even for macroscopic numbers of particles and can be used for quantum metrology in noisy environments. We also propose a scalable experimental realization of these states using existing ion-trap setups.     

Synthesis of quantum superpositions by quantum computation

The quantum search algorithm can be looked at as a technique for synthesizing a particular kind of superposition-one whose amplitude is concentrated in a single basis state. This basis state is defined by a binary function f(&xmacr;) that is nonzero in this desired basis state and zero everywhere else. This paper extends the quantum search algorithm to an algorithm that can create an arbitrarily specified superposition on a space of size N in O(sqrt[N] ) steps. The superposition is specified by a complex valued function f(&xmacr;) that specifies the desired amplitude of the system in basis state &xmacr;.     

Effective size of certain macroscopic quantum superpositions

Several experiments and experimental proposals for the production of macroscopic superpositions naturally lead to states of the general form /phi(1)>( multiply sign in circle N)+/phi 2 >( multiply sign in circle N), where the number of subsystems N is very large, but the states of the individual subsystems have large overlap, // 2=1-epsilon 2. We propose two different methods for assigning an effective particle number to such states, using ideal Greenberger-Horne-Zeilinger states of the form /0>( multiply sign in circle n)+/1>( multiply sign in circle n) as a standard of comparison. The two methods are based on decoherence and on a distillation protocol, respectively. Both lead to an effective size n of the order of N epsilon 2.     

Quantification of macroscopic quantum superpositions within phase space

Based on phase-space structures of quantum states, we propose a novel measure to quantify macroscopic quantum superpositions. Our measure simultaneously quantifies two different kinds of essential information for a given quantum state in a harmonious manner: the degree of quantum coherence and the effective size of the physical system that involves the superposition. It enjoys remarkably good analytical and algebraic properties. It turns out to be the most general and inclusive measure ever proposed that it can be applied to any types of multipartite states and mixed states represented in phase space.     

Large quantum superpositions and interference of massive nanometer-sized objects

We propose a method to prepare and verify spatial quantum superpositions of a nanometer-sized object separated by distances of the order of its size. This method provides unprecedented bounds for objective collapse models of the wave function by merging techniques and insights from cavity quantum optomechanics and matter-wave interferometry. An analysis and simulation of the experiment is performed taking into account standard sources of decoherence. We provide an operational parameter regime using present-day and planned technology.     

Generation of macroscopic superpositions of quantum states by linear coupling to a bath

We demonstrate through an exactly solvable model that collective coupling to any thermal bath induces effectively nonlinear couplings in a quantum many-body (multispin) system. The resulting evolution can drive an uncorrelated large-spin system with high probability into a macroscopic quantum-superposition state. We discuss possible experimental realizations.     

Towards practical quantum cryptography

Quantum cryptography bases the security of quantum key exchange on the laws of quantum physics and is likely to become the first application employing quantum effects for communication. Here we present performance tests of a new design based on polarization encoding of attenuated, coherent light pulses. Our measurements show that this compact setup can achieve an effective key-bit rate in the kHz range with low alignment requirements and thus offers the tools for fast and user-friendly quantum key exchange. Received: 27 July 1999 / Revised version: 3 September 1999 / Published online: 10 November 1999     

On the quantum polarization and entanglement of superpositions of two two-mode coherent states

This work discusses the entanglement and quantum polarization of superpositions of two-mode coherent states of the types |ψ₁〉 = N₁(|α, β〉 + |β, α〉) and |ψ₂〉 = N₂(|−α, −α〉 + |α, α〉). We use the concurrence to measure their entanglements and the quantum Stokes parameters and the Q function in order to analyze their polarization and degree of polarization.     

Towards optimization of quantum circuits

Any unitary operation in quantum information processing can be implemented via a sequence of simpler steps — quantum gates. However, actual implementation of a quantum gate is always imperfect and takes a finite time. Therefore, searching for a short sequence of gates — efficient quantum circuit for a given operation, is an important task. We contribute to this issue by proposing optimization of the well-known universal procedure proposed by Barenco et al. [Phys. Rev. A 52, 3457 (1995)]. We also created a computer program which realizes both Barenco’s decomposition and the proposed optimization. Furthermore, our optimization can be applied to any quantum circuit containing generalized Toffoli gates, including basic quantum gate circuits.      

Towards a spin-ensemble quantum memory for superconducting qubits

This article reviews efforts to build a new type of quantum device, which combines an ensemble of electronic spins with long coherence times, and a small-scale superconducting quantum processor. The goal is to store over long times arbitrary qubit states in orthogonal collective modes of the spin-ensemble, and to retrieve them on-demand. We first present the protocol devised for such a multi-mode quantum memory. We then describe a series of experimental results using NV (as in nitrogen vacancy) center spins in diamond, which demonstrate its main building blocks: the transfer of arbitrary quantum states from a qubit into the spin ensemble, and the multi-mode retrieval of classical microwave pulses down to the single-photon level with a Hahn-echo like sequence. A reset of the spin memory is implemented in-between two successive sequences using optical repumping of the spins.     

Geometric measure of pairwise quantum discord for superpositions of multipartite generalized coherent states

We give the explicit expressions of the pairwise quantum correlations present in superpositions of multipartite coherent states. A special attention is devoted to the evaluation of the geometric quantum discord. The dynamics of quantum correlations under a dephasing channel is analyzed. A comparison of geometric measure of quantum discord with that of concurrence shows that quantum discord in multipartite coherent states is more resilient to dissipative environments than is quantum entanglement. To illustrate our results, we consider some special superpositions of Weyl–Heisenberg, SU(2)$\mathit{SU}(2)$ and SU(1,1)$\mathit{SU}(1,1)$ coherent states which interpolate between Werner and Greenberger–Horne–Zeilinger states.     

The quantum poisson-Lie T-duality and mirror symmetry

Poisson-Lie T-duality in quantum N=2 superconformal Wess-Zumino-Novikov-Witten models is considered. The Poisson-Lie T-duality transformation rules of the super-Kac-Moody algebra currents are found from the conjecture that, as in the classical case, the quantum Poisson-Lie T-duality transformation is given by an automorphism which interchanges the isotropic subalgebras of the underlying Manin triple in one of the chirality sectors of the model. It is shown that quantum Poisson-Lie T-duality acts on the N=2 super-Virasoro algebra generators of the quantum models as a mirror symmetry acts: in one of the chirality sectors it is a trivial transformation while in another chirality sector it changes the sign of the U(1) current and interchanges the spin-3/2 currents. A generalization of Poisson-Lie T-duality for the quantum Kazama-Suzuki models is proposed. It is shown that quantum Poisson-Lie T-duality acts in these models as a mirror symmetry also. Zh. éksp. Teor. Fiz. 116, 11–25 (July 1999) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Towards hybrid circuit quantum electrodynamics with quantum dots

Cavity quantum electrodynamics allows one to study the interaction between light and matter at the most elementary level. The methods developed in this field have taught us how to probe and manipulate individual quantum systems like atoms and superconducting quantum bits with an exquisite accuracy. There is now a strong effort to extend further these methods to other quantum systems, and in particular hybrid quantum dot circuits. This could turn out to be instrumental for a noninvasive study of quantum dot circuits and a realization of scalable spin quantum bit architectures. It could also provide an interesting platform for quantum simulation of simple fermion–boson condensed matter systems. In this short review, we discuss the experimental state of the art for hybrid circuit quantum electrodynamics with quantum dots, and we present a simple theoretical modeling of experiments.