We present a Bell-type polarization experiment using two independent sources of polarized optical photons, and detecting the temporal coincidence of pairs of uncorrelated photons which have never been entangled in the apparatus. Very simply, our measurements have tested the quantum-mechanical equivalent of the classical Malus' law on an incoherent beam of polarized photons obtained from two separate and independent laser sources greatly reduced in intensities.The outcome of the experiment gives evidence of violation of the Bell-like inequalities. Drawing the conclusions of the present work, we invoke the distinction between the concepts of state-preparation and measurement to understand this result.
Bell inequality violating entangled states are the working horse for many potential quantum information processing applications, including secret sharing, cryptographic key distribution and communication complexity reduction in distributed computing. Here we explicitly demonstrate the power of certain multi-qubit states to improve the efficiency of partners in joint computation of some multi-qubit function, despite the fact that there could be no correlations between all distributed particles. It is important to stress that the class of functions that can be computed more efficiently is widene…
We present results of a bright polarization-entangled photon source operating at 1552 nm via type-II collinear degenerate spontaneous parametric down-conversion in a periodically poled potassium titanyl phosphate crystal. We report a conservative inferred pair generation rate of 123,000 pairs/s/mW into collection modes. Minimization of spectral and spatial entanglement was achieved by group velocity matching the pump, signal and idler modes and through properly focusing the pump beam. By utilizing a pair of calcite beam displacers, we are able to overlap photons from adjacent down-conversion p…
We study polarization properties of the macroscopic analogues of two-photon Bell states. The effect of hidden polarization, i.e., polarization in the second (and higher) orders in the intensity is observed for the triplet states while the singlet one is demonstrated to be nearly unpolarized at least up to the fourth order. The arbitrary-order degree of polarization is introduced and applied to the macroscopic Bell states.
The polarization properties of macroscopic Bell states are characterized using three-dimensional quantum polarization tomography. This method utilizes three-dimensional inverse Radon transform to reconstruct the polarization quasiprobability distribution function of a state from the probability distributions measured for various Stokes observables. The reconstructed 3D distributions obtained for the macroscopic Bell states are compared with those obtained for a coherent state with the same mean photon number. The results demonstrate squeezing in one or more Stokes observables.
A silicon quantum photonic circuit was proposed and demonstrated as an integrated quantum light source for telecom band polarization entangled Bell state generation and dynamical manipulation. Biphoton states were firstly generated in four silicon waveguides by spontaneous four wave mixing. They were transformed to polarization entangled Bell states through on-chip quantum interference and quantum superposition, and then coupled to optical fibers. The property of polarization entanglement in generated photon pairs was demonstrated by two-photon interferences under two non-orthogonal polarizati…
Polarization-entangled photon pair generation based on two scalar scattering processes of the vector four photon scattering has been demonstrated experimentally in high nonlinear microstructure fiber with birefringence. By controlling the pump polarization state, polarization-entangled Bell states can be realized. It is provides a simple way to realize efficient and compact fiber based polarization-entangled photon pair sources.
Quantum systems that have never interacted can become nonlocally correlated through a process called entanglement swapping. To characterize nonlocality in this context, we introduce local models where quantum systems that are initially uncorrelated are described by uncorrelated local variables. While a pair of maximally entangled qubits prepared in the usual way (i.e., emitted from a common source) requires a visibility close to 70% to violate a Bell inequality, we show that an entangled pair generated through entanglement swapping will already violate a Bell inequality for visibilities as low…
A complete and deterministic Bell state measurement was realized by a simple linear optics experimental scheme which adopts 2-photon polarization-momentum hyperentanglement. The scheme, which is based on the discrimination among the single photon Bell states of the hyperentangled state, requires the adoption of standard single photon detectors. The four polarization Bell states have been measured with average fidelity $F=0.889\pm0.010$ by using the linear momentum degree of freedom as the ancilla. The feasibility of the scheme has been characterized as a function of the purity of momentum enta…
We emphasize the Bell state analyzer, a beamsplitter, as an efficient means of detecting two-photon polarization entanglement. Whereas the optimal entanglement witness for spatially separated photons requires coordinated measurement in three bases, the local Bell state analyzer enables an efficient entanglement witness in a single polarization basis. We use Bayesian mean estimation to compare the efficiency of these two witnesses. We report the method and results of this comparison.
Here we demonstrate, for the first time, violation of Bell's inequality using a triggered quantum dot photon-pair source without post-selection. Furthermore, the fidelity to the expected Bell state can be increased above 90% using temporal gating to reject photons emitted at times when collection of uncorrelated light is more probable. A direct measurement of a CHSH Bell inequality is made showing a clear violation, highlighting that a quantum dot entangled photon source is suitable for communication exploiting non-local quantum correlations.
In an entanglement swapping process two initially uncorrelated qubits become entangled, without any direct interaction. We present a model using local variables aiming at reproducing this remarkable process, under the realistic assumption of finite detection efficiencies. The model assumes that the local variables describing the two qubits are initially completely uncorrelated. Nevertheless, we show that once conditioned on the Bell measurement result, the local variables bear enough correlation to simulate quantum measurement results with correlation very close to the quantum prediction. When…
Contrary to the usual assumption that the experimental preparation of pure entangled states can be described by mixed states due to white noise, a more realistic description for polarization-entangled states produced by parametric down-conversion is that they are mixed states due to decoherence in a preferred polarization basis. This distinction between white and colored noise is crucial when we look for maximal violations of Bell's inequalities for two-qubit and two-qutrit entangled states. We find that violations of Bell's inequalities with realistic noise for polarization-entangled photons …
We present a complete hyperentangled Bell state analysis protocol for two-photon four-qubit states which are simultaneously entangled in the polarization and time-bin degrees of freedom. The 16 hyperentangled states can be unambiguously distinguished via two steps. In the first step, the polarization entangled state is distinguished deterministically and nondestructively with the help of the cross-Kerr nonlinearity. Then, in the second step, the time-bin state is analyzed with the aid of the polarization entanglement. We also discuss the applications of our protocol for quantum information pro…
In an experiment designed to overcome the loophole of observer dependent reality and satisfying the counterfactuality condition, we measured polarization correlations of 1S0 proton pairs produced in 12C(d,2He) and 1H(d,He) reactions in one setting. The results of these measurements are used to test the Bell and Wigner inequalties against the predictions of quantum mechanics.
We have investigated the polarization entanglement between photon pairs generated from a biexciton in a CuCl single crystal via resonant hyper parametric scattering. The pulses of a high repetition pump are seen to provide improved statistical accuracy and the ability to test Bell's inequality. Our results clearly violate the inequality and thus manifest the quantum entanglement and nonlocality of the photon pairs. We also analyzed the quantum state of our photon pairs using quantum state tomography.
Experimental tests of Bell-type inequalities distinguishing between quantum mechanics and local realistic theories remain of considerable interest if performed on massive particles, for which no conclusive result has yet been obtained. Only two-particle experiments may specifically test the concept of spatial nonlocality in quantum theory, whereas single-particle experiments may generally test the concept of quantum noncontextuality. Here we have performed the first Bell-type experiment with a beam of thermal-neutron pairs in the singlet state of spin, as originally suggested by J. S. Bell. Th…
The Wigner representation of parametric down conversion in the Heisenberg picture is applied to the study of the Rome teleportation experiment. We investigate the physical meaning of the zeropoint inputs at the different areas of the experimental setup. In particular, we establish a quantitative relationship between the zeropoint sets of modes that are needed for the preparation of the quantum state to be teleported, the idle channels inside the one-photon polarization-momentum Bell-state analyser, and the possibility of performing teleportation of a polarization state whith certainty.
Logic qubit entanglement, which is also called the concatenated Greenberger-Horne-Zeilinger (C-GHZ) state, is robust in practical noisy environment. In this paper, we will describe an efficient approach to realize the complete polarization Bell-state analysis which is encoded in the logic qubit. We showed that the logic Bell-state can be distinguished in two steps with the help of the parity-check measurement (PCM), which is constructed by the cross-Kerr nonlinearity. We also explain that this approach can be used to distinguish arbitrary C-GHZ state with $N$ logic qubits. This protocol is use…
We experimentally demonstrate that violations of Bell's inequalities for two-photon polarization-entangled states with colored noise are extremely robust, whereas this is not the case for states with white noise. Controlling the amount of noise by using the timing compensation scheme introduced by Kim et al. [Phys. Rev. A 67, 010301(R) (2003)], we have observed violations even for states with very high noise, in excellent agrement with the predictions of Cabello et al. [Phys. Rev. A 72, 052112 (2005)].
The generation and detection of maximally-entangled two-particle states, `Bell states,' are crucial tasks in many quantum information protocols such as cryptography and teleportation. Unfortunately, they require strong inter-particle interactions lacking in optics. For this reason, it has not previously been possible to perform complete Bell state determination in optical systems. In this work, we show how a recently developed quantum interference technique for enhancing optical nonlinearities can make efficient Bell-state measurement possible. We also discuss weaknesses of the scheme includin…
We report the generation of polarization entangled photon pairs in the 1550-nm wavelength band using spontaneous four-wave mixing in a dispersion-shifted fiber loop. The use of the fiber-loop configuration made it possible to generate polarization entangled states very stably. With accidental coincidences subtracted, we obtained coincidence fringes with >90 % visibilities, and observed a violation of Bell's inequality by seven standard deviations. We also confirmed the preservation of the quantum correlation between the photons even after they had been separated by 20 km of optical fiber.
The question whether Quantum Mechanics describes all aspects of both the micro-world of elementary particles and living organisms adequately is still open. A Bell inequality test without locality and detection loopholes will deliver the answer when applied to macroscopic systems. Here we show that an experimentally feasible loophole-free Bell test is possible using only multi-photon polarization entanglement and linear optics. We apply a preselection protocol which produces genuine macroscopic superpositions and entanglement, thus eliminating postselection and dark counts. Such superpositions …
Hyperentangled states can outperform their classical counterparts on solving certain tasks. Here we present a simplified scheme for completely distinguishing two-photon hyperentangled Bell states in polarization, spatial, and time-bin degrees of freedom (DOFs). Unity fidelity can be achieved in principle without strong couple limitation between photon and quantum dot (QD), and the incomplete and imperfect QD-cavity interactions are prevented by single-photon detectors. In addition, auxiliary photons or DOFs are not required in our scheme. The necessary linear optical elements are fewer than th…
We apply the Wigner function formalism to the study of two-photon polarization-momentum hyperentanglement generated in parametric down conversion. It is shown that the consideration of a higher number of degrees of freedom is directly related to the extraction of additional uncorrelated sets of zeropoint modes at the source. We present a general expression for the description of the quantum correlations corresponding to the sixteen Bell base states, in terms of four beams whose amplitudes are correlated through the stochastic properties of the zeropoint field. A detailed analysis of the two ex…
We derive N-particle Bell-type inequalities under the assumption of partial separability, i.e. that the N-particle system is composed of subsystems which may be correlated in any way (e.g. entangled) but which are uncorrelated with respect to each other. These inequalities provide, upon violation, experimentally accessible sufficient conditions for full N-particle entanglement, i.e. for N-particle entanglement that cannot be reduced to mixtures of states in which a smaller number of particles are entangled. The inequalities are shown to be maximally violated by the N-particle Greenberger-Horne…
Bell inequalities (BIs) derived in terms of quantum probability statistics are extended to general bipartite-entangled states of arbitrary spins with parallel polarization. The original formula of Bell for the two-spin singlet is slightly modified in the parallel configuration, while, the inequality for- mulated by Clauser-Horne-Shimony-Holt remains not changed. The violation of BIs indeed resulted from the quantum non-local correlation for spin-1=2 case. However, the inequalities are always satisfied for the spin-1 entangled states regardless of parallel or antiparallel polarizations of two s…
Logic-qubit entanglement is a promising resource in quantum information processing, especially in future large-scale quantum networks. In the paper, we put forward an efficient entanglement purification protocol (EPP) for nonlocal mixed logic entangled states with the bit-flip error in the logic qubits of the logic Bell state, resorting to the photon-atom interaction in low-quality (Q) cavity and atomic state measurement. Different from existing EPPs, this protocol can also purify the logic phase-flip error, and the bit-flip error and the phase-flip error in physic qubit. During the protocol, …
We use polarization-entangled photon pairs to demonstrate quantum nonlocality in an experiment suitable for advanced undergraduates. The photons are produced by spontaneous parametric downconversion using a violet diode laser and two nonlinear crystals. The polarization state of the photons is tunable. Using an entangled state analogous to that described in the Einstein-Podolsky-Rosen ``paradox,'' we demonstrate strong polarization correlations of the entanged photons. Bell's idea of a hidden variable theory is presented by way of an example and compared to the quantum prediction. A test of th…
We report a nonlocal interferometer capable of detecting entanglement and identifying Bell states statistically. This is possible due to the interferometer's unique correlation dependence on the anti-diagonal elements of the density matrix, which have distinct bounds for separable states and unique values for the four Bell states. The interferometer consists of two spatially separated balanced Mach-Zehnder or Sagnac interferometers that share a polarization entangled source. Correlations between these interferometers exhibit non-local interference, while single photon interference is suppresse…
Practically Enhanced Hyperentanglement Concentration for Polarization-spatial Hyperentangled Bell States with Linear Optics and Common Single-photon Detectors
Bell's inequality violation (BIQV) for correlations of polarization is studied for a {\it product} state of two two-mode squeezed vacuum (TMSV) states. The violation allowed is shown to attain its maximal limit for all values of the squeezing parameter, $ζ$. We show via an explicit example that a state whose entanglement is not maximal allow maximal BIQV. The Wigner function of the state is non negative and the average value of either polarization is nil.
Bell-state analysis is a considerable challenge and an essential requirement for reliable implementation of quantum communication proposals. An open question is the one for the maximal fraction of successful Bell measurements. It has been pointed out that no scheme using only linear elements can implement a Bell state analyzer. Some effort has paid attention to the complete polarization-entangled Bell-state analysis using linear optics, with the aid of auxiliary means. Here we present a symmetry-broken scheme with linear optics only, without any aid of other auxiliary means, for discriminating…
We report a novel Bell-state synthesizer in which an interferometric entanglement concentration scheme is used. An initially mixed polarization state from type-II spontaneous parametric down-conversion becomes entangled after the interferometric entanglement concentrator. This Bell-state synthesizer is universal in the sense that the output polarization state is not affected by spectral filtering, crystal thickness, and, most importantly, the choice of pump source. It is also robust against environmental disturbance and a more general state, partially mixed$-$partially entangled state, can be …
Photon-number correlation measurements are performed on bright squeezed vacuum states using a standard Bell-test setup, and quantum correlations are observed for conjugate polarization-frequency modes. We further test the entanglement witnesses for these states and demonstrate the violation of the separability criteria, which infers that all the macroscopic Bell states, containing typically $10^6$ photons per pulse, are polarization entangled. The study also reveals the symmetry of macroscopic Bell states with respect to local polarization transformations.
We demonstrate the generation of narrowband biphotons with polarization-frequency coupled hy- perentanglement from spontaneous four-wave mixing in cold atoms. The coupling between polariza- tion and frequency is realized through a frequency shifter and linear optics. When the polarization- frequency degrees of freedom are decoupled, it is robust to create polarization and frequency Bell states, confirmed by the polarization quantum-state tomography and the two-photon temporal quan- tum beating. Making use of the polarization-frequency coupling to transfer polarization phase retard to the entan…
We analyze features of mixed biphoton polarization states which arise from pure states of polarization-frequency biphoton ququarts after averaging over frequencies of photons. For mixed states we find their concurrence C, Schmidt parameter K and degree of polarization P, as well as the von Neumann mutual information I. In some simple cases we find also the relative entropy S_{rel} and the degree of classical correlations C_{cl}. We show that in mixed states the Schmidt parameter does not characterize anymore the degree of entanglement, as it does in pure states. Nevertheless, the Schmidt param…
We describe a nonlinear interferometric setup to perform a complete optical Bell measurement, i.e. to unambigously discriminate the four polarization entangled EPR-Bell photon pairs. The scheme is robust against detector inefficiency.
The theoretical cross section for Compton scattering of maximally entangled Bell photons has yet to be rigorously confirmed by experiments. Test cases of Bell states for use in Compton scattering experiments can now be expanded given reports of creating all 4 Bell states in the hard X-ray regime by the process of spontaneous parametric down-conversion. We outline an experiment and apply a matrix method to parameterize Compton scattering theory using the phase matching angles. When the azimuths of two hypothetical photon counters are recorded at angles of 0 degrees and 90 degrees, and the ratio…
We demonstrate hybrid entanglement of photon pairs via the experimental violation of a Bell inequality with two different degrees of freedom (DOF), namely the path (linear momentum) of one photon and the polarization of the other photon. Hybrid entangled photon pairs are created by Spontaneous Parametric Down Conversion and coherent polarization to path conversion for one photon. For that photon, path superposition is analyzed, and polarization superposition for its twin photon. The correlations between these two measurements give an S-parameter of S=2.653+/-0.027 in a CHSH inequality and thus…
Device independent protocols rely on the violation of Bell inequalities to certify properties of the resources available. The violation of the inequalities are meaningless without a few well-known assumptions. One of these is measurement independence, the property that the source of the states measured in an inequality is uncorrelated from the measurements selected. Since this assumption cannot be confirmed, we consider the consequences of relaxing it and find that the definition chosen is critically important to the observed behavior. Considering a definition that is a bound on the min-entrop…
We show how a property of dualism, which can exist in the entanglement of identical particles, can be tested in the usual photonic Bell measurement apparatus with minor modifications. Two different sets of coincidence measurements on the same experimental setup consisting of a Hong-Ou-Mandel interferometer demonstrate how the same two-photon state can emerge entanglement in the polarization or the momentum degree of freedom depending on the dynamical variables used for labeling the particles. Our experiment demonstrates how the same source can be used as both a polarization entangled state, as…
Here we propose an implementation of all possible Positive Operator Value Measures (POVMs) of two-photon polarization states. POVMs are the most general class of quantum measurements. Our setup requires linear optics, Bell State measurements and an entangled three-photon ancilla state, which can be prepared separately and in advance (or 'off-line'). As an example we give the detailed settings for a simultaneous measurement of all four Bell States for an arbitrary two-photon polarization state, which is impossible with linear optics alone.
We present an algebraic description of the sets of local correlations in arbitrary networks, when the parties have finite inputs and outputs. We consider networks generalizing the usual Bell scenarios by the presence of multiple uncorrelated sources. We prove a finite upper bound on the cardinality of the value sets of the local hidden variables. Consequently, we find that the sets of local correlations are connected, closed and semialgebraic, and bounded by tight polynomial Bell-like inequalities.
We report the generation of polarization-entangled photons, using a quantum dot single photon source, linear optics and photodetectors. Two photons created independently are observed to violate Bell's inequality. The density matrix describing the polarization state of the postselected photon pairs is also reconstructed, and agrees well with a simple model predicting the quality of entanglement from the known parameters of the single photon source. Our scheme provides a method to generate no more than one entangled photon pair per cycle, a feature useful to enhance quantum cryptography protocol…
We introduce a simplified form of Stokes operators for quantum optical fields that involve the known concept of binning. Behind polarization analyzer photon numbers (more generally intensities) are measured. If the value obtained in one of the outputs, say H, is greater the than in the other one, V, then the value of the simplified Stokes operator is, say, 1, otherwise it is -1. For equal photon numbers we put 0. Such observables do not have all properties of the Stokes operators, but surprisingly can be employed in Bell type measurements, involving polarization analyzers. They are especially …
Can a Bell test with no detection loophole be demonstrated for multi-photon entangled states of light within the current technology? We examine the possibility of a postselection-free CHSH-Bell inequality test wih an unsymmetrical polarization singlet. To that end we employ a preselection procedure which is performed prior to the test. It allows using imperfect (coarse-grained) binary photodetection in the test. We show an example of preselection scheme which improves violation of the CHSH inequality with the micro-macro polarization singlet produced by the optimal quantum cloning. The presele…
We show a mechanism that projects a pair of neutral two-level atoms from an initially uncorrelated state to a maximally entangled state while they remain spacelike separated. The atoms begin both excited in a common electromagnetic vacuum, and the radiation is collected with a partial Bell-state analyzer. If the interaction time is short enough and a certain two-photon Bell state is detected after the interaction, a high degree of entanglement, even maximal, can be generated while one atom is outside the light cone of the other, for arbitrary large interatomic distances.
Using the process of cavity-enhanced spontaneous parametric down-conversion (SPDC), we generate a narrow-band polarization-entangled photon pair resonant on the rubidium (Rb) D1 line (795 nm). The degenerate single-mode photon pair is selected by multiple temperature controlled etalons. The linewidth of generated polarization-entangled photon pairs is 15 MHz which matches the typical atomic memory bandwidth. The measured Bell parameter for the polarization-entangled photons S=2.73+-0.04 which violates the Bell-CHSH inequality by ~18 standard deviations. The presented entangled photon pair sour…
We report a source of polarization-entangled photon pairs in the 1550-nm telecommunication band, which is based on non-collinear spontaneous parametric down-conversion in a periodically poled lithium niobate crystal pumped by picosecond pulses. This source is realized utilizing a polarization-based Sagnac interferometer employing a type-0 non-collinear quasi-phase-matching configuration. Polarization entanglement is verified through measurement of the polarization-correlation interference fringes with visibility >96% and by testing the experimental violation of the Clauser-Horne-Shimony-Holt (…
We propose a method for the generation of a large variety of entangled states, encoded in the polarization degrees of freedom of N photons, within the same experimental setup. Starting with uncorrelated photons, emitted from N arbitrary single photon sources, and using linear optical tools only, we demonstrate the creation of all symmetric states, e.g., GHZ- and W-states, as well as all symmetric and non-symmetric total angular momentum eigenstates of the N qubit compound.
Hyperentangled Bell-state analysis (HBSA) is critical for high-capacity quantum communication. Here we design two effective schemes for error-heralded deterministic generation and self-assisted complete analysis of hyperentangled Bell states for two-photon systems in both the polarization and spatial-mode degrees of freedom, assisted by single-sided quantum-dot-cavity systems. We construct an error-heralded block with a singly charged quantum dot inside a single-sided optical microcavity, two circular polarization beam splitters, one half-wave plate, and one single-photon detector, in which th…
A quantum key distribution protocol with classical Bob based on polarization entangled photon pairs is presented. It approximates a single photon and exploited the inherent randomness of quantum measurements to attain highly secure keys and high efficiency of the transmission.
We theoretically investigate the joint photodetection probabilities of the biexciton-exciton cascade in single semiconductor quantum dots and analytically derive the density matrix and the Bell's inequalities of the entangled state. Our model includes different mechanisms that may spoil or even destroy entanglement such as dephasing, energy splitting of the relay excitonic states and incoherent population exchange between these relay levels. We explicitly relate the fidelity of entanglement to the dynamics of these processes and derive a threshold for violation of Bell's inequalities. Applied …
Bell-state analysis (BSA) is essential in quantum communication, but it is impossible to distinguish unambiguously the four Bell states in the polarization degree of freedom (DOF) of two-photon systems with only linear optical elements, except for the case in which the BSA is assisted with hyperentangled states, the simultaneous entanglement in more than one DOF. Here, we propose a scheme to distinguish completely the 16 hyperentangled Bell states in both the polarization and the spatial-mode DOFs of two-photon systems, by using the giant nonlinear optics in quantum dot-cavity systems. This sc…
An Einstein-Podolsky-Rosen (EPR)-like argument using events separated by a time-like interval strongly suggestes that measuring the polarization state of a photon of an entangled pair changes the polarization state of the other distant photon. Trough a very simple demonstration, the Wigner-D'Espagnat inequality is used to show that in order to prove Bell's theorem neither the assumption that there is a well-defined space of complete states $λ$ of the particle pair and well-defined probability distribution $ρ(λ)$ over this space nor the use of counterfactuals is necessary. These results reinfor…
A family of local models containing two angles as hidden variables is defined for experiments measuring polarization correlation of optical photons. Searching for the best model of the family, that is giving predictions most close to quantum mechanics, allows deriving Bell-type inequalities which may be tested with relatively low detection efficiency.
We calculate the amount of polarization-entanglement induced by two-photon interference at a lossless beam splitter. Entanglement and its witness are quantified respectively by concurrence and the Bell-CHSH parameter. In the presence of a Mandel dip, the interplay of two kinds of which-path information -- temporal and polarization -- gives rise to the existence of entangled polarization-states that cannot violate the Bell-CHSH inequality.
We show that polarization entangled photons at x-ray energies can be generated via spontaneous parametric down conversion. Each of the four Bell states can be generated by choosing the angle of incidence and polarization of the pumping beam.
