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Security bounds for key distribution protocols using coherent and squeezed states and homodyne measurements are presented. These bounds refer to (i) general attacks and (ii) collective attacks where Eve interacts individually with the sent states, but delays her measurement until the end of the reconciliation process. For the case of a lossy line and coherent states, it is first proven that a secure key distribution is possible up to 1.9 dB of losses. For the second scenario, the security bounds are the same as for the completely incoherent attack.

This paper provides necessary and sufficient conditions for constructing a universal quantum computer over continuous variables. As an example, it is shown how a universal quantum computer for the amplitudes of the electromagnetic field might be constructed using simple linear devices such as beam-splitters and phase shifters, together with squeezers and nonlinear devices such as Kerr-effect fibers and atoms in optical cavities. Such a device could in principle perform `quantum floating point' computations. Problems of noise, finite precision, and error correction are discussed.

We present schemes for the generation and evaluation of continuous variable entanglement of bright optical beams and give a brief overview of the variety of optical techniques and quantum communication applications on this basis. A new entanglement-based quantum interferometry scheme with bright beams is suggested. The performance of the presented schemes is independent of the relative interference phase which is advantageous for quantum communication applications.

Teleportation of optical field states (as continuous quantum variables) is usually described in terms of Wigner functions. This is in marked contrast to the theoretical treatment of teleportation of qubits. In this paper we show that by using the holomorphic representation of the canonical commutation relations, teleportation of continuous quantum variables can be treated in complete analogy to the case of teleportation of qubits. In order to emphasize this analogy, short descriptions of the basic experimental schemes both for teleportation of qubits and of continuous variables are included. We conclude our paper with a brief discussion of the effectiveness of our description of continuous variable teleportation and of the role of localization of quantum states in teleportation problems.

The cloning of quantum variables with continuous spectra is investigated. We define a Gaussian 1-to-2 cloning machine, which copies equally well two conjugate variables such as position and momentum or the two quadrature components of a light mode. The resulting cloning fidelity for coherent states, namely $F=2/3$, is shown to be optimal. An asymmetric version of this Gaussian cloner is then used to assess the security of a continuous-variable quantum key distribution scheme that allows two remote parties to share a Gaussian key. The information versus disturbance tradeoff underlying this continuous quantum cryptographic scheme is then analyzed for the optimal individual attack. Methods to convert the resulting Gaussian keys into secret key bits are also studied. The extension of the Gaussian cloner to optimal $N$-to-$M$ continuous cloners is then discussed, and it is shown how to implement these cloners for light modes, using a phase-insensitive optical amplifier and beam splitters. Finally, a phase-conjugated inputs $(N,N')$-to-$(M,M')$ continuous cloner is defined, yielding $M$ clones and $M'$ anticlones from $N$ replicas of a coherent state and $N'$ replicas of its phase-conjugate (with $M'-M=N'-N$). This novel kind of cloners is shown to outperform the standard $N$-to-$M$ cloners in some situations.

We describe a continuous variables coherent states quantum key distribution system working at 1550 nm, and entirely made of standard fiber optics and telecom components, such as integrated-optics modulators, couplers and fast InGaAs photodiodes. The setup is composed of an emitter randomly modulating a coherent state in the complex plane with a doubly Gaussian distribution, and a receiver based on a shot noise limited time-resolved homodyne detector. By using a reverse reconciliation protocol, the device can transfer a raw key rate up to 1 Mb/s, with a proven security against Gaussian or non-Gaussian attacks. The dependence of the secret information rate of the present fiber set-up is studied as a function of the line transmission and excess noise.

We present a continuous-variable quantum key distribution protocol combining a continuous but slightly non-Gaussian modulation together with a efficient reverse reconciliation scheme. We establish the security of this protocol against collective attacks which correspond to a linear quantum channel. In particular, all Gaussian attacks are considered in our framework. We show that this protocol outperforms all known practical protocols, even taking into account finite size effects.

We demonstrate experimentally how to remove an arbitrary node from a continuous-variable cluster state and how to shorten any quantum wires of such a state. These two basic operations, performed in an unconditional fashion, are a manifestation of quantum erasure and can be employed to obtain various graph states from an initial cluster state. Starting with a sufficiently large cluster, the resulting graph states can then be used for universal quantum information processing. In the experiment, all variations of this cluster-shaping are demonstrated on a four-mode linear cluster state through homodyne measurements and feedforward.

We experimentally demonstrate, with an all-optical setup, a nonlocal deterministic quantum non-demolition interaction gate applicable to quantum states at nodes separated by a physical distance and connected by classical communication channels. The gate implementation, based on entangled states shared in advance, local operations, and classical communication, runs completely in parallel fashion at both the local nodes, requiring minimum resource. The nondemolition character of the gate up to the local unitary squeezing is verified by the analysis using several coherent states. A genuine quantum nature of the gate is confirmed by the capability of deterministically producing an entangled state at the output from two separable input states. The all-optical nonlocal gate operation can be potentially incorporated into distributed quantum computing with atomic or solid state systems as a cross-processor unitary operation.

We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously and imprecisely measured by the classical system. The effective equations of motion for the classical system therefore consist of treating the quantum variable $x$ as a stochastic c-number $\x (t) $ the probability distibution for which is given by the theory of continuous quantum measurements. The resulting theory is similar to the usual mean field equations (in which $x$ is replaced by its quantum expectation value) but with two differences: a noise term, and more importantly, the state of the quantum subsystem evolves according to the stochastic non-linear Schrodinger equation of a continuously measured system. In the case in which the quantum system starts out in a superposition of well-separated localized states, the classical system goes into a statistical mixture of trajectories, one trajectory for each individual localized state.

We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously and imprecisely measured by the classical system. The effective equations of motion for the classical system therefore consist of treating the quantum variable $x$ as a stochastic c-number $\x (t) $ the probability distibution for which is given by the theory of continuous quantum measurements. The resulting theory is similar to the usual mean field equations (in which $x$ is replaced by its quantum expectation value) but with two differences: a noise term, and more importantly, the state of the quantum subsystem evolves according to the stochastic non-linear Schrodinger equation of a continuously measured system. In the case in which the quantum system starts out in a superposition of well-separated localized states, the classical system goes into a statistical mixture of trajectories, one trajectory for each individual localized state.

We demonstrate that continuous-variable quantum error correction based on Gaussian ancilla states and Gaussian operations (for encoding, syndrome extraction, and recovery) can be very useful to suppress the effect of non-Gaussian error channels. For a certain class of stochastic error models, reminiscent of those typically considered in the qubit case, quantum error correction codes designed for single-channel errors may enhance the transfer fidelities even when errors occur in every channel employed for transmitting the encoded state. In fact, in this case, the error-correcting capability of the continuous-variable scheme turns out to be higher than that of its discrete-variable analogues.

We investigate the properties of an atmospheric channel for free space quantum communication with continuous polarization variables. In our prepare-and-measure setup, coherent polarization states are transmitted through an atmospheric quantum channel of 100m length on the roof of our institute's building. The signal states are measured by homodyne detection with the help of a local oscillator (LO) which propagates in the same spatial mode as the signal, orthogonally polarized to it. Thus the interference of signal and LO is excellent and atmospheric fluctuations are autocompensated. The LO also acts as spatial and spectral filter, which allows for unrestrained daylight operation. Important characteristics for our system are atmospheric channel influences that could cause polarization, intensity and position excess noise. Therefore we study these influences in detail. Our results indicate that the channel is suitable for our quantum communication system in most weather conditions.

Ideally, quantum teleportation should transfer a quantum state without distortion and without providing any information about that state. However, quantum teleportation of continuous electromagnetic field variables introduces additional noise, limiting the fidelity of the quantum state transfer. In this article, the operator describing the quantum state transfer is derived. The transfer operator modifies the probability amplitudes of the quantum state in a shifted photon number base by enhancing low photon numbers and suppressing high photon numbers. This modification of the statistical weight corresponds to a measurement of finite resolution performed on the original quantum state. The limited fidelity of quantum teleportation is thus shown to be a direct consequence of the information obtained in the measurement.

By analogy to classical cryptography, we develop a "quantum public key" based cryptographic scheme in which the two public and private keys consist in each of two entangled beams of squeezed light. An analog message is encrypted by modulating the phase of the beam sent in public. The knowledge of the degree of non classical correlation between the beam quadratures measured in private and in public allows only the receiver to decrypt the message. Finally, in a view towards absolute security, we formally prove that any external intervention of an eavesdropper makes him vulnerable to any subsequent detection.

We present the wavelength attack on practical continuous variables quantum key distribution system with heterodyne protocol, in which the transmittance of beam splitters at Bob's station is wavelength-dependent. Our strategy is proposed independently analogous to that of Han's group (arxiv: 1206.6550v1), but in Han's paper the shot noise of the two beams that Eve sends to Bob transmitting after the homodyne detectors is unconsidered. However, shot noise is the main contribution to the deviation of Bob's measurements from Eve's when implementing the wavelength attack, so it must be considered accurately. In this paper, we firstly analyze the solutions of the equations specifically that must be satisfied in this attack, which is unconsidered rigorously in Han's paper. Then we calculate the shot noise of the homodyne detectors accurately and conclude that the wavelength attack can be implemented successfully in some parameter regime.

We analyse the distribution of secure keys using quantum cryptography based on the continuous variable degree of freedom of entangled photon pairs. We derive the information capacity of a scheme based on the spatial entanglement of photons from a realistic source, and show that the standard measures of security known for quadrature-based continuous variable quantum cryptography (CV-QKD) are inadequate. A specific simple eavesdropping attack is analysed to illuminate how secret information may be distilled well beyond the bounds of the usual CV-QKD measures.

Superadditivity effects in the classical capacity of discrete multi-access channels (MACs) and continuous variable (CV) Gaussian MACs are analysed. New examples of the manifestation of superadditivity in the discrete case are provided including, in particular, a channel which is fully symmetric with respect to all senders. Furthermore, we consider a class of channels for which {\it input entanglement across more than two copies of the channels is necessary} to saturate the asymptotic rate of transmission from one of the senders to the receiver. The 5-input entanglement of Shor error correction codewords surpass the capacity attainable by using arbitrary two-input entanglement for these channels. In the CV case, we consider the properties of the two channels (a beam-splitter channel and a "non-demolition" XP gate channel) analyzed in [Czekaj {\it et al.}, Phys. Rev. A {\bf 82}, 020302 (R) (2010)] in greater detail and also consider the sensitivity of capacity superadditivity effects to thermal noise. We observe that the estimates of amount of two-mode squeezing required to achieve capacity superadditivity are more optimistic than previously reported.

We propose an error correction coding algorithm for continuous quantum variables. We use this algorithm to construct a highly efficient 5-wavepacket code which can correct arbitrary single wavepacket errors. We show that this class of continuous variable codes is robust against imprecision in the error syndromes. A potential implemetation of the scheme is presented.

We show how to communicate Heisenberg-limited continuous (quantum) variables between Alice and Bob in the case where they occupy two inertial reference frames that differ by an unknown Lorentz boost. There are two effects that need to be overcome: the Doppler shift and the absence of synchronized clocks. Furthermore, we show how Alice and Bob can share Doppler-invariant entanglement, and we demonstrate that the protocol is robust under photon loss.

We introduce the quantum fractional Hadamard transform with continuous variables. It is found that the corresponding quantum fractional Hadamard operator can be decomposed into a single-mode fractional operator and two single-mode squeezing operators. This is extended to the entangled case by using the bipartite entangled state representation. The new transformation presents more flexibility to represent signals in the fractional Hadamard domain with extra freedom provided by an angle and two-squeezing parameters.

Recent experiments have shown that nature violates noncontextual inequalities regardless of the state of the physical system. So far, all these inequalities involve measurements of dichotomic observables. We show that state-independent quantum contextuality can also be observed in the correlations between measurements of observables with genuinely continuous spectra, highlighting the universal character of the effect.

The phase conjugation of an unknown Gaussian state cannot be realized perfectly by any physical process. A semi-classical argument is used to derive a tight lower bound on the noise that must be introduced by an approximate phase conjugation operation. A universal transformation achieving the optimal imperfect phase conjugation is then presented, which is the continuous counterpart of the universal-NOT transformation for quantum bits. As a consequence, it is also shown that more information can be encoded into a pair of conjugate Gaussian states than using twice the same state.

The purpose of this short tutorial paper is to review various criteria that have been used to characterize the quantum character of correlations in optical systems, such as "gemellity", QND correlation, intrication, EPR correlation and Bell correlation, to discuss and compare them. This discussion, restricted to the case of measurements of continuous optical variables, includes also an extension of known criteria for "twin beams" to the case of imbalanced correlations.

Quantum computing promises to exploit the laws of quantum mechanics for processing information in ways fundamentally different from today's classical computers, leading to unprecedented efficiency. One-way quantum computation, sometimes referred to as the cluster model of quantum computation, is a very promising approach to fulfil the capabilities of quantum information processing. The cluster model is realizable through measurements on a highly entangled cluster state with no need for controlled unitary evolutions. Here we demonstrate unconditional one-way quantum computation experiments for continuous variables using a linear cluster state of four entangled optical modes. We implement an important set of quantum operations, linear transformations, in the optical phase space through one-way computation. Though not sufficient, these are necessary for universal quantum computation over continuous variables, and in our scheme, in principle, any such linear transformation can be unconditionally and deterministically applied to arbitrary single-mode quantum states.

The cloning of quantum variables with continuous spectra is analyzed. A universal - or Gaussian - quantum cloning machine is exhibited that copies equally well the states of two conjugate variables such as position and momentum. It also duplicates all coherent states with a fidelity of 2/3. More generally, the copies are shown to obey a no-cloning Heisenberg-like uncertainty relation.

This dissertation serves as a general introduction to Wigner functions, phase space, and quantum metrology but also strives to be useful as a how-to guide for those who wish to delve into the realm of using continuous variables, to describe quantum states of light and optical interferometry. We discuss the advantages of Wigner functions and their use to describe many quantum states of light. Throughout our metrology discussions, we will also discuss various quantum limits and use quantum Fisher information to show optimal bounds. When applicable, we also discuss the use of quantum Gaussian information and how it relates to our Wigner function treatment. The remainder of our discussion focuses on investigating the effects of photon addition and subtraction to various states of light and analyze the nondeterministic nature of this process. We use examples of $m$ photon additions to a coherent state as well as discuss the properties of an $m$ photon subtracted thermal state. We also provide an argument that this process must always be a nondeterministic one, or the ability to violate quantum limits becomes apparent. We show that using phase measurement as one's metric is much more restrictive, which limits the usefulness of photon addition and subtraction. When we consider SNR however, we show improved SNR statistics, at the cost of increased measurement time. In this case of SNR, we also quantify the efficiency of the photon addition and subtraction process.

It is well known that usual quantum teleportation protocols cannot transport energy. Recently, new protocols called quantum energy teleportation (QET) have been proposed, which transport energy by local operations and classical communication with the ground states of many-body quantum systems. In this paper, we compare two different QET protocols for transporting energy with electromagnetic field. In the first protocol, a 1/2 spin (a qubit) is coupled with the quantum fluctuation in the vacuum state and measured in order to obtain one-bit information about the fluctuation for the teleportation. In the second protocol, a harmonic oscillator is coupled with the fluctuation and measured in order to obtain continuous-variable information about the fluctuation. In the spin protocol, the amount of teleported energy is suppressed by an exponential damping factor when the amount of input energy increases. This suppression factor becomes power damping in the case of the harmonic oscillator protocol. Therefore, it is concluded that obtaining more information about the quantum fluctuation leads to teleporting more energy. This result suggests a profound relationship between energy and quantum information.

We devise a scheme that protects quantum coherent states of light from probabilistic losses, thus achieving the first continuous-variable quantum erasure-correcting code. If the occurrence of erasures can be probed, then the decoder enables, in principle, a perfect recovery of the original light states. Otherwise, if supplemented with postselection based on homodyne detection, this code can be turned into an efficient erasure-filtration scheme. The experimental feasibility of the proposed protocol is carefully addressed.

We propose a continuous variable analog of quantum controlled-NOT gates based on a system of exciton-polaritons in semiconductor microcavities. This can be realized by the engineering of parametric interaction between control and target polariton modes, which can be varied in time. As an explicit setup we use a system of dipolaritons, which allows for enhancement of parametric interaction by auxiliary classical fields and scalable multigate system realization. The calculated fidelity is shown to exceed 99% for realistic system parameters.

We investigate how the entanglement properties of a two-mode state can be improved by performing a coherent superposition operation of photon subtraction and addition, proposed by Lee and Nha [Phys. Rev. A 82, 053812 (2010)], on each mode. We show that the degree of entanglement, the EPR-type correlation, and the performance of quantum teleportation can be all enhanced for the output state when the coherent operation is applied to a two-mode squeezed state. The effects of the coherent operation are more prominent than those of the mere photon subtraction and the addition particularly in the small squeezing regime, whereas the optimal operation becomes the photon subtraction in the large-squeezing regime.

Very recently we have witnessed a new development of quantum information, the so-called continuous variable (CV) quantum information theory. Such a further development has been mainly due to the experimental and theoretical advantages offered by CV systems, i.e., quantum systems described by a set of observables, like position and momentum, which have a continuous spectrum of eigenvalues. According to this novel trend, quantum information protocols like quantum teleportation have been suitably extended to the CV framework. Here, we briefly review some mathematical tools relative to CV systems and we consequently develop the concepts of quantum entanglement and teleportation in the CV framework, by analogy with the qubit-based approach. Some connections between teleportation fidelity and entanglement properties of the underlying quantum channel are inspected. Next, we face the study of CV quantum teleportation networks where more users share a multipartite state and an arbitrary pair of them performs quantum teleportation. In this context, we show alternative protocols and we investigate the optimal strategy that maximizes the performance of the network.

We consider the quantum processor based on a chain of trapped ions to propose an architecture wherein the motional degrees of freedom of trapped ions (position and momentum) could be exploited as the computational Hilbert space. We adopt a continuous-variables approach to develop a toolbox of quantum operations to manipulate one or two vibrational modes at a time. Together with the intrinsic non-linearity of the qubit degree of freedom, employed to mediate the interaction between modes, arbitrary manipulation and readout of the ionic wave function could be achieved.

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.

This thesis presents three different results in quantum information theory. The first result addresses the theoretical foundations of quantum metrology. The Heisenberg limit considered as the ultimate limit in quantum metrology sets a lower bound on how precisely a physical quantity can be measured given a certain amount of resources in any possible measurement. Recently, however, several measurement procedures have been proposed in which the Heisenberg limit seemed to be surpassed. This led to an extensive debate over the question how the sensitivity scales with the physical resources and the computational resources that are used in estimation procedures. Here, we reconcile the physical definition of the relevant resources with the information-theoretical scaling in terms of the query complexity of a quantum network. This leads to a novel and ultimate Heisenberg limit that applies to all conceivable measurement procedures. The second result reveals a close relationship between quantum metrology and the Deutsch-Jozsa algorithm over continuous-variable quantum systems. Here, we develop a general procedure, characterized by two parameters, that unifies parameter estimation and the Deutsch-Jozsa algorithm. The procedure estimates a value of an unknown parameter with Heisenberg-limited precision or solves the Deutsch-Jozsa problem in a single run without the use of any entanglement. The third result illustrates how physical principles that govern interaction of light and matter can be efficiently employed to create a computational resource for a (one-way) quantum computer. More specifically, we demonstrate theoretically a scheme based on atomic ensembles and the dipole blockade mechanism for generation of the so-called cluster states in a single step. This procedure is significantly more efficient than any known robust probabilistic entangling operation.

We introduce new quantum key distribution protocols using quantum continuous variables, that are secure against individual attacks for any transmission of the optical line between Alice and Bob. In particular, it is not required that this transmission is larger than 50 %. Though squeezing or entanglement may be helpful, they are not required, and there is no need for quantum memories or entanglement purification. These protocols can thus be implemented using coherent states and homodyne detection, and they may be more efficient than usual protocols using quantum discrete variables.

A fast quantum search algorithm for continuous variables is presented. The result is the quantum continuous variable analog of Grover's algorithm originally proposed for qubits. A continuous variable analog of the Hadamard (i.e., Fourier transform) operation is used in conjunction with inversion about the average of quantum states to allow the approximate identification of an unknown quantum state in a way that gives a square-root speed-up over search algorithms using classical continuous variables. Also, we show that this quantum search algorithm is robust for a generalised Fourier transformation on continuous variables.

We experimentally investigate nonlinear couplings between vibrational modes of strings of cold ions stored in linear ion traps. The nonlinearity is caused by the ions' Coulomb interaction and gives rise to a Kerr-type interaction Hamiltonian H = n_r*n_s, where n_r,n_s are phonon number operators of two interacting vibrational modes. We precisely measure the resulting oscillation frequency shift and observe a collapse and revival of the contrast in a Ramsey experiment. Implications for ion trap experiments aiming at high-fidelity quantum gate operations are discussed.

Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault tolerant architecture. This has led to the point that continuous-variable quantum computing can indeed be thought of as a viable alternative for universal quantum computing. With that in mind, we present a new algorithm for continuous-variable quantum computers which gives an exponential speedup over the best known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonic quantum field theory, a problem that is believed to be hard using a classical computer. Building on this, we give an experimental implementation based on cluster states that is feasible with today's technology.

We propose entangled (M+1)-mode quantum states as a multiuser quantum channel for continuous-variable communication. Arbitrary quantum states can be sent via this channel simultaneously to M remote and separated locations with equal minimum excess noise in each output mode. For a set of coherent-state inputs, the channel realizes optimum symmetric 1-to-M cloning at a distance (``telecloning''). It also provides the optimal cloning of coherent states without the need of amplifying the state of interest. The generation of the multiuser quantum channel requires no more than two 10\log_{10}[(\sqrt{M}-1)/(\sqrt{M}+1)] dB squeezed states and M beam splitters.

Quantum information is a rapidly advancing area of interdisciplinary research. It may lead to real-world applications for communication and computation unavailable without the exploitation of quantum properties such as nonorthogonality or entanglement. We review the progress in quantum information based on continuous quantum variables, with emphasis on quantum optical implementations in terms of the quadrature amplitudes of the electromagnetic field.

Fidelity F{classical} = 1/2 has been established as setting the boundary between classical and quantum domains in the teleportation of coherent states of the electromagnetic field (S. L. Braunstein, C. A. Fuchs, and H. J. Kimble, J. Mod. Opt. 47, 267 (2000)). Two recent papers by P. Grangier and F. Grosshans (quant-ph/0009079 and quant-ph/0010107) introduce alternate criteria for setting this boundary and as a result claim that the appropriate boundary should be F = 2/3. Although larger fidelities would lead to enhanced teleportation capabilities, we show that the new conditions of Grangier and Grosshans are largely unrelated to the questions of entanglement and Bell-inequality violations that they take to be their primary concern. With regard to the quantum-classical boundary, we demonstrate that fidelity F{classical} = 1/2 remains the appropriate point of demarcation. The claims of Grangier and Grosshans to the contrary are simply wrong, as we show by an analysis of the conditions for nonseparability (that complements our earlier treatment) and by explicit examples of Bell-inequality violations.

We demonstrate a contradiction of quantum mechanics with local hidden variable theories for continuous variable quadrature phase amplitude (``position'' and ``momentum'') measurements, by way of a violation of a Bell inequality. For any quantum state, this contradiction is lost for situations where the quadrature phase amplitude results are always macroscopically distinct. We show that for optical realisations of this experiment, where one uses homodyne detection techniques to perform the quadrature phase amplitude measurement, one has an amplification prior to detection, so that macroscopic fields are incident on photodiode detectors. The high efficiencies of such detectors may open a way for a loophole-free test of local hidden variable theories.

We show how continuous variable systems can allow the direct communication of messages with an acceptable degree of privacy. This is possible by combining a suitable phase-space encoding of the plain message with real-time checks of the quantum communication channel. The resulting protocol works properly when a small amount of noise affects the quantum channel. If this noise is non-tolerable, the protocol stops leaving a limited amount of information to a potential eavesdropper.

We discuss a quantum key distribution scheme in which small phase and amplitude modulations of quantum limited, CW light beams carry the key information. We identify universal constraints on the level of shared information between the intended receiver (Bob) and any eavesdropper (Eve) and use this to make a general evaluation of the security and efficiency of the scheme. We show that a scheme based on coherent light offers competitive secret key bit transmission rates.

We consider the problem of privacy in direct communications, showing how quantum mechanics can be useful to guarantee a certain level of confidentiality. In particular, we review a continuous variable approach recently proposed by us [S. Pirandola et al., Europhys. Lett. 84, 20013 (2008)]. Here, we analyze the degree of privacy of this technique against a broader class of attacks, which includes non-Gaussian eavesdropping.

Quantum cryptography with the predetermined key was experimentally realized using Einstein-Podolsky-Rosen(EPR) correlations of continuously bright optical beams. Only one of two EPR correlated beams is transmitted with the signals modulated on quadrature phases and amplitudes, and the other one is retained by the authorized receiver. The modulated small signals are totally submerged in the large quantum noise of the signal beam, therefore nobody except the authorized receiver can decode the signals. Usability of imperfect quantum correlation, high transmission and detection efficiencies, and security provided by quantum mechanics are the favorable features of the presented scheme.

We discuss the criteria presently used for evaluating the efficiency of quantum teleportation schemes for continuous variables. It is argued that the fidelity criterion used so far has some severe drawbacks, and that a fidelity value larger than 2/3 is actually required for successful quantum teleportation. This value has never been reached experimentally so far.

We present two experimental schemes to perform continuous variable (2,3) threshold quantum secret sharing on the quadratures amplitudes of bright light beams. Both schemes require a pair of entangled light beams. The first scheme utilizes two phase sensitive optical amplifiers, whilst the second uses an electro-optic feedforward loop for the reconstruction of the secret. We examine the efficacy of quantum secret sharing in terms of fidelity, as well as the signal transfer coefficients and the conditional variances of the reconstructed output state. We show that both schemes in the ideal case yield perfect secret reconstruction.

We investigate phase-insensitive linear amplification at the quantum limit for single- and two-mode states and show that there exists a broad class of non-Gaussian states whose nonclassicality survives even at an arbitrarily large gain. We identify the corresponding observable nonclassical effects and find that they include, remarkably, two-mode entanglement. The implications of our results for quantum cloning outside the Gaussian regime are also addressed.