A scheme for optimal Gaussian cloning of optical coherent states is proposed and experimentally demonstrated. Its optical realization is based entirely on simple linear optical elements and homodyne detection. The optimality of the presented scheme is only limited by detection inefficiencies. Experimentally we achieved a cloning fidelity of about 65%, which almost touches the optimal value of 2/3.
We show how to implement the optimal Gaussian $N$-to-$M$ cloning with linear optics and homodyne detection. We also show that the Gaussian $N$-to-$M$ cloning of known-phase coherent states can be performed with the fidelity $\sqrt \frac{2 M N}{2M N+M -N}$ by linear optics and homodyne detection, and with $\frac{2}{\sqrt{1+\frac{1}{N}}+\sqrt {1-\frac{1}{M}}}$ by utilizing quadrature squeezing. From the classical limit of the cloning (1-to-$\infty$ cloning), a necessary condition of continuous variable quantum key distribution using known-phase coherent states is provided.
We propose an optical implementation of the Gaussian continuous-variable quantum cloning machines. We construct a symmetric N -> M cloner which optimally clones coherent states and we also provide an explicit design of an asymmetric 1 -> 2 cloning machine. All proposed cloning devices can be built from just a single non-degenerate optical parametric amplifier and several beam splitters.
We describe an optical scheme for optimal Gaussian n to m cloning of coherent states. The scheme, which generalizes a recently demonstrated scheme for 1 to 2 cloning, involves only linear optical components and homodyne detection.
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…
It has been shown theoretically that a light amplifier working on the physical principle of stimulated emission should achieve optimal quantum cloning of the polarization state of light. We demonstrate close-to-optimal universal quantum cloning of polarization in a standard fiber amplifier for telecom wavelengths. For cloning 1 --> 2 we find a fidelity of 0.82, the optimal value being 5/6 = 0.83.
After a brief introduction to the quantum no-cloning theorem and its link with the linearity and causality of quantum mechanics, the concept of quantum cloning machines is sketched, following, whenever possible, the chronology of the main results. The important classes of quantum cloning machines are reviewed, in particular state-independent and state-dependent cloning machines. The 1-to-2 cloning problem is then studied from a formal point of view, using the isomorphism between completely positive maps and operators, which leads to the so-called double-Bell ansatz. This also yields an efficie…
Beyond the no-cloning theorem, the universal symmetric quantum cloning machine was first addressed by Buzek and Hillery. Here, we realized the one-to-two qubits Buzek-Hillery cloning machine with linear optical devices. This method relies on the representation of several qubits by a single photon. We showed that, the fidelities between the two output qubits and the original qubit are both 5/6 (which proved to be the optimal fidelity of one-to-two qubits universal cloner) for arbitrary input pure states.
A linear optical probabilistic scheme for the optimal cloning of a pair of orthogonally-polarized photons is devised, based on single- and two-photon interferences. It consists in a partial symmetrization device, realized with a modified unbalanced Mach-Zehnder interferometer, followed by two independent Hong-Ou-Mandel interferometers. This scheme has the advantage that it enables quantum cloning without the need for stimulated amplification in a nonlinear medium. It can also be modified so to make an optical two-qubit partial SWAP gate, thereby providing a potentially useful tool to linear op…
We investigate the performances of a selective cloning machine based on linear optical elements and Gaussian measurements, which allows to clone at will one of the two incoming input states. This machine is a complete generalization of a 1 to 2 cloning scheme demonstrated by U. L. Andersen et al. [Phys. Rev. Lett. vol. 94, 240503 (2005)]. The input-output fidelity is studied for generic Gaussian input state and the effect of non-unit quantum efficiency is also taken into account. We show that if the states to be cloned are squeezed states with known squeezing parameter, then the fidelity can b…
We analyze in details a scheme for cloning of Gaussian states based on linear optical components and homodyne detection recently demonstrated by U. L. Andersen et al. [PRL 94 240503 (2005)]. The input-output fidelity is evaluated for a generic (pure or mixed) Gaussian state taking into account the effect of non-unit quantum efficiency and unbalanced mode-mixing. In addition, since in most quantum information protocols the covariance matrix of the set of input states is not perfectly known, we evaluate the average cloning fidelity for classes of Gaussian states with the degree of squeezing and …
We consider a new approach for storing quantum information by macroscopic atomic excitations of two level atomic system. We offer the original scheme of quantum cloning of optical field into the cavity polaritons containing the phase insensitive parametrical amplifier and atomic cell placed in the cavity. The high temperature quasi-condensation (and/or condensation) phenomenon for polaritons arising in the cavity under the certain conditions is proposed for the first time.
Just as classical information systems require buffers and memory, the same is true for quantum information systems. The potential that optical quantum information processing holds for revolutionising computation and communication is therefore driving significant research into developing optical quantum memory. A practical optical quantum memory must be able to store and recall quantum states on demand with high efficiency and low noise. Ideally, the platform for the memory would also be simple and inexpensive. Here, we present a complete tomographic reconstruction of quantum states that have b…
A simultaneous, contextual experimental demonstration of the two processes of cloning an input qubit and of flipping it into the orthogonal qubit is reported. The adopted experimental apparatus, a Quantum-Injected Optical Parametric Amplifier (QIOPA) is transformed simultaneously into a Universal Optimal Quantum Cloning Machine (UOQCM) and into a Universal NOT quantum-information gate. The two processes, indeed forbidden in their exact form for fundamental quantum limitations, will be found to be universal and optimal, i.e. the measured fidelity of both processes F<1 will be found close to the…
Based on the detection loophole-free photon key distribution (PKD) compatible with classical optical systems, an optical key distribution (OKD) protocol is presented for unconditionally secured cryptography in fiber-optic communications networks using addressable continuous phase basis, where each communication channel is composed of paired transmission lines. The unconditional security in OKD lies in quantum superposition between the paired lines of each channel. The continuous phase basis in OKD can be applied for one-time-pad optical cryptography in networks, whose network address capacity …
In the paper we consider a new approach for storage and cloning of quantum information by three level atomic (molecular) systems in the presence of the electromagnetically induced transparency (EIT) effect. For that, the various schemes of transformation into the bright and dark polaritons for quantum states of optical field in the medium are proposed. Physical conditions of realization of quantum nondemolition (QND) storage of quantum optical state are formulated for the first time. We have shown that the best storage and cloning of can be achieved with the atomic ensemble in the Bose-Einstei…
Some multipartite quantum states can be generated in a sequential manner which may be implemented by various physical setups like microwave and optical cavity QED, trapped ions, and quantum dots etc. We analyze the general N to M qubits Universal Quantum Cloning Machine (UQCM) within a sequential generation scheme. We show that the N to M sequential UQCM is available. The case of d-level quantum states sequential cloning is also presented.
We propose a scheme to unconditionally entangle the internal states of atoms trapped in separate high finesse optical cavities. The scheme uses the technique of quantum reservoir engineering in a cascaded cavity QED setting, and for ideal (lossless) coupling between the cavities generates an entangled pure state. Highly entangled states are also shown to be possible for realizable cavity QED parameters and with nonideal coupling.
Atomic frequency comb (AFC) made of an ensemble of atoms with a periodic optical resonance was originally proposed as a viable approach for quantum memory for photons. In this paper, we examine the quantum cloning capacity of an AFC in terms of the spectral distribution of the atomic populations in the energy levels associated by the optical transition. Expressions are derived for the memory readout efficiency, signal to noise ratio, and fidelity for an input at the single photon level. When applied to a square toothed AFC, our analysis shows that there is a region where amplification from the…
We study state-dependent quantum cloning which can outperform universal cloning. This is possible by using some a priori information on a given quantum state to be cloned. Specifically, we propose a generalization and optical implementation of quantum optimal mirror phase-covariant cloning, which refers to optimal cloning of sets of qubits of known modulus of expectation value of Pauli's Z operator. Our results can be applied for cloning of an arbitrary mirror-symmetric distribution of qubits on Bloch sphere including in special cases the universal cloning and phase-covariant cloning. We show …
The fidelity of a quantum transformation is strongly linked with the prior partial information of the state to be transformed. We illustrate this interesting point by proposing and demonstrating the superior cloning of coherent states with prior partial information. More specifically, we propose two simple transformations that under the Gaussian assumption optimally clone symmetric Gaussian distributions of coherent states as well as coherent states with known phases. Furthermore, we implement for the first time near-optimal state-dependent cloning schemes relying on simple linear optics and f…
We present the first experimental implementation of a multifunctional device for the optimal cloning of one to two qubits. Previous implementations have always been designed to optimize the cloning procedure with respect to one single type of a priori information about the cloned state. In contrast, our "all-in-one" implementation is optimal for several prominent regimes such as universal cloning, phase-covariant cloning, and also the first ever realized mirror phase-covariant cloning, when the square of the expected value of Pauli's Z operator is known in advance. In all these regimes the exp…
We report on two optical realizations of the $1 \to 2$ asymmetric phase-covariant cloning machines for polarization states of single photons. The experimental setups combine two-photon interference and tunable polarization filtering that enables us to control the asymmetry of the cloners. The first scheme involves a special unbalanced bulk beam splitter exhibiting different splitting ratios for vertical and horizontal polarizations, respectively. The second implemented scheme consists of a balanced fiber coupler where photon bunching occurs, followed by a free-space part with polarization filt…
The celebrated quantum no-cloning theorem states that an arbitrary quantum state cannot be cloned perfectly. This raises questions about cloning of classical states, which have also attracted attention. Here, we present a physical approach to the classical cloning process showing how cloning can be realised using Hamiltonians. After writing down a canonical transformation that clones classical states, we show how this can be implemented by Hamiltonian evolution. We then propose an experiment using the tools of nonlinear optics to realise the ideas presented here. Finally, to understand the clo…
The quantum cloner machine maps an unknown arbitrary input qubit into two optimal clones and one optimal flipped qubit. By combining linear and non-linear optical methods we experimentally implement a scheme that, after the cloning transformation, restores the original input qubit in one of the output channels, by using local measurements, classical communication and feedforward. This significant teleportation-like method demonstrates how the information is preserved during the cloning process. The realization of the reversion process is expected to find useful applications in the field of mod…
In this paper, we present an efficient implementation method of physical layer of Y-00 which can support a secure communication and a quantum key distribution (more generally key expansion) by IMDD(intensity modulation/direct detection) or FSK(frequency shift keying)optical fiber communication network. Although the general proof of the security is not yet given, a brief sketch of security analysis is shown, which involve an entanglement attack.
We investigate the optimal distribution of quantum information over multipartite systems in asymmetric settings. We introduce cloning transformations that take $N$ identical replicas of a pure state in any dimension as input, and yield a collection of clones with non-identical fidelities. As an example, if the clones are partitioned into a set of $M_A$ clones with fidelity $F^A$ and another set of $M_B$ clones with fidelity $F^B$, the trade-off between these fidelities is analyzed, and particular cases of optimal $N \to M_A+M_B$ cloning machines are exhibited. We also present an optimal $1 \to…
Quantum no-cloning, the impossibility of perfectly cloning an arbitrary unknown quantum state, is one of the most fundamental limitations due to the laws of quantum mechanics, which underpin the physical security of quantum key distribution. Quantum physics does allow, however, approximate cloning with either imperfect state fidelity and/or probabilistic success. Whereas approximate quantum cloning of single-particle states has been tested previously, experimental cloning of quantum entanglement -- a highly non-classical correlation -- remained unexplored. Based on a multiphoton linear optics …
A simultaneous realization of the Universal Optimal Quantum Cloning Machine (UOQCM) and of the Universal-NOT gate by a quantum injected optical parametric amplification (QIOPA), is reported. The two processes, forbidden in their exact form for fundamental quantum limitations, are found universal and optimal, and the measured fidelity F<1 is found close to the limit values evaluated by quantum theory. This work may enlighten the yet little explored interconnections of fundamental axiomatic properties within the deep structure of quantum mechanics.
We study machines that take N identical replicas of a pure qudit state as input and output a set of M_A clones of a given fidelity and another set of $M_B$ clones of another fidelity. The trade-off between these two fidelities is investigated, and numerous examples of optimal N -> M_A+M_B cloning machines are exhibited using a generic method. A generalisation to more than two sets of clones is also discussed. Finally, an optical implementation of some such machines is proposed. This paper is an extended version of [xxx.arxiv.org/abs/quant-ph/0411179].
The unconditional entanglement swapping for continuous variables is experimentally demonstrated. Two initial entangled states are produced from two nondegenerate optical parametric amplifiers operating at deamplification. Through implementing the direct measurement of Bell-state between two optical beams from each amplifier the remaining two optical beams, which have never directly interacted with each other, are entangled. The quantum correlation degrees of 1.23dB and 1.12dB below the shot noise limit for the amplitude and phase quadratures resulting from the entanglement swapping are straigh…
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…
Light fields can be amplified by measuring the field amplitude reflected at a beam splitter of reflectivity R and adding a coherent amplitude proportional to the measurement result to the transmitted field. By applying the quantum optical realization of this amplification scheme to single photon inputs, it is possible to clone the polarization states of photons. We show that optimal cloning of single photon polarization is possible when the gain factor of the amplification is equal to the inverse squareroot of 1-R.
We report on experimental implementation of the optimal universal asymmetric 1->2 quantum cloning machine for qubits encoded into polarization states of single photons. Our linear optical machine performs asymmetric cloning by partially symmetrizing the input polarization state of signal photon and a blank copy idler photon prepared in a maximally mixed state. We show that the employed method of measurement of mean clone fidelities exhibits strong resilience to imperfect calibration of the relative efficiencies of single-photon detectors used in the experiment. Reliable characterization of the…
Cloning of arbitrary images encoded onto the spatial profile of a laser beam onto that of a second beam is theoretically investigated. The two fields couple to an atomic lambda system in a coherent population trapping configuration. In particular, the case in which the probe and control fields are of comparable strength is considered. By considering more and more complex structures, we eventually find that our method is suitable to clone arbitrary images, which we demonstrated by a full numerical simulation of the propagation dynamics of both applied fields in the atomic medium, with the three…
We propose an interesting scheme for distributed orbital state quantum cloning with atomic ensembles based on the quantum Zeno dynamics. These atomic ensembles which consist of identical three-level atoms are trapped in distant cavities connected by a single-mode integrated optical star coupler. These qubits can be manipulated through appropriate modulation of the coupling constants between atomic ensemble and classical field, and the cavity decay can be largely suppressed as the number of atoms in the ensemble qubits increases. The fidelity of each cloned qubit can be obtained with analytic r…
We consider the quantum cloning of continuous variable entangled states. This is achieved by introducing two symmetric entanglement cloning machines (or e-cloners): a local e-cloner and a global e-cloner; where we look at the preservation of entanglement in the clones under the condition that the fidelity of the clones is maximized. These cloning machines are implemented using simple linear optical elements such as beam splitters and homodyne detection along with squeeze gates. We show that the global e-cloner out-performs the local e-cloner both in terms of the fidelity of the cloned states a…
The high resilience to de-coherence shown by a recently discovered Macroscopic Quantum Superposition (MQS) generated by a quantum injected optical parametric amplifier (QI-OPA) and involving a number of photons in excess of 5x10^4 motivates the present theoretical and numerical investigation. The results are analyzed in comparison with the properties of the MQS based on coherent states and NOON states, in the perspective of the comprehensive theory of the subject by W.H.Zurek. In that perspective the concepts of "pointer state", "einselection" are applied to the new scheme.
Long-distance quantum communication requires quantum repeaters to overcome photon loss in optical fibers. Here we demonstrate a repeater node with two memory atoms in an optical cavity. Both atoms are individually and repeatedly entangled with photons that are distributed until each communication partner has independently received one of them. An atomic Bell-state measurement followed by classical communication serves to establish a key. We demonstrate scaling advantage of the key rate, increase the effective attenuation length by a factor of two, and beat the error-rate threshold of 11\% for …
We consider two quantum cryptographic schemes relying on encoding the key into qudits, i.e. quantum states in a d-dimensional Hilbert space. The first cryptosystem uses two mutually unbiased bases (thereby extending the BB84 scheme), while the second exploits all the d+1 available such bases (extending the six-state protocol for qubits). We derive the information gained by a potential eavesdropper applying a cloning-based individual attack, along with an upper bound on the error rate that ensures unconditional security against coherent attacks.
We present the results of a linear optics photonic implementation of a quantum circuit that simulates a phase covariant cloner, by using two different degrees of freedom of a single photon. We experimentally simulate the action of two mirrored $1\rightarrow 2$ cloners, each of them biasing the cloned states into opposite regions of the Bloch sphere. We show that by applying a random sequence of these two cloners, an eavesdropper can mitigate the amount of noise added to the original input state and therefore prepare clones with no bias but with the same individual fidelity, masking its presenc…
This paper proposes a scheme for creating and storing quantum entanglement over long distances. Optical cavities that store this long-distance entanglement in atoms could then function as nodes of a quantum network, in which quantum information is teleported from cavity to cavity. The teleportation can be carried out unconditionally via measurements of all four Bell states, using a method of sequential elimination.
In this report, we simulate practical feature of Yuen-Kim protocol for quantum key distribution with unconditional secure. In order to demonstrate them experimentally by intensity modulation/direct detection(IMDD) optical fiber communication system, we use simplified encoding scheme to guarantee security for key information(1 or 0). That is, pairwise M-ary intensity modulation scheme is employed. Furthermore, we give an experimental implementation of YK protocol based on IMDD.
The propagation of a weak optical pulse through an atomic system in closed $Λ$ configuration is investigated in which the hyper fine levels are coupled by a microwave pulse. Under three photon resonance condition, it is observed that the probe pulse shape gets cloned by the shape of the microwave pulse along propagation through the medium. The temporal position of the probe pulse is dragged to that of the microwave pulse. A simple expression for the linear susceptibility of the medium for the corresponding transition is derived in the Fourier domain. From the numerical analysis of dynamics usi…
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 …
We propose schemes for the unconditional preparation of a two-mode squeezed state of effective bosonic modes realized in a pair of atomic ensembles interacting collectively with optical cavity and laser fields. The scheme uses Raman transitions between stable atomic ground states and under ideal conditions produces pure entangled states in the steady state. The scheme works both for ensembles confined within a single cavity and for ensembles confined in separate, cascaded cavities.
We consider the optimal cloning of quantum coherent states with single-clone and joint fidelity as figures of merit. Both optimal fidelities are attained for phase space translation covariant cloners. Remarkably, the joint fidelity is maximized by a Gaussian cloner, whereas the single-clone fidelity can be enhanced by non-Gaussian operations: a symmetric non-Gaussian 1-to-2 cloner can achieve a single-clone fidelity of approximately 0.6826, perceivably higher than the optimal fidelity of 2/3 in a Gaussian setting. This optimal cloner can be realized by means of an optical parametric amplifier …
We experimentally demonstrate phase-insensitive linear optical amplification which preserves the idler at the output. Since our amplification operation is unitary up to small excess noise, it is reversible beyond the classical limit. The entanglement between the two output modes is the resource for the reversibility. The amplification gain of 2.0 is demonstrated. In addition, combining this amplifier with a beamsplitter, we also demonstrate approximate cloning of coherent states where an anticlone is present. We investigate the reversibility by reconstructing the initial state from the output …
We propose the improved decoy state quantum key distribution incorporating finite statistics due to the finite code length and report on its demonstration. In our experiment, four different intensities including the vacuum state for optimal pulses are used and the key generation rate of 200 bps is achieved in the 20 km telecom optical fiber transmission keeping the eavesdropper's mutual information with the final key less than 2^{-9}.
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…
Major obstacles against efficient long distance quantum communication are photon losses during transmission and the probabilistic nature of Bell measurement causing exponential scaling in time and resource with distance. To overcome these difficulties, while conventional quantum repeaters require matter-based operations with long-lived quantum memories, recent proposals have employed encoded multiple photons in entanglement, providing an alternative way for scalability. In pursuing scalable quantum communications, naturally arising questions are thus whether any ultimate limit exists in all-op…
We identify a broad class of physical processes in an optical quantum circuit that can be efficiently simulated on a classical computer: this class includes unitary transformations, amplification, noise, and measurements. This simulatability result places powerful constraints on the capability to realize exponential quantum speedups as well as on inducing an optical nonlinear transformation via linear optics, photodetection-based measurement and classical feedforward of measurement results, optimal cloning, and a wide range of other processes.
Entanglement drives nearly all proposed quantum information technologies. By up-converting part of a 1550 nm two-mode squeezed vacuum state to 532 nm, we demonstrate the generation of strong continuous-variable entanglement between widely separated frequencies. Nonclassical correlations were observed in joint quadrature measurements of the 1550 and 532 nm fields, showing a maximum noise suppression 5.5 dB below vacuum. Our versatile technique combines strong nonclassical correlations, large bandwidth, and in principle, the ability to entangle the telecommunication wavelength of 1550 nm with an…
The problem of unconditional security of quantum cryptography (i.e. the security which is guaranteed by the fundamental laws of nature rather than by technical limitations) is one of the central points in quantum information theory. We propose a relativistic quantum cryptosystem and prove its unconditional security against any eavesdropping attempts. Relativistic causality arguments allow to demonstrate the security of the system in a simple way. Since the proposed protocol does not employ collective measurements and quantum codes, the cryptosystem can be experimentally realized with the prese…
Superpositions of two orthogonal single-photon polarization states are commonly used as optical qubits. If such qubits are sent by continuous variable quantum teleportation, the modifications of the qubit states due to imperfect entanglement cause an increase in the average photon number of the output state. This effect can be interpreted as an accidental quantum cloning of the single photon input. We analyze the output statistics of the single photon teleportation and derive the transfer and cloning fidelities from the equations of the polarization qubit.
We present an experimental realization of a low-noise, phase-insensitive optical amplifier using a four-wave mixing interaction in hot Rb vapor. Performance near the quantum limit for a range of amplifier gains, including near unity, can be achieved. Such low-noise amplifiers are essential for so-called quantum cloning machines and are useful in quantum information protocols. We demonstrate that amplification and ``cloning'' of one half of a two-mode squeezed state is possible while preserving entanglement.
We propose a linear-optical setup for heralded qubit amplification with tunable output qubit fidelity. We study its success probability as a function of output qubit fidelity showing that at the expense of lower fidelity, the setup can considerably increase probability of successful operation. These results are subsequently applied in a proposal for state dependent qubit amplification. Similarly to state-dependent quantum cloning, the a priori information about the input state allows to optimize the qubit amplification procedure to obtain better fidelity versus success probability trade-off.
We demonstrate an unconditional high-fidelity teleporter capable of preserving the broadband entanglement in an optical squeezed state. In particular, we teleport a squeezed state of light and observe $-0.8 \pm 0.2$dB of squeezing in the teleported (output) state. We show that the squeezing criterion translates directly into a sufficient criterion for entanglement of the upper and lower sidebands of the optical field. Thus, this result demonstrates the first unconditional teleportation of broadband entanglement. Our teleporter achieves sufficiently high fidelity to allow the teleportation to b…
