We present a detailed experimental analysis of a free-propagating light pulse prepared in a "Schrödinger kitten" state, which is defined as a quantum superposition of "classical" coherent states with small amplitudes. This kitten state is generated by subtracting one photon from a squeezed vacuum beam, and it clearly presents a negative Wigner function. The predicted influence of the experimental parameters is in excellent agreement with the experimental results. The amplitude of the coherent states can be amplified to transform our "Schrödinger kittens" into bigger Schrödinger cats, providing an essential tool for quantum information processing.

Schrödinger's cat is a Gedankenexperiment in quantum physics, in which an atomic decay triggers the death of the cat. Because quantum physics allow atoms to remain in superpositions of states, the classical cat would then be simultaneously dead and alive. By analogy, a 'cat' state of freely propagating light can be defined as a quantum superposition of well separated quasi-classical states-it is a classical light wave that simultaneously possesses two opposite phases. Such states play an important role in fundamental tests of quantum theory and in many quantum information processing tasks, including quantum computation, quantum teleportation and precision measurements. Recently, optical Schrödinger 'kittens' were prepared; however, they are too small for most of the aforementioned applications and increasing their size is experimentally challenging. Here we demonstrate, theoretically and experimentally, a protocol that allows the generation of arbitrarily large squeezed Schrödinger cat states, using homodyne detection and photon number states as resources. We implemented this protocol with light pulses containing two photons, producing a squeezed Schrödinger cat state with a negative Wigner function. This state clearly exhibits several quantum phase-space interference fringes between the 'dead' and 'alive' components, and is large enough to become useful for quantum information processing and experimental tests of quantum theory.

We describe the observation of a "degaussification" protocol that maps individual pulses of squeezed light onto non-Gaussian states. This effect is obtained by sending a small fraction of the squeezed vacuum beam onto an avalanche photodiode, and by conditioning the single-shot homodyne detection of the remaining state upon the photon-counting events. The experimental data provide clear evidence of phase-dependent non-Gaussian statistics. This protocol is closely related to the first step of an entanglement distillation procedure for continuous variables.

We report on the implementation of a reverse-reconciliated coherent-state continuous-variable quantum key distribution system, with which we generated secret keys at a rate of more than 2 kb/s over 25 km of optical fiber. Time multiplexing is used to transmit both the signal and phase reference in the same optical fiber. Our system includes all experimental aspects required for a field implementation of a quantum key distribution setup. Real-time reverse reconciliation is achieved by using fast and efficient LDPC error correcting codes.

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We experimentally demonstrate that the entanglement between Gaussian entangled states can be increased by non-Gaussian operations. Coherent subtraction of single photons from Gaussian quadrature-entangled light pulses, created by a nondegenerate parametric amplifier, produces delocalized states with negative Wigner functions and complex structures more entangled than the initial states in terms of negativity. The experimental results are in very good agreement with the theoretical predictions.

We discuss quantum key distribution protocols using quantum continuous variables. We show that such protocols can be made secure against individual gaussian attacks regardless the transmission of the optical line between Alice and Bob. %while other ones require that the line transmission is larger than 50%. This is achieved by reversing the reconciliation procedure subsequent to the quantum transmission, that is, using Bob's instead of Alice's data to build the key. Although squeezing or entanglement may be helpful to improve the resistance to noise, they are not required for the protocols to remain secure with high losses. Therefore, these protocols can be implemented very simply by transmitting coherent states and performing homodyne detection. Here, we show that entanglement nevertheless plays a crucial role in the security analysis of coherent state protocols. Every cryptographic protocol based on displaced gaussian states turns out to be equivalent to an entanglement-based protocol, even though no entanglement is actually present. This equivalence even holds in the absence of squeezing, for coherent state protocols. This ``virtual'' entanglement is important to assess the security of these protocols as it provides an upper bound on the mutual information between Alice and Bob if they had used entanglement. The resulting security criteria are compared to the separability criterion for bipartite gaussian variables. It appears that the security thresholds are well within the entanglement region. This supports the idea that coherent state quantum cryptography may be unconditionally secure.

Quantum mechanics imposes that any amplifier that works independently on the phase of the input signal has to introduce some excess noise. The impossibility of such a noiseless amplifier is rooted into unitarity and linearity of quantum evolution. A possible way to circumvent this limitation is to interrupt such evolution via a measurement, providing a random outcome able to herald a successful -and noiseless -amplification event. Here we show a successful realisation of such an approach; we perform a full characterization of an amplified coherent state using quantum homodyne tomography, and observe a strong heralded amplification, with about 6dB gain and a noise level significantly smaller than the minimal allowed for any ordinary phase-independent device.Quantum optical detection techniques are so advanced that quantum fluctuations are the main source of noise. Therefore, when amplifying optical signals, one has to look at intrinsic limitations of the process: any amplifier cannot work independently on the phase of the input, unless some additional noise is added [1]. The origin of this limitation is that adding extra noise is needed for the output field to obey Heisenberg's uncertainty relation. Also, it is connected to the impossibility of realizing arbitrarily faithful copies of a quantum signal [2,3], and it is thus deeply rooted in the linear and unitary evolution of quantum mechanical systems.Various aspects of this limitation have been studied by using optical parametric amplifiers [4,5,6,7]. For instance, a non-degenerate optical parametric amplifier amplifies all input phases, and introduces the minimal level of added noise, which degrades the signal-to-noise ratio [1]. The same process, driven in the degenerate regime, may provide amplification preserving the signalto-noise ratio. However, this occurs in a phase-dependent fashion: only the part of the signal in phase with the pump light will be amplified, while the part which is 90 degrees out of phase with the pump will be deamplified [4,5].A more intriguing idea is to find a way to tamper with the linear evolution of quantum mechanics; this is actually possible, though non-deterministically, by conditioning our observation upon the result of a measurement [8]. Noiseless amplification can then take place, but only a fraction of the times, and the correct operation is heralded. This strategy is commonly adopted for building effective nonlinearities in linear quantum optical gates [9,10].Here we follow the proposal of Ralph and Lund [11] to demonstrate experimentally that heralded nondeterministic amplification can realise processes which would be impossible for usual amplifiers. Unlike another realisation [12], we have direct access to the output state via state tomography, so we can provide a complete description of the process, and analyse the limitations arising from non-ideal components. Our study is relevant in the long-term view of the integration of amplifiers in quantum communication lines [13].The conceptual layout of the noiseless amplifier...