Quantum continuous variables [1] are being explored [2,3,4,5,6,7,8,9,10,11,12,13,14] as an alternative means to implement quantum key distribution, which is usually based on single photon counting [15]. 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 [13]. Complete secret key extraction is achieved using a reverse reconciliation [14] technique followed by privacy amplification. The reverse reconciliation technique is in principle secure for any value of the line transmission, against gaussian individual attacks based on entanglement and quantum memories. Our table-top experiment yields a net key transmission rate of about 1.7 megabits per second for a loss-free line, and 75 kilobits per second for a line with losses of 3.1 dB. We anticipate that the scheme should remain effective for lines with higher losses, particularly because the present limitations are essentially technical, so that significant margin for improvement is available on both the hardware and software.

We propose several methods for quantum key distribution (QKD) based upon the generation and transmission of random distributions of coherent or squeezed states, and we show that they are 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 "non-classical" features such as squeezing. Their security is a direct consequence of the no-cloning theorem, that limits the signal to noise ratio of possible quantum measurements on the transmission line. Our approach can also be used for evaluating various QKD protocols using light with gaussian statistics.PACS numbers: 03.67. Dd, 42.50.Dv, 89.70.+c Since the experimental demonstration of quantum teleportation of coherent states [1], a lot of interest has arisen in continuous variable quantum information processing. In particular, a stimulating question is whether quantum continuous variables (QCV) may provide a valid alternative to the usual "single photon" quantum key distribution schemes [2]. Most present proposals to use QCV for QKD [3][4][5][6][7][8][9][10][11][12][13][14][15]. are based upon the use of "nonclassical" light beams, such as squeezed light, or pairs of light beams that are correlated for two different quadratures components (the so-called "EPR" beams, by analogy with the historical paper by Einstein, Podolski and Rosen [16]). But recent work on this subject [17] underlined the crucial importance of the continuous variable version of the no-cloning theorem [18], as soon as security is concerned in any exchange using QCV.In this letter, we show that there is actually no need for squeezed light : an equivalent level of security may be obtained by simply generating and transmitting random distributions of coherent states. The security of this novel protocols is related to the no-cloning theorem, that limits possible eavesdropping even though the transmitted light has no "non-classical" feature such as squeezing. We show that our analysis can be also applied to other protocols using light with gaussian statistics, i.e. squeezed or EPR beams, making thus the comparison easier. The basic tools for this analysis are the ones that have been extensively used for linearized quantum optics, including in particular optical quantum non-demolition (QND) measurements [19]. Before presenting our protocol, we will briefly review the current literature on continuous variables QKD.Here we consider security against individual attacks only, and we do not address the issue of unconditionnal security, that was demonstrated by Gottesman and Preskill [3] for squeezed states protocols (unconditional security of coherent states protocols remains an open question). Security against individual attacks was previously considered by many authors. Hillery proposed a QKD scheme based on binary modulated squeezed light [4]. Cerf et al showed it could be improved considering gaussian modulation [5,6] and described a reconciliation protocol [6,7] to implement...

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.PACS numbers: 03.67. Dd, 03.67.Hk In 1984 Bennet and Brassard introduced the concept of Quantum Cryptography and presented the first Quantum Key Distribution (QKD) protocol: BB84 [1]. The original idea was that in Quantum Mechanics, and contrary to Classical Physics, the observation of a system invariably perturbs the system under observation. Therefore, if two honest parties, Alice and Bob, establish a quantum channel and use it to send information, an eavesdropper's presence could be detected by analyzing how the noise-free channel has changed. It was then shown that QKD protocols are completely secure against any eavesdropping attacks as long as the bit error rates do not exceed a certain value (see for instance [2] and references therein). In the meantime, new applications of Quantum Mechanics to certain information tasks started to develop: coin tossing, dense coding, teleportation...All these results first appeared in the context of discrete systems, but many of them were later translated into the language of Continuous Variables (CV) systems. This is per se an interesting theoretical problem. However, the main motivation for dealing with these systems comes from a practical point of view: although the set of feasible operations is reduced, the so-called Gaussian operations are easy to implement and amazingly precise. Quantum cryptography with continuous variables systems [3,4,5,6,7,8] was the most immediate result: the transmission of coherent or squeezed pulses of light, together with homodyne measurements, allows performing QKD with very high key rates [9].The security analysis of these new protocols is not straightforward. First of all, the commonly used reconciliation and privacy amplification protocols are designed to correct and distill secret bits from binary random variables, although some have been adapted to continuous variables [10,11]. Second, the dimension of the Hilbert space on which the CV systems are defined is infinite in theory, which makes a complete tomography impossible in principle, thus preventing Alice and Bob to know precisely the state they are actually sharing. Therefore, security proofs for CV protocols have to consider the optimal attack by Eve when Alice and Bob know their state is in some set, usually defined by the momenta of the quadratures up to second order [12]. In her search for information, Eve's possible attacks can be classified in three different types [13]: individual attacks, where Eve interacts individually with the sent states and measures them individually before public reconciliation; collective attacks, where Eve applies the same unitary individual attack over the sent states, but performs her (possibly collective) meas...

The goal of this paper is to extend the framework of finite-size analysis recently developed for quantum key distribution to continuous-variable protocols. We do not solve this problem completely here, and we mainly consider the finite-size effects on the parameter estimation procedure. Despite the fact that some questions are left open, we are able to give an estimation of the secret key rate for protocols which do not contain a postselection procedure. As expected, these results are significantly more pessimistic than those obtained in the asymptotic regime. However, we show that recent continuous-variable protocols are able to provide fully secure secret keys in the finite-size scenario, over distances larger than 50 km.

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.

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.

We discuss the criteria presently used for evaluating the efficiency of quantum teleportation schemes for continuous variables. Using an argument based upon the difference between 1-to-2 quantum cloning (quantum duplication) and 1-to-infinity cloning (classical measurement), we show that a fidelity value larger than 2/3 is required for successful quantum teleportation of coherent states. This value has not been reached experimentally so far.

We present a study of the charge state conversion of single nitrogen-vacancy (NV) defects hosted in nanodiamonds (NDs). We first show that the proportion of negatively-charged NV − defects, with respect to its neutral counterpart NV 0 , decreases with the size of the ND. We then propose a simple model based on a layer of electron traps located at the ND surface which is in good agreement with the recorded statistics. By using thermal oxidation to remove the shell of amorphous carbon around the NDs, we demonstrate a significant increase of the proportion of NV − defects in 10-nm NDs. These results are invaluable for further understanding, control and use of the unique properties of negatively-charged NV defects in diamond.