Testing the Clauser-Horne-Shimony-Holt inequality using observables with arbitrary spectrum

The Clauser-Horne-Shimony and Holt inequality applies when measurements with binary outcomes are performed on physical systems under the assumption of local realism. Testing such inequalities in the quantum realm usually involves either measurements of two--valued quantum observables or pre-defining a context dependent binning procedure. Here we establish the conditions to test the Clauser-Horne-Shimony and Holt inequality using any quantum observable. Our result applies to observables with an arbitrary spectrum and no prior knowledge of their underlying Hilbert space's dimension is required. Finally, we demonstrate the proposed general measurement strategy, that can be seen as positive operator valued measurements performed on the system, using the formalism of modular variables applied to the transverse degrees of freedom of single photons.Comment: 10 pages, 4 figures, including a new Sec.

Finite temperature reservoir engineering and entanglement dynamics

We propose experimental methods to engineer reservoirs at arbitrary temperature which are feasible with current technology. Our results generalize to mixed states the possibility of quantum state engineering through controlled decoherence. Finite temperature engineered reservoirs can lead to the experimental observation of thermal entanglement --the appearance and increase of entanglement with temperature-- to the study of the dependence of finite time disentanglement and revival with temperature, quantum thermodynamical effects, among many other applications, enlarging the comprehension of temperature dependent entanglement properties

Quantum search with non--orthogonal entangled states

We propose a classical to quantum information encoding system using non--orthogonal states and apply it to the problem of searching an element in a quantum list. We show that the proposed encoding scheme leads to an exponential gain in terms of quantum resources and, in some cases, to an exponential gain in the number of runs of the protocol. In the case where the output of the search algorithm is a quantum state with some particular physical property, the searched state is found with a single query to the introduced oracle. If the obtained quantum state must be converted back to classical information, our protocol demands a number of repetitions that scales polynomially with the number of qubits required to encode a classical string

Quantum search with modular variables

We give a dimension independent formulation of the quantum search algorithm introduced in [L. K. Grover, Phys. Rev. Lett. {\bf 79}, 325 (1997)]. This algorithm provides a quadratic gain when compared to its classical counterpart by manipulating quantum two--level systems, qubits. We show that this gain, already known to be optimal, is preserved, irrespectively of the dimension of the system used to encode quantum information. This is shown by adapting the protocol to Hilbert spaces of any dimension using the same sequence of operations/logical gates as its original qubit formulation. Our results are detailed and illustrated for a system described by continuous variables, where qubits can be encoded in infinitely many distinct states using the modular variable formalism

Generation of bright squeezed light at 1.06 μm\mu m using cascaded non-linearities in a triply resonant c.w. PPLN OPO

We have used an ultra-low threshold continuous-wave Optical Parametric Oscillator (OPO) to reduce the quantum fluctuations of the reflected pump beam below the shot noise limit. The OPO consisted of a triply resonant cavity containing a Periodically-Poled Lithium Niobate crystal pumped by a Nd:YAG laser and giving signal and idler wavelengths close to 2.12 microns and a threshold as low as 300 microwatts. We detected the quantum fluctuations of the pump beam reflected by the OPO using a slightly modified homodyne detection technique. The measured noise reduction was 30 % (inferred noise reduction at the output of the OPO 38 %).Comment: 9 pages, 6 figures, accepted in Phys. Rev. A, uses REVTeX

Quantum information processing in phase space: A modular variables approach

Binary quantum information can be fault tolerantly encoded in states defined in infinite dimensional Hilbert spaces. Such states define a computational basis, and permit a perfect equivalence between continuous and discrete universal operations. The drawback of this encoding is that the corresponding logical states are unphysical, meaning infinitely localized in phase space. We use the modular variables formalism to show that, in a number of protocols relevant for quantum information and for the realization of fundamental tests of quantum mechanics, it is possible to loosen the requirements on the logical subspace without jeopardizing their usefulness or their successful implementation. Such protocols involve measurements of appropriately chosen modular observables that permit the readout of the encoded discrete quantum information from the corresponding logical states. Finally, we demonstrate the experimental feasibility of our approach by applying it to the transverse degrees of freedom of single photons.Comment: 15 pages, 4 figure

Quantum information with modular variables

We introduce a novel strategy, based on the use of modular variables, to encode and deterministically process quantum information using states described by continuous variables. Our formalism leads to a general recipe to adapt existing quantum information protocols, originally formulated for finite dimensional quantum systems, to infinite dimensional systems described by continuous variables. This is achieved by using non unitary and non-gaussian operators, obtained from the superposition of gaussian gates, together with adaptative manipulations in qubit systems defined in infinite dimensional Hilbert spaces. We describe in details the realization of single and two qubit gates and briefly discuss their implementation in a quantum optical set-up

An alternative representation for pure symmetric states of qubits and its applications to entanglement classification

We prove that the vast majority of symmetric states of qubits can be decomposed in a unique way into a superposition of spin 1/2 coherent states. For the case of two qubits, the proposed decomposition reproduces the Schmidt decomposition and therefore, in the case of a higher number of qubits, can be considered as its generalization. We analyze the geometrical aspects of the proposed representation and its invariant properties under the action of local unitary and local invertible transformations. As an application, we identify the most general classes of entanglement and representative states for any number of qubits in a symmetric state.Comment: A qubit "flip" on the equations (13), (14) has been corrected. Equations (20), (21) have been modified in accordanc

Quantum Communication Between Remote Mechanical Resonators

Mechanical resonators represent one of the most promising candidates to mediate the interaction between different quantum technologies, bridging the gap between efficient quantum computation and long-distance quantum communication. In this letter, we introduce a novel interferometric scheme where the interaction of a mechanical resonator with input/output quantum pulses is controlled by an independent classical drive. We design protocols for state teleportation and direct quantum state transfer, between distant mechanical resonators. The proposed device, feasible with state-of-the-art technology, can serve as building block for the implementation of long-distance quantum networks of mechanical resonators

Continuous discretization of infinite dimensional Hilbert spaces

In quantum theory, observables with a continuous spectrum are known to be fundamentally different from those with a discrete and finite spectrum. While some fundamental tests and applications of quantum mechanics originally formulated for discrete variables have been translated to continuous ones, this is not the case in general. For instance, despite their importance, no experimental demonstration of nonlocality exists in the continuous variables regime. Attempts to bridge this gap and put continuous variables on a closer footing to discrete ones used dichotomization. However, this approach considers only discrete properties of the continuum, and its infinitesimal properties are not fully exploited. Here we show that it is possible to manipulate, detect and classify continuous variable states using observables with a continuous spectrum revealing properties and symmetries which are analogous to finite discrete systems. Our approach leads to an operational way to define and adapt, to arbitrary continuous quantum systems, quantum protocols and algorithms typical to discrete systems.Comment: 5 pages + Supplementary Informatio