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 limit values evaluated by quantum theory. A contextual theoretical and experimental investigation of these processes, which may represent the basic difference between the classical and the quantum worlds, can reveal in a unifying manner the detailed structure of quantum information. It may also enlighten the yet little explored interconnections of fundamental axiomatic properties within the deep structure of quantum mechanics. PACS numbers: 03.67.-a, 03.65.Ta, 03.65.Ud
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.
We investigate the multiphoton states generated by high-gain optical parametric amplification of a single injected photon, polarization encoded as a ''qubit''. The experiment configuration exploits the optimal phase-covariant cloning in the high gain regime. The interference fringe pattern showing the non local transfer of coherence between the injected qubit and the mesoscopic amplified output field involving up to 4000 photons has been investigated. A probabilistic new method to extract full information about the multiparticle output wavefunction has been implemented.
We demonstrate that a phase-independent quantum amplifier of a polarization qubit is a complementary amplifier of the heralded qubit amplifier [N. Gisin, S. Pironio and N. Sangouard, Phys. Rev. Lett. 105, 070501 (2010)]. It employs the multi-functional cloner in 1 to 2 copying regime, capable of providing approximate copies of qubits given by various probability distributions, and is optimized for distributions with axial symmetry. Direct applications of the proposed solution are possible in quantum technologies, doubling the range where quantum information is coherently broadcast. It also out…
We investigate the multiparticle quantum superposition and the persistence of multipartite entanglement of the quantum superposition generated by the quantum injected high-gain optical parametric amplification of a single photon. The physical configuration based on the optimal universal quantum cloning has been adopted to investigate how the entanglement and the quantum coherence of the system persists for large values of the nonlinear parametric gain g.
We discuss the recently introduced concept of non-deterministic noiseless linear amplification, demonstrating that such an operation can only be performed perfectly with vanishing probability of success. We show that a weak measurement, which imprints the weak value of an observable of a pre-selected and post-selected system onto a probe system, can be used to approximate probabilistic noiseless amplification. This result may be applied to various tasks in continuous variable quantum information, including entanglement concentration, probabilistic cloning, and in quantum repeaters. We discuss …
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 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.
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…
The impossibility of perfectly copying (or cloning) an arbitrary quantum state is one of the basic rules governing the physics of quantum systems. The processes that perform the optimal approximate cloning have been found in many cases. These "quantum cloning machines" are important tools for studying a wide variety of tasks, e.g. state estimation and eavesdropping on quantum cryptography. This paper provides a comprehensive review of quantum cloning machines (both for discrete-dimensional and for continuous-variable quantum systems); in addition, it presents the role of cloning in quantum cry…
A transformation achieving the optimal symmetric N-to-M cloning of coherent states is presented. Its implementation only requires a phase-insensitive linear amplifier and a network of beam splitters. An experimental demonstration of this continuous-variable cloner should therefore be in the scope of current technology. The link between optimal quantum cloning and optimal amplification of quantum states is also pointed out.
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.
The idea of signal amplification is ubiquitous in the control of physical systems, and the ultimate performance limit of amplifiers is set by quantum physics. Increasing the amplitude of an unknown quantum optical field, or more generally any harmonic oscillator state, must introduce noise. This linear amplification noise prevents the perfect copying of the quantum state, enforces quantum limits on communications and metrology, and is the physical mechanism that prevents the increase of entanglement via local operations. It is known that non-deterministic versions of ideal cloning and local en…
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…
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.
We construct the optimal 1 to 2 cloning transformation for the family of displaced thermal equilibrium states of a harmonic oscillator, with a fixed and known temperature. The transformation is Gaussian and it is optimal with respect to the figure of merit based on the joint output state and norm distance. The proof of the result is based on the equivalence between the optimal cloning problem and that of optimal amplification of Gaussian states which is then reduced to an optimization problem for diagonal states of a quantum oscillator. A key concept in finding the optimum is that of stochasti…
We introduce the concept of non-deterministic noiseless linear amplification. We propose a linear optical realization of this transformation that could be built with current technology. We discuss two applications; ideal probabilistic cloning of coherent states and distillation of continuous variable entanglement. For the latter example we demonstrate that highly pure entanglement can be distilled from transmission over a lossy channel.
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 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 …
Non-deterministic noiseless amplification of a single mode can circumvent the unique challenges to amplifying a quantum signal, such as the no-cloning theorem, and the minimum noise cost for deterministic quantum state amplification. However, existing devices are not suitable for amplifying the fundamental optical quantum information carrier, a qubit coherently encoded across two optical modes. Here, we construct a coherent two-mode amplifier, to demonstrate the first heralded noiseless linear amplification of a qubit encoded in the polarization state of a single photon. In doing so, we increa…
We show theoretically that the multi-photon states obtained by cloning single-photon qubits via stimulated emission can be distinguished with the naked human eye with high efficiency and fidelity. Focusing on the "micro-macro" situation realized in a recent experiment [F. De Martini, F. Sciarrino, and C. Vitelli, Phys. Rev. Lett. 100, 253601 (2008)], where one photon from an original entangled pair is detected directly, whereas the other one is greatly amplified, we show that performing a Bell experiment with human-eye detectors for the amplified photon appears realistic, even when losses are …
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.
By amplifying photonic qubits it is possible to produce states that contain enough photons to be seen with a human eye, potentially bringing quantum effects to macroscopic scales [1]. In this paper we theoretically study quantum states obtained by amplifying one side of an entangled photon pair with different types of optical cloning machines for photonic qubits. We propose a detection scheme that involves lossy threshold detectors (such as human eye) on the amplified side and conventional photon detectors on the other side. We show that correlations obtained with such coarse-grained measureme…
The present work reports on an extended research endeavor focused on the theoretical and experimental realization of a macroscopic quantum superposition (MQS) made up with photons. As it is well known, this intriguing, fundamental quantum condition is at the core of a famous argument conceived by Erwin Schroedinger, back in 1935. The main experimental challenge to the actual realization of this object resides generally on the unavoidable and uncontrolled interactions with the environment, i.e. the decoherence leading to the cancellation of any evidence of the quantum features associated with t…
We investigate the resources needed for secure teleportation of coherent states. We extend continuous variable teleportation to include quantum tele-amplification protocols, that allow non-unity classical gains and a pre-amplification or post-attenuation of the coherent state. We show that, for arbitrary Gaussian protocols and a significant class of Gaussian resources, two-way steering is required to achieve a teleportation fidelity beyond the no-cloning threshold. This provides an operational connection between Gaussian steerability and secure teleportation. We present practical recipes sugge…
We study the directional amplification of an optical probe field in a three-mode optomechanical system, where the mechanical resonator interacts with two linearly-coupled optical cavities and the cavities are driven by strong optical pump fields. The optical probe field is injected into one of the cavity modes, and at the same time, the mechanical resonator is subject to a mechanical drive with the driving frequency equal to the frequency difference between the optical probe and pump fields. We show that the transmission of the probe field can be amplified in one direction and de-amplified in …
We consider transitions in quantum networks analogous to those in the two-dimensional Ising model. We show that for a network of active components the transition is between the quantum and the classical behaviour of the network, and the critical amplification coincides with the fundamental quantum cloning limit.
NOON states are path entangled states which can be exploited to enhance phase resolution in interferometric measurements. In the present paper we analyze the quantum states obtained by optical parametric amplification of polarization NOON states. First we study, theoretically and experimentally, the amplification of a 2-photon state by a collinear Quantum Injected Optical Parametric Amplifier (QIOPA). We compared the stimulated emission regime with the spontaneous one, studied by Sciarrino et al. (PRA 77, 012324), finding comparable visibilities between the two cases but an enhancement of the …
We present the first experimental demonstration of the ''optimal'' and ''universal'' quantum entangling process involving qubits encoded in the polarization of single photons. The structure of the ''quantum entangling machine'' consists of the quantum injected optical parametric amplifier by which the contextual realization of the 1->2 universal quantum cloning and of the universal NOT (U-NOT) gate has also been achieved.
We report the successful generation of an entangled multiparticle quantum superposition of pure photon states. They result from a multiple (universal} cloning of a single photon qubit by a high gain, quantum-injected parametric amplifier. The information preserving property of the process suggests for these states the name of ''multi-particle qubits''. They are ideal objects for investigating the emergence of the classical world in quantum systems with increasing complexity, the decoherence processes and may allow the practical implementation of the universal 2-qubit logic gates.
We show how polarisation measurements on the output fields generated by parametric down conversion will reveal a violation of multi-particle Bell inequalities, in the regime of both low and high output intensity. In this case each spatially separated system, upon which a measurement is performed, is comprised of more than one particle. In view of the formal analogy with spin systems, the proposal provides an opportunity to test the predictions of quantum mechanics for spatially separated higher spin states. Here the quantum behaviour possible even where measurements are performed on systems of…
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.
We consider imperfect two-mode bosonic quantum transducers that cannot completely transfer an initial source-system quantum state due to insufficient coupling strength or other non-idealities. We show that such transducers can generically be made perfect by using interference and phase-sensitive amplification. Our approach is based on the realization that a particular kind of imperfect transducer (one which implements a swapped quantum non-demolition (QND) gate) can be made into a perfect one-way transducer using feed-forward and/or injected squeezing. We show that a generic imperfect transduc…
A Macro-state consisting of N= 3.5 x 10^4 photons in a quantum superposition and entangled with a far apart single-photon state (Micro-state) is generated. Precisely, an entangled photon pair is created by a nonlinear optical process, then one photon of the pair is injected into an optical parametric amplifier (OPA) operating for any input polarization state, i.e. into a phase-covariant cloning machine. Such transformation establishes a connection between the single photon and the multi particle fields. We then demonstrate the non-separability of the bipartite system by adopting a local filter…
The squeezed states of light become more and more important in the fields of quantum enhanced precision measurement and quantum information. To get this vital continuous variable quantum resource, the generation of squeezed states of light becomes a key factor. In this paper, a compact telecom fiber-based bright squeezed light (BSL) generator is demonstrated. To our knowledge, this is the first time that BSL has been reported in a fiber-based system to date. To obtain the BSL, a double-pass parametric amplifier based on surface-coated lithium niobate waveguide is employed. When the 1550 nm see…
Superconducting parametric amplifiers are commonly fabricated using planar transmission lines with a non-linear inductance provided by either Josephson junctions or the intrinsic kinetic inductance of the thin film. However, Banys et al. [1] reported non-linear behaviour in a niobium pillbox cavity, hypothesising that below Tc, the pair iris-bulk resonator would act as a superconducting contact surface exploiting a Josephson-like non-linearity. This work investigates this effect further by applying Keysight Technologies' Advanced Design System (ADS) to simulate the cavity using an equivalent c…
We report the realization of an entangled quantum superposition of M=12 photons by a high gain, quantum-injected optical parametric amplification. The system is found so highly resilient against decoherence to exhibit directly accessible mesoscopic interference effects at normal temperature. By modern tomographic methods the non-separability and the quantum superposition are demonstrated for the overall mesoscopic output state of the dynamic ''closed system''. The device realizes the condition conceived by Erwin Schroedinger with his 1935 paradigmatic ''Cat'' apologue, a fundamental landmark i…
Quantum technologies are developing powerful tools to generate and manipulate coherent superpositions of different energy levels. Envisaging a new generation of energy-efficient quantum devices, here we explore how coherence can be manipulated without exchanging energy with the surrounding environment. We start from the task of converting a coherent superposition of energy eigenstates into another. We identify the optimal energy-preserving operations, both in the deterministic and in the probabilistic scenario. We then design a recursive protocol, wherein a branching sequence of energy-preserv…
We study the photon counting noise in optical interferometers used for gravitational wave detection. In order to reduce quantum noise a squeezed vacuum state is injected into the usually unused input port. Here, we specifically investigate the so called `dark port case', when the beam splitter is oriented close to 90° to the incoming laser beam, such that nearly all photons go to one output port of the interferometer, and only a small fraction of photons is seen in the other port (`dark port'). For this case it had been suggested that signal amplification is possible without concurrent noise a…
We study the photon counting noise in optical interferometers used for gravitational wave detection. In order to reduce quantum noise a squeezed vacuum is injected into the usually unused input port. It is investigated under which conditions the gravitational wave signal may be amplified without increasing counting noise concurrently. Such a possibility was suggested as a consequence of the entanglement of the two output ports of a beam splitter. We find that amplification without concurrent increase of noise is not possible for reasonable squeezing parameters. Photon distributions for various…
Fundamentally, the dynamics of micro-macro transitions is instrumental to understanding the process of quantum-to-classical transitions; technologically, it can also facilitate the detection of the microscopic signals in quantum experiments via convenient detectors. Here, we demonstrate a scheme to characterize micro-macro transitions based on a four-wave mixing linear optical amplification process in a hot rubidium vapor. The linear optical amplifier provides a large optical gain of $10^7$ for injected single-photon-level pulses, enabling photon-number-resolving detection by average via non-s…
Branch-resolved Pauli-block spectroscopy of residual conditional phase in two-qubit gates
Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Beijing Key Laboratory of Fault-Tolerant Quantum Computing（容错量子计算北京市重点实验室）；State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University（清华大学物理系低维量子物理国家重点实验室）；Hefei National Laboratory（合肥国家实验室）；School of Medical Technology, Beijing Institute of Technology（北京理工大学医学技术学院）
