Einstein-Podolsky-Rosen Entanglement Research Articles

Experimental demonstration of two-color Einstein–Podolsky–Rosen entanglement in a hot vapor cell

Einstein–Podolsky–Rosen (EPR) entanglement, involving pairs of particles that are entangled in position and momenta, is of special importance for quantum information processing. Practical quantum communication requires a two-color entanglement source: visible-band photons used to excite atoms and the communication band used for signal transmission. In this article, we report on the first experimental demonstration of two-color EPR entanglement based on spontaneous Raman scattering thermal Rb atoms using quantum ghost interference and ghost imaging. This work adopts a fundamental experiment that assists in promoting practical quantum communications and in providing a means to perform quantum imaging.

Theoretical analysis of entanglement enhancement with two cascaded optical cavities

Entanglement source with high entanglement degree is the guarantee for accomplishing the quantum information transmission and process with higher fidelity. Continuous variable Einstein-Podolsky-Rosen (EPR) entangled optical field with quantum correlation of amplitude and phase quadrature is a basic and important quantum resource in the quantum information science area, which can be obtained by a non-degenerate optical parametric amplifier (NOPA) operated below the threshold pump power. Because of the limitation of the imperfect performance of optical components in optical cavity, we should find efficient methods of implementing quantum manipulation to improve the entanglement degree of the entangled state of light. Connecting NOPA1 and NOPA2 in series, the entangled state of light output from the NOPA1 can be manipulated by NOPA2, and the entanglement degree can be enhanced under certain conditions. To improve the entanglement degree to a greater extent, the structure of the NOPA1 is chosen as a half-monolithic standing-wave optical resonator with the triple resonance of the pump and two subharmonic modes. The NOPA1 is able to output the entangled optical fields with an entanglement degree of 8.4 dB, which is the highest entanglement generated by a single device so far. The structure of the NOPA2 can be chosen as a standing-wave optical cavity or a four-mirror ring optical cavity. According to the different structures of the NOPA2, we theoretically design two kinds of optical systems with two cascaded cavities and compare the effects of the two optical systems on the continuous variable EPR entanglement cascaded enhancement in detail. Based on the above contrastive analysis, when the entanglement degree of the input optical fields is 8.4 dB and the transmissivity of the output coupler is lower, the structure of a four-mirror ring optical cavity for NOPA2 cannot enhance the entanglement degree, so the optical system including NOPA2 with standing wave cavity structure and the optical isolator with high transmission efficiency is appropriate. When the transmissivity of the output coupler and transmission efficiency of the optical isolator are higher, the structure of the NOPA2 should be chosen as a standing-wave optical cavity, otherwise the structure of the NOPA2 should be chosen as a four-mirror ring optical cavity. We also theoretically analyze the dependence of the correlation degree of output optical fields on physical parameters. The results show that under the conditions of higher input and output coupling efficiency, higher transmission efficiency and lower intro-cavity loss, the entangled state of light with higher entanglement degree can be obtained experimentally. This provides the reference for obtaining entangled optical fields with higher entanglement degree in the future.

Vortex-phase-dependent momentum and position entanglement generated from cold atoms

The Einstein Podolsky Rosen (EPR) entangled quantum state is of special importance not only for fundamental research in quantum mechanics, but also for information processing in the field of quantum information. Previous EPR entangled state demonstrations were constructed with photons of equal phase wave fronts. More complex scenarios with structured wave fronts have not been investigated. Here, we report the first experimental demonstration of EPR entanglement for photon pairs carrying orbital angular momentum (OAM) information, resulting in an OAM embedded EPR entangled state. We measured the dynamics of the dependence of the ghost interference on relative phase under projection. In addition, the reconstructed matrix in the OAM and EPR position momentum spaces shows a specific hyper entanglement in high dimension.

Synthesis of the Einstein-Podolsky-Rosen entanglement in a sequence of two single-mode squeezers.

We propose and implement a new scheme of generating the optical Einstein-Podolsky-Rosen entangled state. Parametric down-conversion in two nonlinear crystals, positioned back-to-back in the waist of a pump beam, produces single-mode squeezed vacuum states in orthogonal polarization modes; a subsequent beam splitting entangles them and generates the Einstein-Podolsky-Rosen state. The technique takes advantage of the strong nonlinearity associated with type-0 phase-matching configuration while, at the same time, eliminating the need for actively stabilizing the optical phase between the two single-mode squeezers. We demonstrate our method, preparing a 1.4 dB two-mode squeezed state and characterizing it via two-mode homodyne tomography.

Einstein-Podolsky-Rosen Entanglement of Narrow-Band Photons from Cold Atoms

Einstein-Podolsky-Rosen (EPR) entanglement introduced in 1935 deals with two particles that are entangled in their positions and momenta. Here we report the first experimental demonstration of EPR position-momentum entanglement of narrow-band photon pairs generated from cold atoms. By using two-photon quantum ghost imaging and ghost interference, we demonstrate explicitly that the narrow-band photon pairs violate the separability criterion, confirming EPR entanglement. We further demonstrate continuous variable EPR steering for positions and momenta of the two photons. Our new source of EPR-entangled narrow-band photons is expected to play an essential role in spatially multiplexed quantum information processing, such as, storage of quantum correlated images, quantum interface involving hyperentangled photons, etc.

Universal remote quantum computation assisted by the cavity input–output process

Quantum computing may provide potential superiority to solve some difficult problems. We propose a scheme for scalable remote quantum computation based on an interface between the photon and the spin of an electron confined in a quantum dot embedded in a microcavity. By successively interacting auxiliary photon pulses with spins charged in optical cavities, a prototypical quantum controlled–controlled flip gate (Toffoli gate) is achieved on a remote three-spin system using only one Einstein–Podolsky–Rosen entanglement, and local operations and classical communication. Our proposed model is shown to be robust to practical noise and experimental imperfections in current cavity–quantum electrodynamics techniques.

Entanglement in a linear coherent feedback chain of nondegenerate optical parametric amplifiers

This paper is concerned with linear quantum networks of $N$ nondegenerate optical parametric amplifiers (NOPAs), with $N$ up to 6, which are interconnected in a coherent feedback chain. Each network connects two communicating parties (Alice and Bob) over two transmission channels. In previous work we have shown that a dual-NOPA coherent feedback network generates better Einstein-Podolsky-Rosen (EPR) entanglement (i.e., more two-mode squeezing) between its two outgoing Gaussian fields than a single NOPA, when the same total pump power is consumed and the systems undergo the same transmission losses over the same distance. This paper aims to analyze stability, EPR entanglement between two outgoing fields of interest, and bipartite entanglement of two-mode Gaussian states of cavity modes of the $N$-NOPA networks under the effect of transmission and amplification losses, as well as the effect of time delays on the outgoing fields. It is numerically shown that, in the absence of losses and delays, the network with more NOPAs in the chain requires less total pump power to generate the same degree of EPR entanglement. Moreover, we report on the internal entanglement synchronization that occurs in the steady state between certain pairs of Gaussian oscillator modes inside the NOPA cavities of the networks.

Nonlinear entanglement and its application to generating cat States.

The Einstein-Podolsky-Rosen (EPR) paradox, which was formulated to argue for the incompleteness of quantum mechanics, has since metamorphosed into a resource for quantum information. The EPR entanglement describes the strength of linear correlations between two objects in terms of a pair of conjugate observables in relation to the Heisenberg uncertainty limit. We propose that entanglement can be extended to include nonlinear correlations. We examine two driven harmonic oscillators that are coupled via third-order nonlinearity can exhibit quadraticlike nonlinear entanglement which, after a projective measurement on one of the oscillators, collapses the other into a cat state of tunable size.

Theoretical analysis of an ideal noiseless linear amplifier for Einstein–Podolsky–Rosen entanglement distillation

We study the operational regime of a noiseless linear amplifier (NLA) based on quantum scissors that can nondeterministically amplify the one photon component of a quantum state with weak excitation. It has been shown that an arbitrarily large quantum state can be amplified by first splitting it into weak excitation states using a network of beamsplitters. The output states of the network can then be coherently recombined. In this paper, we analyse the performance of such a device for distilling entanglement after transmission through a lossy quantum channel, and look at two measures to determine the efficacy of the NLA. The measures used are the amount of entanglement achievable and the final purity of the output amplified entangled state. We study the performances of both a single and a two-element NLA for amplifying weakly excited states. Practically, we show that it may be advantageous to work with a limited number of stages.

Detecting faked continuous-variable entanglement using one-sided device-independent entanglement witnesses

We demonstrate the principle of one-sided device-independent continuous variable (CV) quantum information. In situations of no trust, we show by enactment how the use of standard CV entanglement criteria can mislead Charlie into thinking Alice and Bob share entanglement, when the data is actually generated classically using a Local Hidden Variable theory based on the Wigner function. We distinguish between criteria that demonstrate CV entanglement, and criteria that demonstrate the CV Einstein-Podolsky-Rosen (EPR) steering paradox. We show that the latter, but not the former, are necessarily one-sided device-independent entanglement witnesses, and can be used by Charlie to signify genuine EPR entanglement, if he trusts only Alice. A monogamy result for the EPR steering paradox confirms security of the shared amplitude values in that case.

Sensitivity to thermal noise of atomic Einstein-Podolsky-Rosen entanglement

We examine the prospect of demonstrating Einstein-Podolsky-Rosen (EPR) entanglement for massive particles using spin-changing collisions in a spinor Bose-Einstein condensate. Such a demonstration has recently been attempted by Gross et al. [Nature 480, 219 (2011)] using a condensate of Rb-87 atoms trapped in an optical lattice potential. For the condensate initially prepared in the (F,m_{F})=(2,0) hyperfine state, with no population in the m_{F}=+-1 states, we predict a significant suppression of the product of inferred quadrature variances below the Heisenberg uncertainty limit, implying strong EPR entanglement. However, such EPR entanglement is lost when the collisions are initiated in the presence of a small (currently undetectable) thermal population n_{th} in the m_{F}=+-1 states. For condensates containing 150 to 200 atoms, we predict an upper bound of n_{th}~1 that can be tolerated in this experiment before EPR entanglement is lost.

Gaussian entanglement for quantum key distribution from a single-mode squeezing source

We report the suitability of an Einstein–Podolsky–Rosen entanglement source for Gaussian continuous-variable quantum key distribution at 1550 nm. Our source is based on a single continuous-wave squeezed vacuum mode combined with a vacuum mode at a balanced beam splitter. Extending a recent security proof, we characterize the source by quantifying the extractable length of a composable secure key from a finite number of samples under the assumption of collective attacks. We show that distances in the order of 10 km are achievable with this source for a reasonable sample size despite the fact that the entanglement was generated including a vacuum mode. Our security analysis applies to all states having an asymmetry in the field quadrature variances, including those generated by superposition of two squeezed modes with different squeezing strengths.

Macroscopic mechanical correlations using single-photon spatial compass state and operational Wigner distribution

We propose a measurement scheme for observing quantum correlations and entanglement in the spatial properties of two macroscopic mirrors. Two spatial versions of compass states are generated by using a single Gaussian mode of single photons in a simple interferometer. The chessboard pattern of spatial compass states reflects the spatial properties of a mirror composed of $N$ quantum mirrors. The displacement and tilt correlations of the two mirrors are manifested by single photons and projection measurements through a measuring device which measures the propensities of the compass states. The technique can extract mechanical correlations of the two mirrors and lock them into the Einstein-Podolsky-Rosen (EPR) correlation. The criteria for EPR entanglement of these mirrors are then verified by sub-Planck structures in the propensity. We formulate the discrete-like property of the propensity, a demonstration of quantum jumps of EPR correlations in phase space, which, hence, enables discrete phase-space quantum computing and information processing.

Tripartite entanglement in qudit stabilizer states and application in quantum error correction

Consider a stabilizer state on $n$ qudits, each of dimension $D$ with $D$ being a prime or squarefree integer, divided into three mutually disjoint sets or parts. Generalizing a result of Bravyi et al. [J. Math. Phys. 47, 062106 (2006)] for qubits ($D=2$), we show that up to local unitaries, the three parts of the state can be written as tensor product of unentangled signle-qudit states, maximally entangled Einstein-Podolsky-Rosen (EPR) pairs, and tripartite Greenberger-Horne-Zeilinger (GHZ) states. We employ this result to obtain a complete characterization of the properties of a class of channels associated with stabilizer error-correcting codes, along with their complementary channels.

Strong Einstein-Podolsky-Rosen entanglement from a single squeezed light source

Einstein-Podolsky-Rosen (EPR) entanglement is a criterion that is more demanding than just certifying entanglement. We theoretically and experimentally analyze the low-resource generation of bipartite continuous-variable entanglement, as realized by mixing a squeezed mode with a vacuum mode at a balanced beam splitter, i.e., the generation of so-called vacuum-class entanglement. We find that in order to observe EPR entanglement the total optical loss must be smaller than $33.3$ $%$. However, arbitrarily strong EPR entanglement is generally possible with this scheme. We realize continuous-wave squeezed light at $1550$ nm with up to $9.9$ dB of nonclassical noise reduction, which is the highest value at a telecom wavelength so far. Using two phase-controlled balanced homodyne detectors we observe an EPR covariance product of $0.502\ifmmode\pm\else\textpm\fi{}0.006<1$, where $1$ is the critical value. We discuss the feasibility of strong Gaussian entanglement and its application for quantum key distribution in a short-distance fiber network.

Scheme for entanglement concentration of unknown atomic entangled states by interference of polarized photons

Based on the interference effect of polarized photons, we propose a practical scheme for entanglement concentration of unknown atomic entangled states. In the scheme, two λλ-type atoms belonging to different entangled pairs are individually trapped in two spatially separated cavities. By the subsequent detection of the polarized photons leaking out of the separate optical cavities, Alice and Bob as two distant parties can probabilistically extract one maximally entangled four-atom Greenberger–Horne–Zeilinger (GHZ) state from two identical partially entangled Einstein–Podolsky–Rosen (EPR) pairs. We also discuss the influence of cavity decay on the success probability of the scheme. The scheme is feasible and within the reach of current experimental technology.

High-Frequency Einstein–Podolsky–Rosen Entanglement via Atomic Memory Effects in Four-Wave Mixing

Atomic memory effects occur when the atomic relaxation times are comparable to or much longer than the cavity relaxation times. We show that by using the memory effects, it is possible to obtain high-frequency Einstein–Podolsky–Rosen entanglement between a pair of Stokes and anti-Stokes fields in a four-wave mixing system. The physical origin is traced to the dynamical Stark splittings of dressed states due to the parametrically amplified fields. This mechanism provides an alternative and efficient way for sideband entanglement.

Einstein-Podolsky-Rosen entanglement in bad cavity case

This paper explores continuous variable entanglement in four-wave mixing when the atomic relaxation time is comparable to and longer than the cavity relaxation time. In this case the atomic memory is included in the field correlations and the entanglement in the output fields can be significantly enhanced. Einstein–Podolsky–Rosen (EPR) entanglement is achievable even in the bad cavity limit. This shows the EPR entanglement generation without need of good cavity.

Quantum interference in enhanced parametric interactions

Parametric interaction of a pair of cavity fields in a near-resonantly driven atomic system is described by a bilinear Hamiltonian that decouples from atomic flip operators and is proportional to the population difference between dressed states. For proper choice of parameters, the parametric interaction is enhanced by at least two orders compared to the dispersively dressed cases. Although spontaneous emission is fed into the cavity fields, destructive interference occurs in the fluctuations of a pair of collective modes. As a result of the two factors, perfect squeezing and Einstein–Podolsky–Rosen entanglement in the output occur when the cavity relaxation rates are much larger than in the dispersive case. The mechanism is applicable to a great variety of multilevel systems and has experimental advantages in the cavity QED generation of squeezed and entangled states of light.

Einstein–Podolsky–Rosen entanglement via nonlinear processes enhanced by electromagnetically induced transparency

We show that Einstein–Podolsky–Rosen (EPR) light entanglement is obtainable via the resonant nonlinear interactions enhanced by electromagnetically induced transparency. A three-level system is used as a unified model, where two metastable states are coupled to each other via microwave, or Raman, or two-photon transition, and the upper metastable state is coupled to the excited state. A pair of inner sidebands is amplified as optical cavity modes via the transition from the excited state to the other metastable state. The analysis is presented by using the dressed-atom squeezed-transformed-mode approach. For a proper ratio of the amplitudes of the applied fields, the sum of the variances for two EPR-like operators approaches zero, which corresponds to EPR entanglement.