Tests of multimode quantum nonlocality with homodyne measurements

We investigate the violation of local realism in Bell tests involving homodyne measurements performed on multimode continuous-variable states. By binning the measurement outcomes in an appropriate way, we prove that the Mermin-Klyshko inequality can be violated by an amount that grows exponentially with the number of modes. Furthermore, the maximum violation allowed by quantum mechanics can be attained for any number of modes, albeit requiring a quantum state whose generation is hardly practicable. Interestingly, this exponential increase of the violation holds true even for simpler states, such as multipartite GHZ states. The resulting benefit of using more modes is shown to be significant in practical multipartite Bell tests by analyzing the increase of the robustness to noise with the number of modes. In view of the high efficiency achievable with homodyne detection, our results thus open a possible way to feasible loophole-free Bell tests that are robust to experimental imperfections. We provide an explicit example of a three-mode state (a superposition of coherent states) which results in a significantly high violation of the Mermin-Klyshko inequality (around 10%) with homodyne measurements.

Gaussian States in Quantum Information

These notes originated out of a set of lectures in Quantum Optics and Quantum Information given by one of us (MGAP) at the University of Napoli and the University of Milano. A quite broad set of issues are covered, ranging from elementary concepts to current research topics, and from fundamental concepts to applications. A special emphasis has been given to the phase space analysis of quantum dynamics and to the role of Gaussian states in continuous variable quantum information.

Thermodynamics of trajectories of a quantum harmonic oscillator coupled to N baths

We undertake a thorough analysis of the thermodynamics of the trajectories followed by a quantum harmonic oscillator coupled to $N$ dissipative baths by using a new approach to large-deviation theory inspired by phase-space quantum optics. As an illustrative example, we study the archetypal case of a harmonic oscillator coupled to two thermal baths, allowing for a comparison with the analogous classical result. In the low-temperature limit, we find a significant quantum suppression in the rate of work exchanged between the system and each bath. We further show how the presented method is capable of giving analytical results even for the case of a driven harmonic oscillator. Based on that result, we analyse the laser cooling of the motion of a trapped ion or optomechanical system, illustrating how the emission statistics can be controllably altered by the driving force.

Entanglement between two superconducting qubits via interaction with nonclassical radiation

We propose a scheme to physically interface superconducting nanocircuits and quantum optics. We address the transfer of quantum information between systems having different physical natures and defined in Hilbert spaces of different dimensions. In particular, we investigate the transfer of the entanglement initially in a nonclassical state of an infinite dimensional system to a pair of superconducting charge qubits. This setup is able to drive an initially separable state of the qubits into an almost pure, highly entangled state suitable for quantum information processing.

Nonlinearity as a resource for nonclassicality in anharmonic systems

Nonclassicality is a key ingredient for quantum enhanced technologies and experiments involving macro- scopic quantum coherence. Considering various exactly-solvable quantum-oscillator systems, we address the role played by the anharmonicity of their potential in the establishment of nonclassical features. Specifically, we show that a monotonic relation exists between the the entropic nonlinearity of the considered potentials and their ground state nonclassicality, as quantified by the negativity of the Wigner function. In addition, in order to clarify the role of squeezing--which is not captured by the negativity of the Wigner function--we focus on the Glauber-Sudarshan P-function and address the nonclassicality/nonlinearity relation using the entanglement potential. Finally, we consider the case of a generic sixth-order potential confirming the idea that nonlinearity is a resource for the generation of nonclassicality and may serve as a guideline for the engineering of quantum oscillators.

Linear Optics Simulation of Quantum Non-Markovian Dynamics

The simulation of open quantum dynamics has recently allowed the direct investigation of the features of system-environment interaction and of their consequences on the evolution of a quantum system. Such interaction threatens the quantum properties of the system, spoiling them and causing the phenomenon of decoherence. Sometimes however a coherent exchange of information takes place between system and environment, memory effects arise and the dynamics of the system becomes non-Markovian. Here we report the experimental realisation of a non-Markovian process where system and environment are coupled through a simulated transverse Ising model. By engineering the evolution in a photonic quantum simulator, we demonstrate the role played by system-environment correlations in the emergence of memory effects.

Experimental linear-optics simulation of multipartite non-locality in the ground state of a quantum Ising ring

Critical phenomena involve structural changes in the correlations of its constituents. Such changes can be reproduced and characterized in quantum simulators able to tackle medium-to-large-size systems. We demonstrate these concepts by engineering the ground state of a three-spin Ising ring by using a pair of entangled photons. The effect of a simulated magnetic field, leading to a critical modification of the correlations within the ring, is analysed by studying two- and three-spin entanglement. In particular, we connect the violation of a multipartite Bell inequality with the amount of tripartite entanglement in our ring.

Self-consistent non-Markovian theory of a quantum-state evolution for quantum-information processing

We study non-Markovian decoherence phenomena by employing projection-operator formalism when a quantum system (a quantum bit or a register of quantum bits) is coupled to a reservoir. By projecting out the degree of freedom of the reservoir, we derive a non-Markovian master equation for the system, which is reduced to a Lindblad master equation in Markovian limit, and obtain the operator sum representation for the time evolution. It is found that the system is decohered slower in the non- Markovian reservoir than the Markovian because the quantum information of the system is memorized in the non-Markovian reservoir. We discuss the potential importance of non-Markovian reservoirs for quantum-information processing.

Correspondence between continuous-variable and discrete quantum systems of arbitrary dimensions

We establish a mapping between a continuous-variable (CV) quantum system and a discrete quantum system of arbitrary dimension. This opens up the general possibility to perform any quantum information task with a CV system as if it were a discrete system. The Einstein-Podolsky-Rosen state is mapped onto the maximally entangled state in any finite-dimensional Hilbert space and thus can be considered as a universal resource of entanglement. An explicit example of the map and a proposal for its experimental realization are discussed.

Efficient quantum computation using coherent states

We study universal quantum computation using optical coherent states. A teleportation scheme for a coherent-state qubit is developed and applied to gate operations. This scheme is shown to be robust to detection inefficiency.

Quantum-information processing for a coherent superposition state via a mixed entangled coherent channel

An entangled two-mode coherent state is studied within the framework of 2 x 2-dimensional Hilbert space. An entanglement concentration scheme based on joint Bell-state measurements is worked out. When the entangled coherent state is embedded in vacuum environment, its entanglement is degraded but not totally lost. It is found that the larger the initial coherent amplitude, the faster entanglement decreases. We investigate a scheme to teleport a coherent superposition state while considering a mixed quantum channel. We find that the decohered entangled coherent state may be useless for quantum teleportation as it gives the optimal fidelity of teleportation less than the classical limit 2/3.

Simulation of quantum random walks using the interference of a classical field

We suggest a theoretical scheme for the simulation of quantum random walks on a line using beam splitters, phase shifters, and photodetectors. Our model enables us to simulate a quantum random walk using of the wave nature of classical light fields. Furthermore, the proposed setup allows the analysis of the effects of decoherence. The transition from a pure mean-photon-number distribution to a classical one is studied varying the decoherence parameters.

Quantum nonlocality test for continuous-variable states with dichotomic observables

There have been theoretical and experimental studies on quantum nonlocality for continuous variables, based on dichotomic observables. In particular, we are interested in two cases of dichotomic observables for the light field of continuous variables: One case is even and odd numbers of photons and the other case is no photon and the presence of photons. We analyze various observables to give the maximum violation of Bell's inequalities for continuous-variable states. We discuss an observable which gives the violation of Bell's inequality for any entangled pure continuous-variable state. However, it does not have to be a maximally entangled state to give the maximal violation of Bell's inequality. This is attributed to a generic problem of testing the quantum nonlocality of an infinite- dimensional state using a dichotomic observable.