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 emphasis on photon-added coherent and squeezed vacuum states. In particular, we show that adding photons to a squeezed vacuum yields superpositions of quantum states which show all the typical features of Schrödinger-cat-like states.
Beam splitter mediated entanglement of nonlinear photon-added coherent states was studied by Honarasa, Bagheri and Gharaati [1]. We believe that this work contains errors in numerical computations of linear entropy and Mandel parameter which lead to wrong conclusions. We point out the possible errors and describe the necessary corrections. The conclusions based on our arguments are in complete agreement with previously published literature.
We propose an experimentally feasible scheme to generate nonmaximal entanglement between two atomic ensembles. The degree of entanglement is readily tunable. The scheme involves laser manipulation of atomic ensembles, adjustable quarter- and half-wave plates, beam splitter, polarizing beam splitters, and single-photon detectors, and well fits the status of the current experimental technology. Finally we use the nonmaximally entangled state of ensembles to demonstrate quantum nonlocality by detecting the Clauser-Horne-Shimony-Holt inequality.
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.
We propose three criteria for the generation of random digital strings from quantum beam splitters: (i) three or more mutually exclusive outcomes corresponding to the invocation of three- and higher dimensional Hilbert spaces; (ii) the mandatory use of pure states in conjugated bases for preparation and detection; and (iii) the use of entangled singlet (unique) states for elimination of bias.
State preparation via conditional output measurement on a beam splitter is studied, assuming the signal mode is mixed with a mode prepared in a Fock state and photon numbers are measured in one of the output channels. It is shown that the mode in the other output channel is prepared in either a photon-subtracted or a photon-added Jacobi polynomial state, depending upon the difference between the number of photons in the input Fock state and the number of photons in the output Fock state onto which it is projected. The properties of the conditional output states are studied for coherent and squ…
Multiphoton entanglement is an important resource for linear optics quantum computing. Here we show that a wide range of highly entangled multiphoton states, including W-states, can be prepared by interfering single photons inside a Bell multiport beam splitter and using postselection. A successful state preparation is indicated by the collection of one photon per output port. An advantage of the Bell multiport beam splitter is that it redirects the photons without changing their inner degrees of freedom. The described setup can therefore be used to generate polarisation, time-bin and frequenc…
In this paper, we investigate the phase sensitivities in two-path optical interferometry with asymmetric beam splitters. Here, we present the optimal conditions for the transmission ratio and the phase of the beam splitter to gain the highest sensitivities for a general class of non-classical states with parity symmetry. Additionally, we address the controversial question of whether the scheme with a combination of coherent state and photon-added or photon-subtracted squeezed vacuum state is better or worse than the most celebrated one using a combination of coherent state and squeezed vacuum …
Quantum cluster states and entangled state analyzers are essential to measurement-based quantum computing. We propose to generate a quantum cluster-state and to make multipartite entanglement analyzer by using noninteracting free electrons or conduction electrons in quantum dots, based on polarizing beam splitters, charge detectors and single-spin rotations. Our schemes are deterministic without the need of qubit-qubit interaction.
We present an experiment which prepare entanglement between photons that nowhere interacted and whose paths nowhere crossed. The experiment puts together two photons from two (non-maximal) singlet-like photon pairs and make them interfere at an asymmetrical beam splitter. As a result one finds polarization correlations between the other companion photons from the pairs whose paths nowhere crossed each other even when no polarization measurements have been carried out on the former photons. The latter set of photons that nowhere interacted are therefore event-ready prepared by their pair-compan…
Preparation of Schrödinger-cat-like states via conditional output measurement on a beam splitter is studied. In the scheme, a mode prepared in a squeezed vacuum is mixed with a mode prepared in a Fock state and photocounting is performed in one of the output channels of the beam splitter. In this way the mode in the other output channel is prepared in a Schrödinger-cat-like state that is either a photon-subtracted or a photon-added Jacobi polynomial squeezed vacuum state, depending upon the difference between the number of photons in the input Fock state and the number of photons in the output…
A nonclassical feature of the fourth-order interference at a beam splitter, that genuine photon spin singlets are emitted in predetermined directions even when incident photons are unpolarized, has been used in a proposal for an experiment that imposes quantum spin correlation on truly independent photons. In the experiment, two photons from two such singlets interfere at a beam splitter, and as a result the other two photons - which nowhere interacted and whose paths nowhere crossed - exhibit a 100% correlation in polarization, even when no polarization has been measured in the first two phot…
Preparation of entangled states of photons are useful for quantum computing and communication. In this paper, we present a simplistic protocol of entanglement generation using beam splitters with suitable reflectivity. The photons in an initial state with fully classical probability distribution pass through an optical network, made up of sequential beam splitters and are prepared in maximally entangled states. We also present the detailed theoretical analysis of entangled state generation, for an arbitrary number of photons, fed through the input ports of the beam splitters with equal probabi…
We propose to realize the two-mode continuous-variable entanglement of microwave photons in an electro-optic system, consisting of two superconducting microwave resonators and one or two optical cavities filled with certain electro-optic medium. The cascaded and parallel schemes realize such entanglement via coherent control on the dynamics of the system, while the dissipative dynamical scheme utilizes the reservoir-engineering approach and exploits the optical dissipation as a useful resource. We show that, for all the schemes, the amount of entanglement is determined by the ratio of the effe…
The two modes of the Einstein-Podolsky-Rosen quadrature entangled state generated by parametric down-conversion interfere on a beam splitter of variable splitting ratio. Detection of a photon in one of the beam splitter output channels heralds preparation of a signal state in the other, which is characterized using homodyne tomography. By controlling the beam splitting ratio, the signal state can be chosen anywhere between the single-photon and squeezed state.
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…
We describe a protocol capable of preparing an arbitrary state of two photons in several spatial modes using pairs of photons generated by spontaneous parametric down-conversion, linear optical elements and single-photon detectors or post-selection. The protocol involves unitary and non-unitary transformations realizable by beam splitters and phase shifters. Non-unitary transformations are implemented by attenuation filters. The protocol contains several optimization capabilities with the goal of improving overall probability of its success. We also show how entangled two-photon states require…
We report a scheme for deterministic preparation of non-Gaussian quantum states on-demand. In contrast to probabilistic approaches for preparation of non-Gaussian quantum states, conditioned on photon subtraction or addition, we present a scheme that can prepare non-Gaussian quantum states on-demand, by applying a unitary transformation which removes the Gaussianity of measurement statistics of field quadratures, namely a quadrature rotation via transmission through a beam-splitter, using a two-mode photon-number squeezed state as input. The resulting state exhibits a quantum vortex structure …
Photon-subtracted and photon-added Gaussian states are amongst the simplest non-Gaussian states that are experimentally available. It is generally believed that they are some of the best candidates to enhance sensitivity in parameter extraction. We derive here the quantum Cramér-Rao bound for such states and find that for large photon numbers photon-subtraction or -addition only leads to a small correction of the quantum Fisher information (QFI). On the other hand a divergence of the QFI appears for very small squeezing in the limit of vanishing photon number in the case of photon subtraction,…
We report preparation and characterization of coherent superposition states t |0> + alpha |1> of electromagnetic field by conditional measurements on a beamsplitter. The state is generated in one of the beam splitter output channels if a coherent state and a single-photon Fock state |1> are present in the two input ports and a single photon is registered in the other beam splitter output. The single photon thus plays a role of a "catalyst": it is explicitly present in both the input and the output channels of the interaction yet facilitates generation of a nonclassical state of light.
An interesting aspect of multipartite entanglement is that for perfect teleportation and superdense coding, not the maximally entangled W states but a special class of non-maximally entangled W-like states are required. Therefore, efficient preparation of such W-like states is of great importance in quantum communications, which has not been studied as much as the preparation of W states. In this letter, we propose a simple optical scheme for efficient preparation of large-scale polarization based entangled W-like states by fusing two W-like states or expanding a W-like state with an ancilla p…
We use a correlation function analysis of the field quadratures to characterize both the black body radiation emitted by a 50 Ohm load resistor and the quantum properties of two types of beam splitters in the microwave regime. To this end, we first study vacuum fluctuations as a function of frequency in a Planck spectroscopy experiment and then measure the covariance matrix of weak thermal states. Our results provide direct experimental evidence that vacuum fluctuations represent the fundamental minimum quantum noise added by a beam splitter to any given input signal.
In the Gaussian-modulated coherent states (GMCS) quantum key distribution (QKD) protocol, Alice prepares quantum states \emph{actively}: for each transmission, Alice generates a pair of Gaussian-distributed random numbers, encodes them on a weak coherent pulse using optical amplitude and phase modulators, and then transmits the Gaussian-modulated weak coherent pulse to Bob. Here we propose a \emph{passive} state preparation scheme using a thermal source. In our scheme, Alice splits the output of a thermal source into two spatial modes using a beam splitter. She measures one mode locally using …
In this paper, we construct the $m$-photon-added and $m$-photon-subtracted coherent states on a sphere. These states are shown to satisfy the usual conditions of continuity in the label, normalizability and the resolution of identity. The preparation of the constructed states, as the states of radiation field is considered. We examine and analyze the nonclassical properties of these states, including the photon mean number, Mandel parameter and quadrature squeezing. We find that these states are sub-Poissonian in nature, whereas the degree of squeezing is reduced (enhanced) by increasing $m$ f…
We have constructed an asymmetric matter-wave beam splitter and a ring potential on an atom chip with Bose-Einstein condensates using radio-frequency dressing. By applying rf-field parallel to the quantization axis in the vicinity of the static trap minima added to perpendicular rf-fields, versatile controllability on the potentials is realized. Asymmetry of the rf-induced double well is manipulated without discernible displacement of the each well along horizontal and vertical direction. Formation of an isotropic ring potential on an atom chip is achieved by compensating the gradient due to g…
In this paper, a continuous variable B92 quantum key distribution (QKD) protocol is proposed using single photon added and subtracted coherent states, which are prepared by adding and subsequently subtracting a single photon on a coherent state. It is established that in contrast to the traditional discrete variable B92 protocol, this protocol for QKD is intrinsically robust against the unambiguous state discrimination attack, which circumvents the requirement for any uninformative states or entanglement used in corresponding discrete variable case as a remedy for this attack. Further, it is s…
The Braess paradox encountered in classical networks is a counterintuitive phenomenon when the flow in a road network can be impeded by adding a new road or, more generally, the overall net performance can degrade after addition of an extra available choice. In this work, we discuss the possibility of a similar effect in a phase-coherent quantum transport and demonstrate it by example of a simple Y-shaped metallic fork. To reveal the Braess-like partial suppression of the charge flow in such device, it is proposed to transfer two outgoing arms into a superconducting state. We show that the dif…
The usual Su-Schrieffer-Heeger model with an even number of lattice sites possesses two degenerate zero energy modes. The degeneracy of the zero energy modes leads to the mixing between the topological left and right edge states, which makes it difficult to implement the state transfer via topological edge channel. Here, enlightened by the Rice-Male topological pumping, we find that the staggered periodic next-nearest neighbor hoppings can also separate the initial mixed edge states, which ensures the state transfer between topological left and right edge states. Significantly, we construct an…
We examine various manipulations of photon number states which can be implemented by teleportation technique with number sum measurement. The preparations of the Einstein-Podolsky-Rosen resources as well as the number sum measurement resulting in projection to certain Bell state may be done conditionally with linear optical elements, i.e., beam splitters, phase shifters and zero-one-photon detectors. Squeezed vacuum states are used as primary entanglement resource, while single-photon sources are not required.
We propose a scheme allowing a conditional implementation of suitably truncated general single- or multi-mode operators acting on states of traveling optical signal modes. The scheme solely relies on single-photon and coherent states and applies beam splitters and zero- and single-photon detections. The signal flow of the setup resembles that of a multi-mode quantum teleportation scheme thus allowing the individual signal modes to be spatially separated from each other. Some examples such as the realization of cross-Kerr nonlinearities, multi-mode mirrors, and the preparation of multi-photon e…
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…
We investigate coherent perfect absorption (CPA) in quantum optics, in particular when pairs of squeezed coherent states of light are superposed on an absorbing beam splitter. First, by employing quantum optical input-output relations, we derive the absorption coefficients for quantum coherence and for intensity, and reveal how these will differ for squeezed states. Secondly, we present the remarkable properties of a CPA-gate: two identical but otherwise arbitrary incoming squeezed coherent states can be completely stripped off their coherence, producing a pure entangled squeezed vacuum state …
We analyze the linear optical realization of number-sum Bell measurement and number-state manipulation by taking into account the realistic experimental situation, specifically imperfectness of single-photon detector. The present scheme for number-state manipulation is based on the number-sum Bell measurement, which is implemented with linear optical elements, i.e., beam splitters, phase shifters and zero-one-photon detectors. Squeezed vacuum states and coherent states are used as optical sources. The linear optical Bell state detector is formulated quantum theoretically with a probability ope…
We present a framework for studying bosonic non-Gaussian channels of continuous-variable systems. Our emphasis is on a class of channels that we call photon-added Gaussian channels, which are experimentally viable with current quantum-optical technologies. A strong motivation for considering these channels is the fact that it is compulsory to go beyond the Gaussian domain for numerous tasks in continuous-variable quantum information processing such as entanglement distillation from Gaussian states and universal quantum computation. The single-mode photon-added channels we consider are obtained…
According to the fundamental laws of quantum optics, noise is necessarily added to the system when one tries to clone or amplify a quantum state. However, it has recently been shown that the quantum noise related to the operation of a linear phase-insensitive amplifier can be avoided when the requirement of a deterministic operation is relaxed. Nondeterministic noiseless linear amplifiers are therefore realizable. Usually nondeterministic amplifiers rely on using single photon sources. We have, in contrast, recently proposed an amplification scheme in which no external energy is added to the s…
We propose a projection measurement onto encoded Bell states with a static network of linear optical elements. By increasing the size of the quantum error correction code, both Bell measurement efficiency and photon-loss tolerance can be made arbitrarily high at the same time. As a main application, we show that all-optical quantum communication over large distances with communication rates similar to those of classical communication is possible solely based on local state teleportations using optical sources of encoded Bell states, fixed arrays of beam splitters, and photon detectors. As anot…
State preparation via postselected weak measurement in three wave mixing process is studied. Assuming the signal input mode prepared in a vacuum state, coherent state or squeezed vacuum state, separately, while the idler input prepared in weak coherent state and passing the medium characterized by the second-order nonlinear susceptibility. It is shown that when the single photon is detected at one of the output channels of idler beam's path, the signal output channel is prepared in single-photon Fock state, single-photon-added coherent state or single-photon-added squeezed vacuum state with ve…
Variable measurement operators enable the optimization of strategies for testing quantum properties and the preparation of a range of quantum states. Here, we experimentally implement a weak-field homodyne detector that can continuously tune between measuring photon numbers and field quadratures. We combine a quantum signal with a coherent state on a balanced beam splitter and detect light at both output ports using photon-number-resolving transition edge sensors. We observe that the discrete difference statistics converge to the quadrature distribution of the signal as we increase the coheren…
We develop a technique for generating multi-photon nonclassical states via interference between coherent and Fock states using quantum catalysis. By modulating the coherent field strength, the number of catalyst photons and the ratio of the beam splitter upon which they interfere, a wide range of nonclassical phenomena can be created, including squeezing of up to 1.25 dB, anti- and super-bunched photon statistics and states exhibiting over 90% fidelity to displaced coherent superposition states. We perform quantum catalysis experimentally, showing tunability into the nonclassical regime. Our p…
Quantum optics dictates that amplification of a pure state by any linear deterministic amplifier always introduces noise in the signal and results in a mixed output state. However, it has recently been shown that noiseless amplification becomes possible if the requirement of a deterministic operation is relaxed. Here we propose and analyze a noiseless amplification scheme where the energy required to amplify the signal originates from the stochastic fluctuations in the field itself. In contrast to previous amplification setups, our setup shows that a signal can be amplified even if no energy i…
In this work we present a quantum key distribution protocol using continuous-variable non-Gaussian states, homodyne detection and post-selection. The employed signal states are the Photon Added then Subtracted Coherent States (PASCS) in which one photon is added and subsequently one photon is subtracted. We analyze the performance of our protocol, compared to a coherent state based protocol, for two different attacks that could be carried out by the eavesdropper (Eve). We calculate the secret key rate transmission in a lossy line for a superior channel (beam-splitter) attack, and we show that …
A single photon incident on a beam splitter produces an entangled field state, and in principle could be used to violate a Bell-inequality, but such an experiment (without post-selection) is beyond the reach of current experiments. Here we consider the somewhat simpler task of demonstrating EPR-steering with a single photon (also without post-selection). That is, of demonstrating that Alice's choice of measurement on her "half" of a single photon can affect the other "half" of the photon in Bob's lab, in a sense rigorously defined by us and Doherty [Phys. Rev. Lett. 98, 140402 (2007)]. Previou…
Two-mode squeezing is a fascinating example of quantum entanglement manifested in cross-correlations of incompatible observables between two subsystems. At the same time, these subsystems themselves may contain no quantum signatures in their self-correlations. These properties make two-mode squeezed (TMS) states an ideal resource for applications in quantum communication. Here, we generate propagating microwave TMS states by a beam splitter distributing single mode squeezing emitted from distinct Josephson parametric amplifiers along two output paths. We experimentally study the fundamental de…
The analysis of photon count data from the standard nitrogen vacancy (NV) measurement process is treated as a statistical inference problem. This has applications toward gaining better and more rigorous error bars for tasks such as parameter estimation (eg. magnetometry), tomography, and randomized benchmarking. We start by providing a summary of the standard phenomenological model of the NV optical process in terms of Lindblad jump operators. This model is used to derive random variables describing emitted photons during measurement, to which finite visibility, dark counts, and imperfect stat…
