We propose a scheme for continuous-variable telecloning with phase-conjugate inputs (PCI). Two cases of PCI telecloning are considered. The first case is where PCI telecloning produces $M$ clones nonlocally and $M$ anticlones locally, or vice versa. This kind of PCI telecloning requires only one EPR (Einstein-Podolsky-Rosen) entangled, two-mode squeezed state as a resource for building the appropriate multi-mode, multipartite entangled state via linear optics. The other case is a PCI telecloning protocol in which both clones and anticlones are created nonlocally. Such a scheme requires two EPR entangled states for the generation of a suitable multipartite entangled state. As our schemes are reversible, optimal cloning fidelities are achieved in the limit of infinite squeezing.
We propose a scheme of continuous-variable reversible telecloning, which broadcast the information of an unknown state without loss from a sender to several spatially separated receivers exploiting multipartite entanglement as quantum channels. In this scheme, quantum information of an unknown state is distributed into $M$ optimal clones and $M-1$ anticlones using $2M$% -partite entanglement. For the perfect quantum information distribution that is optimal cloning, $2M$-partite entanglement is required to be a maximum two-party entanglement. Comparing with the quantum telecloning proposed by L…
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…
We address generation, propagation and application of multipartite continuous variable entanglement in a noisy environment. In particular, we focus our attention on the multimode entangled states achievable by second order nonlinear crystals, {\em i.e.} coherent states of ${\rm SU}(m,1)$ group. The full inseparability in the ideal case is shown, whereas thresholds for separability are given for the tripartite case in the presence of noise. We then consider coherent states of ${\rm SU}(m,1)$ as support for a telecloning protocol, providing the first example of a completely asymmetric $1 \to m$ …
We present a feasible scheme to use trapped ions Cavity QED system to implement optimal $1\to N$ cloning machine of coherent state. In present scheme, as the ouput of the clone machine, the copies of the cavity mode emerge at the vibrational modes and cavity modes is acted as the ancilla mode in the implementation of the cloning. We further show that such system can be used to generated multimodes quantum state, which can realize optimum symmetric $1\to N$ telecloning of coherent state of distant cavity.
We report the experimental demonstration of continuous variable cloning of phase conjugate coherent states as proposed by Cerf and Iblisdir (Phys. Rev. Lett. 87, 247903 (2001)). In contrast to the proposal of Cerf and Iblisdir, the cloning transformation is accomplished using only linear optical components, homodyne detection and feedforward. Three clones are succesfully produced with fidelities about 89%.
We propose a scheme for continuous-variable quantum cloning of coherent states with phase-conjugate input modes using linear optics. The quantum cloning machine yields $M$ identical optimal clones from $N$ replicas of a coherent state and $N$ its replicas of phase conjugate. This scheme can be straightforwardly implemented with the setup accessible at present since its optical implementation only employs simple linear optical elements and homodyne detection. Compared with the original scheme for continuous variables quantum cloning with phase-conjugate input modes proposed by Cerf and Iblisdir…
We consider the problem of broadcasting quantum information encoded in the average value of the field from N to M>N copies of mixed states of radiation modes. We derive the broadcasting map that preserves the complex amplitude, while optimally reducing the noise in conjugate quadratures. We find that from two input copies broadcasting is feasible, with the possibility of simultaneous purification (superbroadcasting). We prove similar results for purification (M<=N) and for phase-conjugate broadcasting.
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 cont…
We derive necessary conditions in terms of the variances of position and momentum linear combinations for all kinds of separability of a multi-party multi-mode continuous-variable state. Their violations can be sufficient for genuine multipartite entanglement, provided the combinations contain both conjugate variables of all modes. Hence a complete state determination, for example by detecting the entire correlation matrix of a Gaussian state, is not needed.
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.
The debate instigated by the seminal works of Einstein, Podolsky, Rosen, and Bell, put the notions of realism and nonlocality at the core of almost all philosophical and physical discussions underlying the foundations of quantum mechanics. However, while experimental criteria and quantifiers are by now well established for nonlocality, there is no clear quantitative measure for the degree of reality associated with continuous variables such as position and momentum. This work aims at filling this gap. Considering position and momentum as effectively discrete observables, we implement an operat…
Uncertainty relation is one of the fundamental principle in quantum mechanics and plays an important role in quantum information science. We experimentally test the error-disturbance uncertainty relation (EDR) with continuous variables for Gaussian states. Two conjugate continuous-variable observables, amplitude and phase quadratures of an optical mode, are measured simultaneously by using a heterodyne measurement system. The EDR with continuous variables for a coherent state, a squeezed state and a thermal state are verified experimentally. Our experimental results demonstrate that Heisenberg…
We have experimentally demonstrated the efficient creation of highly entangled bipartite continuous variable polarisation states. Exploiting an optimised scheme for the production of squeezing using the Kerr non-linearity of a glass fibre we generated polarisation squeezed pulses with a mean classical excitation in S3. Polarisation entanglement was generated by interfering two independent polarisation squeezed fields on a symmetric beam splitter. The resultant beams exhibit strong quantum noise correlations in the dark S1 - S2 polarisation plane. To verify entanglement generation, we character…
We study Gaussian valence bond states of continuous variable systems, obtained as the outputs of projection operations from an ancillary space of M infinitely entangled bonds connecting neighboring sites, applied at each of $N$ sites of an harmonic chain. The entanglement distribution in Gaussian valence bond states can be controlled by varying the input amount of entanglement engineered in a (2M+1)-mode Gaussian state known as the building block, which is isomorphic to the projector applied at a given site. We show how this mechanism can be interpreted in terms of multiple entanglement swappi…
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.
We have experimentally demonstrated polarization entanglement using continuous variables in an ultra-short pulsed laser system at telecommunication wavelengths. Exploiting the Kerr-nonlinearity of a glass fibre we generated a polarization squeezed pulse with S2 the only non-zero Stokes parameter thus S1 and S3 being the conjugate pair. Polarization entanglement was generated by interference of the polarization squeezed field with a vacuum on a 50:50 beam splitter. The two resultant beams exhibit strong quantum noise correlations in S1 and S3. The sum noise signal of S3 was at the respective sh…
Most continuous-variable quantum key distribution schemes are based on the Gaussian modulation of coherent states followed by continuous quadrature detection using homodyne detectors. In all previous schemes, the Gaussian modulation has been carried out in conjugate quadratures thus requiring two independent modulators for their implementations. Here, we propose and experimentally test a largely simplified scheme in which the Gaussian modulation is performed in a single quadrature. The scheme is shown to be asymptotically secure against collective attacks, and considers asymmetric preparation …
Quantum information protocols are inevitably affected by decoherence which is associated with the leakage of quantum information into an environment. In this paper we address the possibility of recovering the quantum information from an environmental measurement. We investigate continuous variable quantum information, and we propose a simple environmental measurement that under certain circumstances fully restores the quantum information of the signal state although the state is not reconstructed with unit fidelity. We implement the protocol for which information is encoded into conjugate quad…
A continuous key distribution scheme is proposed that relies on a pair of canonically conjugate quantum variables. It allows two remote parties to share a secret Gaussian key by encoding it into one of the two quadrature components of a single-mode electromagnetic field. The resulting quantum cryptographic information vs disturbance tradeoff is investigated for an individual attack based on the optimal continuous cloning machine. It is shown that the information gained by the eavesdropper then simply equals the information lost by the receiver.
We improve the entropic uncertainty relations for position and momentum coarse-grained measurements. We derive the continuous, coarse-grained counterparts of the discrete uncertainty relations based on the concept of majorization. The obtained entropic inequalities involve two Rényi entropies of the same order, and thus go beyond the standard scenario with conjugated parameters. In a special case describing the sum of two Shannon entropies the majorization-based bounds significantly outperform the currently known results in the regime of larger coarse graining, and might thus be useful for ent…
Cloning machines, that is, transformations that achieve the best approximate copying of a quantum state compatible with the no-cloning theorem, have been a fundamental research topic over the last five years. This study is of particular significance given the close connection between quantum cloning and quantum cryptography: using an optimal cloner generally makes it possible to obtain a tight bound on the best individual eavesdropping strategy in a quantum cryptosystem. In this Chapter, the issue of cloning a continuous-variable quantum system will be analyzed, and a Gaussian cloning transfor…
This thesis deals with the study of quantum communication protocols with Continuous Variable (CV) systems. Continuous Variable systems are those described by canonical conjugated coordinates x and p endowed with infinite dimensional Hilbert spaces, thus involving a complex mathematical structure. A special class of CV states, are the so-called Gaussian states. With them, it has been possible to implement certain quantum tasks as quantum teleportation, quantum cryptography and quantum computation with fantastic experimental success. The importance of Gaussian states is two-fold; firstly, its st…
The uncertainty relation for continuous variables due to Byalinicki-Birula and Mycielski expresses the complementarity between two $n$-uples of canonically conjugate variables $(x_1,x_2,\cdots x_n)$ and $(p_1,p_2,\cdots p_n)$ in terms of Shannon differential entropy. Here, we consider the generalization to variables that are not canonically conjugate and derive an entropic uncertainty relation expressing the balance between any two $n$-variable Gaussian projective measurements. The bound on entropies is expressed in terms of the determinant of a matrix of commutators between the measured varia…
We present a novel, detailed study on the usefulness of three-mode Gaussian states states for realistic processing of continuous-variable quantum information, with a particular emphasis on the possibilities opened up by their genuine tripartite entanglement. We describe practical schemes to engineer several classes of pure and mixed three-mode states that stand out for their informational and/or entanglement properties. In particular, we introduce a simple procedure -- based on passive optical elements -- to produce pure three-mode Gaussian states with {\em arbitrary} entanglement structure (u…
We provide a toolbox for continuous variables quantum state engineering and characterization of biphoton states produced by spontaneous parametric down conversion in a transverse pump configuration. We show that the control of the pump beam's incidence spot and angle corresponds to phase space displacements of conjugate collective continuous variables of the biphoton. In particular, we illustrate with numerical simulations on a semiconductor device how this technique can be used to engineer and characterize arbitrary states of the frequency and time degrees of freedom.
The notion of mutual unbiasedness for coarse-grained measurements of quantum continuous variable systems is considered. It is shown that while the procedure of "standard" coarse graining breaks the mutual unbiasedness between conjugate variables, this desired feature can be theoretically established and experimentally observed in periodic coarse graining. We illustrate our results in an optics experiment implementing Fraunhofer diffraction through a periodic diffraction grating, finding excellent agreement with the derived theory. Our results are an important step in developing a formal connec…
Continuous-variable model for arbitrary image propagation via Dirac-comb expansion in Four-Wave Mixing
Universidad de Chile（智利大学）；Millennium Institute for Research in Optics - MIRO（光学研究千年研究所）；Universidade Federal do ABC–UFABC（圣安德烈联邦大学）；Universidad de Concepción（康塞普西翁大学）
The de Finetti representation theorem for continuous variable quantum system is first developed to approximate an N-partite continuous variable quantum state with a convex combination of independent and identical subsystems, which requires the original state to obey permutation symmetry conditioned on successful experimental verification on k of N subsystems. We generalize the de Finetti theorem to include asymmetric bounds on the variance of canonical observables and biased basis selection during the verification step. Our result thereby enables application of infinite-dimensional de Finetti …
