We investigate two-photon entangled states using two important degrees of freedom of the electromagnetic field, namely orbital angular momentum (OAM) and spin angular momentum. For photons propagating in the same direction we apply the idea of $\textit{entanglement duality}$ and develop schemes to do $\textit{entanglement sorting}$ based either on OAM or polarization. In each case the entanglement is tested using appropriate witnesses. We finally present generalizations of these ideas to three- and four-photon entangled states.
We produce polarization entangled states with variable degree of entanglement for twin photons. Entanglement in polarization is coupled to entanglement in position that produces transverse coincidence interference fringes. We show both theoretically and experimentally that, due to this coupling, we can use the interference pattern to measure the polarization degree of entanglement.
We present a deterministic entanglement purification protocol (EPP) working for currently available experiment technique. In this protocol, we resort to the robust time-bin entanglement to purify the polarization entanglement determinately, which is quite different from the previous EPPs. After purification, one can obtain a completely pure maximally entangled pair with the success probability of 100%, in principle. As the maximal polarization entanglement is of vice importance in long-distance quantum communication, this protocol may have a wide application.
We present an efficient entanglement purification protocol with hyperentanglement in which additional spatial entanglement is utilized to purify the two-particle polarization-entangled state. The bit-flip error and phase-flip error can be corrected and eliminated in one step. Two remote parties can obtainmaximally entangled polarization states deterministically and only passive linear optics are employed. We also discuss the protocol with practical quantum source and noisy channel.
Parametric down-conversion can produce photons that are entangled both in polarization and in space. Here we show how the spatial entanglement can be used to purify the polarization entanglement using only linear optical elements. Spatial entanglement as an additional resource leads to a substantial improvement in entanglement output compared to a previous scheme. Interestingly, in the present context the thermal character of down-conversion sources can be turned into an advantage. Our scheme is realizable with current technology.
This work discuss the entanglement and quantum polarization of superpositions of two-mode coherent states. We use the concurrence to measure their entanglements and the quantum Stokes parameters and the Q function in order to analyze their polarization and degree of polarization.
The faithful distribution of entanglement over noisy channels is a vital prerequisite for many quantum technological applications. Quantum information can be encoded in different degrees of freedom (DOF) of photons, where each encoding comes with its own advantages and disadvantages with respect to noise resilience and practicality in manipulation. In this work, we experimentally implement a deterministic entanglement purification protocol that allows us to faithfully distribute entanglement in one DOF over a noisy channel and then remotely transfer it to another DOF for manipulation. In parti…
We characterize theoretically and experimentally the degradation of polarization entanglement in a fiber-optic entanglement distribution system where one of the optical fibers is exposed to the effects of polarization mode dispersion (PMD). We show gradual reduction of entanglement with increasing PMD and find that the highest PMD tolerance is achieved when the bandwidth of the pump used to generate the entangled photons in a $χ^{(3)}$ process is approximately half the bandwidth of the quantum channels.
Polarization features and entanglement of biphoton polarization qutrits are briefly outlined. Schmidt modes of qutrits are found analytically and in a general form by the method different from the standard one and based on the original approach of Erhard Schmidt (1906)
We consider polarization states of three photons, each in the same given spectral-angular mode. A general form of such states is a superposition of four basic three-photon polarization modes, to be referred to as three-photon polarization ququarts. All such states can be considered as consisting of one- and two-photon parts, which can be entangled with each other. The degrees of entanglement and polarization as well as the Schmidt decomposition and Stokes vectors of three-photon polarization ququarts are found and discussed.
We study the decoherence of polarization-entangled photon pairs subject to the effects of polarization mode dispersion, the chief polarization decoherence mechanism in optical fibers. We show that fiber propagation reveals an intriguing interplay between the concepts of entanglement sudden death, decoherence-free sub-spaces and non-locality. We define the boundaries in which entanglement-based quantum communications protocols relying on fiber propagation can be applied.
In this article we make a comparison between the behavior of entanglement and quantum degree of polarization for a special class of states of the radiation field, namely the Bell-type diagonal mixed states. For the three-photon mixed states we have plotted the concurrence and the Chernoff quantum degree of polarization in terms of the parameter, which defines the state. We find the the entanglement and the quantum degree of polarization are incomparable measures.
We examine the modal, spectral, and polarization entanglement properties of photon pairs generated in a nonlinear, periodically poled, two-mode waveguide (1-D planar or 2-D circular) via nondegenerate spontaneous parametric down-conversion. Any of the possible degrees of freedom -- mode number, frequency, or polarization -- can be used to distinguish the down-converted photons while the others serve as attributes of entanglement. Distinguishing the down-converted photons based on their mode numbers enables us to efficiently generate spectral or polarization entanglement that is either narrowba…
We propose a novel scheme to generate polarization entanglement from spatially-correlated photon pairs. We experimentally realized a scheme by means of a spatial correlation effect in a spontaneous parametric down-conversion and a modified Michelson interferometer. The scheme we propose in this paper can be interpreted as a conversion process from spatial correlation to polarization entanglement.
We report the experimental transformation of quadrature entanglement between two optical beams into continuous variable polarization entanglement. We extend the inseparability criterion proposed by Duan, et al. [Duan00] to polarization states and use it to quantify the entanglement between the three Stokes operators of the beams. We propose an extension to this scheme utilizing two quadrature entangled pairs for which all three Stokes operators between a pair of beams are entangled.
Sources of entangled photon pairs using two parametric down-converters are capable of generating interchangeable entanglement in two different degrees of freedom. The connection between these two degrees of freedom allows the control of the entanglement properties of one, by acting on the other degree of freedom. We demonstrate experimentally, the quantum distillation of the position entanglement using polarization analyzers.
We established important relationships between entanglement measures and the order parameter (spin polarization) in nuclear spin systems controlled by the nuclear magnetic resonance (NMR) technique. Since spin polarization can be easily manipulated by the NMR technique, experimentalists are presented with an opportunity to study the dynamic properties of entanglement, i.e., the creation and evolution of entangled states. Our approach may constitute the basis for researching the relations between the entanglement measures and measurable parameters of order in other quantum systems.
Discussed in the study are gravitational noise and the nature of entanglement states. Their role in forming of entangled states. Nonlocal nature of entangled states can be brought about by Polarization Variables. Polarization Variables consists of sum a background of random classical gravitational fields and waves, random electromagnets fields and so on known or unknown, distributed average isotropically in the space. This background is capable of correlating phases the oscillations of microobjects. From this follow, that entanglement polarizations states is the functions of Polarization Varia…
We suggest and demonstrate a scheme to compensate spatial and spectral decoherence effects in the generation of polarization entangled states by type-I parametric downconversion. In our device a programmable spatial light modulator imposes a polarization dependent phase-shift on different spatial sections of the overall downconversion output and this effect is exploited to realize an effective purification technique for polarization entanglement.
We demonstrate experimentally how orbital-angular-momentum entanglement of two photons evolves under influence of atmospheric turbulence. We find that the quantum channel capacity is surprisingly robust: Its typical horizontal decay distance is of the order of 2 kilometers, demonstrating the potential of photonic orbital angular momentum for free-space quantum communication in a metropolitan environment.
We study the quantum properties of the polarization of the light produced in type II spontaneous parametric down-conversion in the framework of a multi-mode model valid in any gain regime. We show that the the microscopic polarization entanglement of photon pairs survives in the high gain regime (multi-photon regime), in the form of nonclassical correlation of all the Stokes operators describing polarization degrees of freedom.
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.
We have experimentally demonstrated polarization entanglement using continuous variables in an ultra-short pulsed laser system at telecommunication wavelengths. Exploiting the Kerr-nonlinearity of a glass fibre we generated a polarization squeezed pulse with S2 the only non-zero Stokes parameter thus S1 and S3 being the conjugate pair. Polarization entanglement was generated by interference of the polarization squeezed field with a vacuum on a 50:50 beam splitter. The two resultant beams exhibit strong quantum noise correlations in S1 and S3. The sum noise signal of S3 was at the respective sh…
The issue raised in this paper is classical in the sense of being ancient: which subset of 4X4 matrices should be accepted as physical Mueller matrices in polarization optics? Non-quantum entanglement between the polarization and spatial degrees of freedom of an electromagnetic beam is shown to provide the physical basis to resolve this issue in a definitive manner.
We propose a polarization-dependent spatial phase modulation method to purify the two-photon polarization entanglement generated by the biexciton cascade decay in a single semiconductor quantum dot. In principle, our method can completely compensate the random phase acquired from the decay of the non-degenerate exciton states in time domain. In frequency domain, our method is equivalent to shifting photon frequency according to its polarization. The method can be applied immediately by existing experimental set-ups.
We present two economical one-step error-correction protocols for multipartite polarization-entangled systems in a Greenberger-Horne-Zeilinger state. One uses spatial entanglement to correct errors in the polarization entanglement of an N-photon system, resorting to linear optical elements. The other uses frequency entanglement to correct errors in the polarization entanglement of an N-photon system. The parties in quantum communication can obtain a maximally entangled state from each N-photon system transmitted with one step in these two protocols, and both of their success probabilities are …
Inspired by laser operation, we address the question of whether stimulated emission into polarization entangled modes can be achieved. We describe a state produced by stimulated emission of the singlet Bell state and propose a setup for creating it. As a first important step towards an entangled-photon laser we demonstrate experimentally interference-enhanced polarization entanglement.
The Shannon dimensionality of orbital angular momentum (OAM) entanglement produced in spontaneous parametric down-conversion can be probed by using multi-sector phase analysers. We demonstrate a spatial light modulator-based implementation of these analysers, and use it to measure a Schmidt number of about 50.
We introduce a scheme for remote entanglement generation for the photon polarization. The technique is based on transferring the initial frequency correlations to specific polarization-frequency correlations by local dephasing and their subsequent removal by frequency up-conversion. On fundamental level, our theoretical results show how to create and transfer entanglement, to particles which never interact, by means of local operations. This possibility stems from the multi-path interference and its control in frequency space. For applications, the developed techniques and results allow for th…
We study the behaviour of the Negativity of Wigner Function (NWF) as a measure of entanglement in non-Gaussian states under quantum polarisation converter devices. We analyze comparatively this quantity with other measures of entanglement in a system prepared in a superposition of two-mode coherent states. We show that the (WF) can be identified as a quantifier of non-Gaussian entanglement.
We report the first experimental characterization of the first-order continuous variable orbital angular momentum states. Using a spatially non-degenerate optical parametric oscillator (OPO) we produce quadrature entanglement between the two first-order Laguerre-Gauss modes. The family of OAM modes is mapped on an orbital Poincare sphere, and the modes position on the sphere is spanned by the three orbital parameters. Using the non-degenerate OPO we produce squeezing of these parameters, and as an illustration, we reconstruct the "cigar-shaped" uncertainty volume on the orbital Poincare sphere…
We study the entanglement evolution of photonic orbital angular momentum qubit states with opposite azimuthal indices $l_0$, in a weakly turbulent atmosphere. Using asymptotic methods, we deduce analytical expressions for the amplitude of turbulence-induced crosstalk between the modes $l_0$ and $-l_0$. Furthermore, we analytically establish distinct, universal entanglement decay laws for Kolmogorov's turbulence model and for two approximations thereof.
Quantum protocols will be more efficient with high-dimensional entangled states. Photons carrying orbital angular momenta can be used to create a high-dimensional entangled state. In this paper we experimentally demonstrate the entanglement of the orbital angular momentum between the Stokes and anti-Stokes photons generated in a hot atomic ensemble using spontaneous four-wave-mixing. This experiment also suggests the existence of the entanglement concerned with spatial degrees of freedom between the hot atomic ensemble and the Stokes photon.
We provide an analytical expression for the entanglement decay of initially maximally entangled orbital angular momentum bi-photon states, when scattered off an obstruction. We show that the decay is controlled by the diffraction-induced mutual overlap between the diffracted field modes, and quantify its dependence on the size and position of the obstruction.
We examine entanglement between number and polarization, or between number and relative phase, for pairs of coherent states and two-mode squeezed vacuum via linear entropy and covariance criteria. We consider the embedding of the two-mode Hilbert space in a larger space to get a well-defined factorization of the number-phase variables. This can be regarded as a kind of proto-entanglement that can be extracted and converted into real particle entanglement via feasible experimental procedures. In particular this reveals interesting entanglement properties of pairs of coherent states.
We investigate the possibility of characterizing two-party entanglement by measuring correlations of Stokes operators in polarized bright light beams. We adapt a general separability criterion to such operators. We then show that entanglement purification can only be singled out for a particular protocol.
Polarization maintenance is a key technology for free-space quantum communication. In this paper, we describe a polarization maintenance design of a transmitting antenna with an average polarization extinction ratio of 887 : 1 by a local test. We implemented a feasible polarization-compensation scheme for satellite motions that has a polarization fidelity more than 0.995. Finally, we distribute entanglement to a satellite from ground for the first time with a violation of Bell inequality by 2.312+-0.096.
Density matrices of pure multiphoton Fock polarization states and of arising from them reduced density matrices of mixed states are expressed in similar ways in terms of matrices of correlators defined as averaged products of equal numbers of creation and annihilation operators. Degree of entanglement of considered states is evaluated for various combinations of parameters of states and character of their reduction.
We report the first quantum entanglement experiment in South Africa. The spatial modes of the entangled photon pair are investigated with their potential for high-dimensional entanglement. The generation, measurement and characterisation of the entangled states are examined in detail, where we show high-dimensional entanglement in a Hilbert space of dimension 25. We highlight the experimental challenges contained within each step and provide practical techniques for future experiments in the quantum regime.
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.
Sources of entanglement are an enabling resource in quantum technology, and pushing the limits of generation rate and quality of entanglement is a necessary pre-requisite towards practical applications. Here, we present an ultra-bright source of polarization-entangled photon pairs based on time-reversed Hong-Ou-Mandel interference. By superimposing four pair-creation possibilities on a polarization beam splitter, pairs of identical photons are separated into two spatial modes without the usual requirement for wavelength distinguishability or non-collinear emission angles. Our source yields hig…
Evaluation of quantum entanglement state between photoelectron spin and emitted photon polarization in spin and polarization resolved XEPECS of $\rm Ti_{2}O_{3}$
Entanglement swapping generates remote quantum correlations between particles that have not interacted and is the cornerstone of long-distance quantum communication, quantum networks, and fundamental tests of quantum science. In the context of spatial modes of light, high-dimensional entanglement provides an avenue to increase the bandwidth of quantum communications and provides more stringent limits for tests of quantum foundations. Here we simultaneously swap the entanglement of multiple orbital angular momentum states of light. The system is based on a degenerate filter that cannot distingu…
We generate and characterise continuous variable polarization entanglement between two optical beams. We first produce quadrature entanglement, and by performing local operations we transform it into a polarization basis. We extend two entanglement criteria, the inseparability criteria proposed by Duan {\it et al.}\cite{Duan00} and the Einstein-Podolsky-Rosen paradox criteria proposed by Reid and Drummond\cite{Reid88}, to Stokes operators; and use them to charactise the entanglement. Our results for the Einstein-Podolsky-Rosen paradox criteria are visualised in terms of uncertainty balls on th…
Propagation of entangled photons in optical fiber is one of the fundamental issues for realizing quantum communication protocols. When entanglement in polarization is considered, arises the problem of compensating for the fiber effect on photons polarization. In this paper we demonstrate an effective solution where a Faraday mirror allows to cancel undesired effects of polarization drift in fiber. This technique is applied to a protocol for generating Bell states by a narrow temporal selection of the second-order intensity correlation function.
So far experimental confirmation of entanglement has been restricted to qubits, i.e. two-state quantum systems including recent realization of three- and four-qubit entanglements. Yet, an ever increasing body of theoretical work calls for entanglement in quantum system of higher dimensions. Here we report the first realization of multi-dimensional entanglement exploiting the orbital angular momentum of photons, which are states of the electromagnetic field with phase singularities (doughnut modes). The properties of such states could be of importance for the efforts in the field of quantum com…
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.
The singular nature of a non-integer spiral phase plate allows easy manipulation of spatial degrees of freedom of photon states. Using two such devices, we have observed very high dimensional (D > 3700) spatial entanglement of twin photons generated by spontaneous parametric down-conversion.
We show that the transfer of the plane wave spectrum of the pump beam to the fourth-order transverse spatial correlation function of the two-photon field generated by spontaneous parametric down-conversion leads to the conservation and entanglement of orbital angular momentum of light. By means of a simple experimental setup based on fourth-order (or two-photon) interferometry, we show that our theoretical model provides a good description for down-converted fields carrying orbital angular momentum.
We present a one-step deterministic entanglement purification protocol with linear optics and postselection. Compared with the Simon-Pan protocol (Phys. Rev. Lett. 89, 257901 (2002)), this one-step protocol has some advantages. First, it can get a maximally entangled pair with only one step, not only improve the fidelity of less-entangled photon pairs by performing the protocol repeatedly. Second, it works in a deterministic way, not a probabilistic one, which will reduce a great deal of entanglement resources. Third, it does not require the polarization state be entangled, only spatial entang…
Entanglement Distribution over a Polarization-Stabilized Aerial Fiber
National Institute of Standards and Technology（美国国家标准与技术研究院）；Joint Quantum Institute, University of Maryland（马里兰大学联合量子研究所）；Morgan State University（摩根州立大学）；Qunnect Inc.（Qunnect公司）
The need for spatial and spectral filtering in the generation of polarization entanglement is eliminated by combining two coherently-driven type-II spontaneous parametric downconverters. The resulting ultrabright source emits photon pairs that are polarization entangled over the entire spatial cone and spectrum of emission. We detect a flux of $\sim$12 000 polarization-entangled pairs/s per mW of pump power at 90% quantum-interference visibility, and the source can be temperature tuned for 5 nm around frequency degeneracy. The output state is actively controlled by precisely adjusting the rela…
We calculate the effect of polarization-dependent scattering by disorder on the degree of polarization-entanglement of two beams of radiation. Multi-mode detection converts an initially pure state into a mixed state with respect to the polarization degrees of freedom. The degree of entanglement decays exponentially with the number of detected modes if the scattering mixes the polarization directions and algebraically if it does not.
By using an optical device based on the integration of a GRaded-INdex (GRIN) rod lens and a single-mode optical fiber we efficiently collected photon pairs generated by spontaneous parametric down-conversion. We show that this system preserves the polarization entanglement of the 2-photon states. Hence this device, characterized by a remarkable easiness of alignment and allowing for high coupling efficiency of single-mode radiation, can be used with photons entangled in various degrees of freedom, such as polarization and spatial momentum, and to interconnect different sides of complex optical…
The pairwise entanglement and local polarization of the ground state are discussed by studying the Heisenberg XX model in finite qubit case. The results show that: the ground state is composed by the micro state with the minimal total spin 0 (for even qubit) or 1/2 (for odd qubit), local polarization (LP) has intimate relation with the probability of the micro state in the ground state, the stronger the LP the smaller the probability, the same LP corresponding to the same probability; the pairwise entanglement of the ground state is the biggest in all the eigenvectors. We find when the qubit i…
Quantum entanglement is at the heart of quantum information sciences and quantum technologies. In the optical domain, the most common type of quantum entanglement is polarization entanglement, which is usually created in a postselection manner involving destructive photon detection and thus hindering further applications which require readily available entanglement resources. In this work, we propose a scheme to prepare multipartite entangled states of polarized photons in a heralded manner, i.e., without postselection. We exploit the quantum scissors technique to truncate a given continuous-v…
