Stellar Representation of Non-Gaussian Quantum States.

The so-called stellar formalism allows us to represent the non-Gaussian properties of single-mode quantum states by the distribution of the zeros of their Husimi Q function in phase space. We use this representation in order to derive an infinite hierarchy of single-mode states based on the number of zeros of the Husimi Q function: the stellar hierarchy. We give an operational characterization of the states in this hierarchy with the minimal number of single-photon additions needed to engineer them, and derive equivalence classes under Gaussian unitary operations.

Delayed-choice test of quantum complementarity with interfering single photons.

We report an experimental test of quantum complementarity with single-photon pulses sent into a Mach-Zehnder interferometer with an output beam splitter of adjustable reflection coefficient R. In addition, the experiment is realized in Wheeler's delayed-choice regime. Each randomly set value of R allows us to observe interference with visibility V and to obtain incomplete which-path information characterized by the distinguishability parameter D.

Experimental realization of Wheeler's delayed-choice gedanken experiment.

Wave-particle duality is strikingly illustrated by Wheeler's delayed-choice gedanken experiment, where the configuration of a two-path interferometer is chosen after a single-photon pulse has entered it: Either the interferometer is closed (that is, the two paths are recombined) and the interference is observed, or the interferometer remains open and the path followed by the photon is measured. We report an almost ideal realization of that gedanken experiment with single photons allowing unambiguous which-way measurements. The choice between open and closed configurations, made by a quantum random number generator, is relativistically separated from the entry of the photon into the interferometer.

Optimality of Gaussian attacks in continuous-variable quantum cryptography.

We analyze the asymptotic security of the family of Gaussian modulated quantum key distribution protocols for continuous-variables systems. We prove that the Gaussian unitary attack is optimal for all the considered bounds on the key rate when the first and second momenta of the canonical variables involved are known by the honest parties.

Collective attacks and unconditional security in continuous variable quantum key distribution.

We present here an information theoretic study of Gaussian collective attacks on the continuous variable key distribution protocols based on Gaussian modulation of coherent states. These attacks, overlooked in previous security studies, give a finite advantage to the eavesdropper in the experimentally relevant lossy channel, but are not powerful enough to reduce the range of the reverse reconciliation protocols. Secret key rates are given for the ideal case where Bob performs optimal collective measurements, as well as for the realistic cases where he performs homodyne or heterodyne measurements.

Continuous-variable quantum cryptography is secure against non-Gaussian attacks.

A general study of arbitrary finite-size coherent attacks against continuous-variable quantum cryptographic schemes is presented. It is shown that, if the size of the blocks that can be coherently attacked by an eavesdropper is fixed and much smaller than the key size, then the optimal attack for a given signal-to-noise ratio in the transmission line is an individual Gaussian attack. Consequently, non-Gaussian coherent attacks do not need to be considered in the security analysis of such quantum cryptosystems.

Quantum key distribution using gaussian-modulated coherent states.

Quantum continuous variables are being explored as an alternative means to implement quantum key distribution, which is usually based on single photon counting. The former approach is potentially advantageous because it should enable higher key distribution rates. Here we propose and experimentally demonstrate a quantum key distribution protocol based on the transmission of gaussian-modulated coherent states (consisting of laser pulses containing a few hundred photons) and shot-noise-limited homodyne detection; squeezed or entangled beams are not required.

Continuous variable quantum cryptography using coherent states.

We propose several methods for quantum key distribution (QKD) based on the generation and transmission of random distributions of coherent or squeezed states, and we show that they are secure against individual eavesdropping attacks. These protocols require that the transmission of the optical line between Alice and Bob is larger than 50%, but they do not rely on "sub-shot-noise" features such as squeezing. Their security is a direct consequence of the no-cloning theorem, which limits the signal-to-noise ratio of possible quantum measurements on the transmission line.