We propose a simple scheme to generate an arbitrary photon-added coherent state of a travelling optical field by using only a set of degenerate parametric amplifiers and single-photon detectors. Particularly, when the single-photon-added coherent state (SPACS) is observed by following, e.g., the novel technique of Zavatta \emph{$et al.$} (Science 306, 660 (2004)), we also obtain the generalized optical entangled $W$ state. Finally, a qualitative analysis of possible losses in our scheme is given.
We propose a feasible scheme to realize the optical entanglement of single-photon-added coherent state (SPACS) and show that, besides the Sanders entangled coherent state, the entangled SPACS also leads to new forms of hybrid entanglement of quantum Fock state and classical coherent state. We probe the essential difference of two types of hybrid entangled state (HES). This HES provides a novel link between the discrete- and the continuous-variable entanglement in a natural way.
In this paper, We investigate three-mode photon-added Greenberger-Horne-Zeilinger (GHZ) entangled coherent states by repeatedly operating the photon-added operator on the GHZ entangled coherent states. The product of two Laguerre polynomials is demonstrated to be connected to the normalizing constant. The influence of the operation on the non-classical and non-Gaussian behavior of the GHZ entangled coherent states is investigated. Sub-Poissonian statistics, such as Mandel's parameter and the negativity of the Wigner function, show that non-classical properties can enhance GHZ entangled coheren…
We study the degree of entanglement of arbitrary superpositions of $m,n$ photon-added coherent states (PACS) $|ψ\rangle \propto u |α,m\rangle |β,n \rangle+ v |β,n\rangle |α,m\rangle$ using the concurrence, and obtain the general conditions for maximal entanglement. We show that photon addition process can be identified as an entanglement enhancer operation for superpositions of coherent states (SCS). Specifically for the known bipartite positive SCS: $|ψ\rangle \propto |α\rangle_a |-α\rangle_b + |-α\rangle_a |α\rangle_b $ whose entanglement tends to zero for $α\to 0$, can be maximal if al leas…
We propose a scheme for conditional generation of two-mode N-photon path-entangled states of traveling light field. These states may find applications in quantum optical lithography and they may be used to improve the sensitivity of interferometric measurements. Our method requires only single-photon sources, linear optics (beam splitters and phase shifters), and photodetectors with single photon sensitivity.
We propose a measurement protocol to generate path-entangled NOON states conditionally from two pulsed type II optical parametric oscillators. We calculate the fidelity of the produced states and the success probability of the protocol. The trigger detectors are assumed to have finite dead time, and for short pulse trigger fields they are modeled as on/off detectors with finite efficiency. Continuous-wave operation of the parametric oscillators is also considered.
The maximally entangled mixed states of Munro, James, White, and Kwiat [Phys. Rev. A {\bf 64} (2001) 030302] are shown to exhibit interesting features vis a vis conditional entropic measures. The same happens with the Ishizaka and Hiroshima states [Phys. Rev. A {\bf 62} 022310 (2000)], whose entanglement-degree can not be increased by acting on them with logic gates. Special types of entangled states that do not violate classical entropic inequalities are seen to exist in the space of two qubits. Special meaning can be assigned to the Munro {\it et al.} special participation ratio of 1.8.
We propose a universal scheme for the probabilistic generation of an arbitrary multimode entangled state of light with finite expansion in Fock basis. The suggested setup involves passive linear optics, single photon sources, strong coherent laser beams, and photodetectors with single-photon resolution. The efficiency of this setup may be greatly enhanced if, in addition, a quantum memory is available.
We show that conditional output measurement on a beam splitter may be used to produce photon-added states for a large class of signal-mode quantum states, such as thermal states, coherent states, squeezed states, displaced photon-number states, and coherent phase states. Combining a mode prepared in such a state and a mode prepared in a photon-number state, the state of the mode in one of the output channels of the beam splitter ``collapses'' to a photon-added state, provided that no photons are detected in the other output channel. We present analytical and numerical results, with special emp…
A system of cascaded qubits interacting via the oneway exchange of photons is studied. While for general operating conditions the system evolves to a superposition of Bell states (a dark state) in the long-time limit, under a particular resonance condition no steady state is reached within a finite time. We analyze the conditional quantum evolution (quantum trajectories) to characterize the asymptotic behavior under this resonance condition. A distinct bimodality is observed: for perfect qubit coupling, the system either evolves to a maximally entangled Bell state without emitting photons (the…
The single-photon-added coherent state (SPACS), as an intermediate classical-to-purely-quantum state, was first realized recently by Zavatta \emph{$et al.$} (Science 306, 660 (2004)). We show here that the success probability of their SPACS generation can be enhanced by a simple method which leads to simultaneous creations of a discrete-variable entangled state and a SPACS or even a hybrid-variable entangled SPACS in two different channels. The impacts of the input thermal noise are also analyzed.
We address the intrinsic multimode nature of the quantum state of light obtained by pulsed spontaneous parametric downconversion and develop a theoretical model based only on experimentally accessible quantities. We exploit the pairwise entanglement as a resource for conditional multimode measurements and derive closed formulas for the detection probability and the density matrix of the conditional states. We present a set of experiments performed to validate our model in different conditions that are in excellent agreement with experimental data. Finally, we evaluate nonGaussianity of the con…
In [\href{http://www.sciencedirect.com/science/article/pii/037596019290711T}{Phys. Lett. A {\bf 166}, 293 (1992)}] Popescu characterized nonlocality of pure $n$-partite entangled systems by studying bipartite violation of local realism when $n-2$ number of parties perform projective measurements on their particles. A pertinent question in this scenario is whether similar characterization is possible for $n$-partite mixed entangled states also. In the present work we have followed an analogous approach so as to explore whether given a tripartite mixed entangled state the conditional bipartite s…
An approach for generating the entangled photonic states |F1,F2>+|F2,F1> from two arbitrary states |F1> and |F2> is proposed. The protocol is implemented by the conditionally induced beam-splitter coupling which leads to the selective swapping between two photonic modes. Such coupling occurs in a quantum system prepared in the superposition of two ground states with only one of them being involved in the swapping. All the entangled states in the category, such as entangled pairs of coherent states or Fock states (N00N states), can be efficiently produced in the same way by this method.
Evaluating the Wigner function of quantum states in the entangled state representation is introduced, based on which we present a new approach for deriving time evolution formula of Wigner function in laser process. Application of this fomula to calculating time evolution of photon number is also presented, as an example, the case when the initial state is photon-added coherent state is discussed.
We present an scheme to generate entangled state between two traveling modes for fixed number of photon, which is based on beam splitter transformation and conditional zero photon counters.
The problem of photon adding and subtracting is studied, using conditional output measurement on a beam splitter. It is shown that for various classes of states the corresponding photon-added and -subtracted states can be prepared. Analytical results are presented, with special emphasis on photon-added and -subtracted squeezed vacuum states, which are found to represent two different types of Schroedinger-cat-like states. Effects of realistic photocounting and Fock-state preparation are discussed.
The quantum fluctuations of a physical property can be observed in the measurement statistics of any measurement that is at least partially sensitive to that physical property. Quantum theory indicates that the effective distribution of values taken by the physical property depends on the specific measurement context based on which these values are determined and weak values have been identified as the contextual values describing this dependence of quantum fluctuations on the measurement context. Here, the relation between classical statistics and quantum contextuality is explored by consider…
Conditions to generate high-purity entangled vacuum-evacuated coherent states ($|0>|α>^0 - |-α>^0 |0>$ were studied for two cascade-placed beam splitters, with one squeezed state input and two coherent state inputs whenever a single photon is detected. Controlling the amplitudes and the phases of the beams allows for various amplitudes of the vacuum-evacuated coherent states ($|α>^ 0 = |α> -e^{-|α|^2} |0> $) up to $α= 2.160$ to be manipulated with high-purity.
We show that the recently proposed scheme of teleportation of continuous variables [S.L. Braunstein and H.J. Kimble, Phys. Rev. Lett. 80, 869 (1998)] can be improved by a conditional measurement in the preparation of the entangled state shared by the sender and the recipient. The conditional measurement subtracts photons from the original entangled two-mode squeezed vacuum, by transmitting each mode through a low-reflectivity beam splitter and performing a joint photon-number measurement on the reflected beams. In this way the degree of entanglement of the shared state is increased and so is t…
Using the thermal field dynamics theory to convert the thermal state to a "pure" state in doubled Fock space, it is found that the average value of e^{fa^{†}a} under squeezed thermal state (STS) is just the generating function of Legendre polynomials, a remarkable result. Based on this point, the normalization and photon-number distributions of m-photon added (or subtracted) STS are conviently obtained as the Legendre polynomials. This new concise method can be expanded to the entangled case.
In this paper, we describe how to realize conditional frequency entanglement swapping and to produce probabilisticly a three-photon frequency entangled state from two pairs of frequency entangled states by using an Acoustic-Optical-Modulator. Both schemes are very simple and may be implementable in practice.
We show that a continuous range of nonclassical states of light can be generated using conditional measurements on the idler mode of an optical parametric amplifier. The output state is prepared by introducing a coherent state in the signal mode of the amplifier with a single photon in the idler mode, followed by a conditional measurement of a single photon in the output idler mode. By varying the gain of the amplifier, this approach can produce a coherent state, a photon-added state, a displaced number state, or a continuous range of other nonclassical states with intermediate properties. We …
We study single photon optomechanics conditioned on photon counting events. By selecting only detection events that occur long after a photon pulse arrives at the cavity, the optomechanical interaction time can be increased, allowing a large momentum kick to be applied to the oscillator. We apply this to two optomechanical cavities set up within a Mach-Zhender interferometer driven by a single photon source. The conditional state of the mechanical modes in such a system becomes an entangled cat state for detection times resulting in maximum mechanical amplitude in phase space. Further we study…
The relations of antilinear maps, bipartite states and quantum channels is summarized. Antilinear maps are applied to describe bipartite states and entanglement. Teleportation is treated in this general formalism with an emphasis on conditional schemes applying partially entangled pure states. It is shown that in such schemes the entangled state shared by the parties, and those measured by the sender should ``match'' each other.
We report measurements of time-frequency entangled photon pairs and heralded single photons at telecommunications wavelengths, generated using a periodically-poled, lithium niobate on insulator (LNOI) waveguide pumped optically by a diode laser. We achieve a high Coincidences-to-Accidentals Ratio (CAR) at high pair brightness, a low value of the conditional self-correlation function [$g^{(2)}$(0)], and high two-photon energy-time Franson interferometric visibility, which demonstrate the high quality of the entangled photon pairs and heralded single photons.
We propose a linear optical scheme that can conditionally generate high NOON states using polarization modes. This scheme provides advantages over the previous proposals on path-entangled NOON states in view of success probability or required resources of optical elements. We also investigate two experimental schemes feasible within existing technology that can produce the NOON-like or the NOON state for N = 4.
We introduce a kind of entangled state---photon-addition two-mode squeezed thermal state (TMSTS) by adding photons to each mode of the TMSTS. Using the P-representation of thermal state, the compact expression of the normalization factor is derived, a Jacobi polynomial. The nonclassicality is investigated by exploring especially the negativity of Wigner function. The entanglement is discussed by using Shchukin-Vogel criteria. It is shown that the photon-addtion to the TMSTS may be more effective for the entanglement enhancement than the photon-subtraction from the TMSTS. In addition, the quant…
Conditional interference patterns can be obtained with twin photons from spontaneous parametric down-conversion and the phase of the pattern can be controlled by the relative transverse position of the signal and idler detectors. Using a configuration that produces entangled photons in both polarization and transverse momentum we report on the control of the conditional patterns by acting on the polarization degree of freedom.
Using the quantum teleportation in continuous variables as a test scheme, we compare two entangled transformations - mixing of signals on a beamsplitter and by the CZ operation. We evaluate these transformations in terms of the errors added to teleported oscillators. We have shown that the CZ operation leads to the lower error of teleportation. This error can be further reduced by choosing appropriate weight coefficients for the CZ transforms. We have compared the errors of the theoretical CZ scheme and its practical implementation in the optical design. Although the CZ optical scheme adds int…
The generation and storage of entangled photons play important roles in quantum information technique. Spontaneous Raman scattering (SRS) in atomic ensembles provides a promising method to generate entangled photons capable of storage. In the past experiments, a spin-wave-photon entangled state is produced via SRS in an atomic ensemble, with which a pair of entangled photons is obtained. Here, we report a scheme of simultaneously generating two spin-wave-photon entangled states in an atomic ensemble by collecting Stokes photons at two different directions. Based on the obtained two atom-photon…
We theoretically demonstrate a method for producing the maximally path-entangled state (1/Sqrt[2]) (|N,0> + exp[iN phi] |0,N>) using intensity-symmetric multiport beamsplitters, single photon inputs, and either photon-counting postselection or conditional measurement. The use of postselection enables successful implementation with non-unit efficiency detectors. We also demonstrate how to make the same state more conveniently by replacing one of the single photon inputs by a coherent state.
We propose a conditional scheme to generate entangled two-photons generalized binomial states inside two separate single-mode high-Q cavities. This scheme requires that the two cavities are initially prepared in entangled one-photon generalized binomial states and exploits the passage of two appropriately prepared two-level atoms one in each cavity. The measurement of the ground state of both atoms is finally required when they exit the cavities. We also give a brief evaluation of the experimental feasibility of the scheme.
We consider a model Hamiltonian describing the interaction of a single-mode radiation field with the atoms of a nonlinear medium, and study the dynamics of entanglement for specific non-entangled initial states of interest: namely, those in which the field mode is initially in a Fock state, a coherent state, or a photon-added coherent state. The counterparts of near-revivals and fractional revivals are shown to be clearly identifiable in the entropy of entanglement. The ``overlap fidelity'' of the system is another such indicator, and its behaviour corroborates that of the entropy of entanglem…
The production of conditional quantum states and quantum operations based on the result of measurement is now seen as a key tool in quantum information and metrology. We propose a new type of photon number detector. It functions non-deterministically, but when successful, it has high fidelity. The detector, which makes use of an n-photon auxiliary Fock state and high efficiency Homodyne detection, allows a tunable tradeoff between fidelity and probability. By sacrificing probability of operation, an excellent approximation to a photon number detector is achieved.
In this paper, an experiment of quantum diffraction of position-momentum entangled photons from a straight sharp edge is presented. Path of a single photon of an entangled pair is partially blocked by a sharp edge whereas the other photon is detected at a stationary location without revealing the which-path information of the other photon. Quantum diffraction pattern of the sharp edge is revealed only in the correlated conditional detection of spatially separated photons and no diffraction pattern is formed in local detections of individual photons. Theoretical analysis of the quantum diffract…
Non Gaussian states and processes are useful resources in quantum information with continuous variables. An experimentally accessible criterion has been proposed to measure the degree of non Gaussianity of quantum states, based on the conditional entropy of the state with a Gaussian reference. Here we adopt such criterion to characterise an important class of non classical states, single-photon added coherent states. Our studies demonstrate the reliability and sensitivity of this measure, and use it to quantify how detrimental is the role of experimental imperfections in our realisation.
We review entangled coherent state research since its first implicit use in 1967 to the present. Entangled coherent states are important to quantum superselection principles, quantum information processing, quantum optics, and mathematical physics. Despite their inherent fragility they have produced in a conditional propagating-wave quantum optics realization. Fundamentally the states are intriguing because they are entanglements of the coherent states, which are in a sense the most classical of all states of a dynamical system.
The model of a quantum-optical device for a conditional preparation of entangled states from input mixed states is presented. It is demonstrated that even thermal or pseudo-thermal radiation can be entangled in such a way, that Bell-inequalities are violated.
We present a realistic purification scheme for pure non-maximally entangled states. In the scheme, Alice and Bob at two distant parties first start with two shared but less entangled photon pairs to produce a conditional four-photon GHZ state, then perform a 45-degree polarization measurement onto one of the two photons at each party such that the remaining two photons are projected onto a maximally entangled state.
We discuss the generation of entangled states of two two-level atoms inside an optical resonator. When the cavity decay is continuously monitored, the absence of photon-counts is associated with the presence of an atomic entangled state. In addition to being conceptually simple, this scheme could be demonstrated with presently available technology. We describe how such a state is generated through conditional dynamics, using quantum jump methods, including both cavity damping and spontaneous emission decay, and evaluate the fidelity and relative entropy of entanglement of the generated state c…
A simple experimental setup consisting of a spontaneous parametric down-conversion source and passive linear optics is proposed for conditional preparation of a maximally entangled polarization state of two photons. Successful preparation is unambiguously heralded by coincident detection of four auxiliary photons. The proposed scheme utilizes the down-conversion term corresponding to the generation of three pairs of photons. We analyze imperfect detection of the auxiliary photons and demonstrate that its deleterious effect on the fidelity of the prepared state can be suppressed at the cost of …
The polarization analysis of quantized probe light transmitted through an atomic ensemble has been used to prepare entangled collective atomic states. In a "balanced" detection configuration, where the difference signal from two detection ports is analyzed, the continuous monitoring of a component of the Stokes field vector provides a means for conditional projective measurements on the atomic system. Here, we make use of classical driving fields, in the pulsed regime, and of an "unbalanced" detection setup (single detector) where the effective photon number of scattered photons is the detecte…
A novel ultrabright parametric source of polarization entangled photon pairs with striking spatial characteristics is reported. The distribution of the output electromagnetic k-modes excited by Spontaneous Parametris Down Conversion and coupled to the output detectors can be very broad. It could coincide with the full set of phase-matched excited modes, at least in principle. In this case a relevant conditional quasi-pure output state should be realized. By these (approximate) states realized over a full Entanglement-Ring output distribution, the non local properties of the generated entanglem…
Future quantum optical networks will require the ability to route entangled photons at high speeds, with minimal loss and added in-band noise, and---most importantly---without disturbing the photons' quantum state. Here we present an all-optical switch which fulfills these requirements and characterize its performance at the single photon level. It exhibits a 200-ps switching window, 120:1 contrast, 1.5-dB loss, and induces no measurable degradation in the switched photons' entangled-state fidelity (< 0.002). As a proof-of-principle demonstration of its capability, we use the switch to demulti…
There are a number of different strategies to measure the phase shift between two pathways of light more efficiently than suggested by the standard quantum limit. One way is to use highly entangled photons. Another way is to expose photons to a non-linear or interacting Hamiltonian. This paper emphasises that the conditional dynamics of open quantum systems provides an interesting additional tool for quantum-enhanced metrology. As a concrete example, we review a recent scheme which exploits the conditional dynamics of a laser-driven optical cavity with spontaneous photon emission inside a quan…
We experimentally demonstrate the noiseless teleportation of a single photon by conditioning on quadrature Bell measurement results near the origin in phase space and thereby circumventing the photon loss that otherwise occurs even in optimal gain-tuned continuous-variable quantum teleportation. In general, thanks to this loss suppression, the noiseless conditional teleportation can preserve the negativity of the Wigner function for an arbitrary pure input state and an arbitrary pure entangled resource state. In our experiment, the positive value of the Wigner function at the origin for the un…
We investigate how the entanglement characteristics of a non-Gaussian entangled state are increased or decreased by a local photon subtraction operation. The non-Gaussian entangled state is generated by injecting a single-mode non-Gaussian state and a vacuum state into a 50:50 beam splitter. We consider a photon-added coherent state and an odd coherent state as a single-mode non-Gaussian state. In the regime of small amplitude, we show that the performance of quantum teleportation and the second-order Einstein-Podolsky- Rosen-type correlation can both be enhanced, whereas the degree of entangl…
We theoretically analyze the Einstein-Podolsky-Rosen (EPR) correlation, the quadrature squeezing, and the continuous-variable quantum teleportation when considering non-Gaussian entangled states generated by applying multiple-photon subtraction and multiple-photon addition to a two-mode squeezed vacuum state (TMSVs). Our results indicate that in the case of the multiple-photon-subtracted TMSVs with symmetric operations, the corresponding EPR correlation, the two-mode squeezing degree, the sum squeezing, and the fidelity of teleporting a coherent state or a squeezed vacuum state can be enhanced…
A scheme is proposed to entangle two systems that have not interacted by using an ancillary particle in a Mach-Zehnder interferometer, by making a suitable post--selection of the particle followed by a conditional feedback on one of the subsystems to be entangled. For a strong interaction, the process works deterministically. For a weaker interaction only the probability of success is reduced, but the output continues to be a maximally entangled state.
