Einstein Podolsky Rosen Correlations Research Articles

Measurement of two-photon position–momentum Einstein–Podolsky–Rosen correlations through single-photon intensity measurements

The measurement of the position–momentum Einstein–Podolsky–Rosen (EPR) correlations of a two-photon state is important for many quantum information applications ranging from quantum key distribution to coincidence imaging. However, all the existing techniques for measuring the position–momentum EPR correlations involve coincidence detection and thus suffer from issues that result in less accurate measurements. In this article, we propose and demonstrate an experimental scheme that does not require coincidence detection for measuring the EPR correlations. Our technique works for two-photon states that are pure, irrespective of whether the state is separable or entangled. We theoretically show that if the pure two-photon state satisfies a certain set of conditions then the position–momentum EPR correlations can be obtained by doing the intensity measurements on only one of the photons. We experimentally demonstrate this technique for pure two-photon states produced by type-I spontaneous parametric down-conversion, and to the best of our knowledge, we report the most accurate experimental measurement of position–momentum EPR correlations.

Improving entanglement of even entangled coherent states via superposition of number-conserving operations

A scheme for improving entanglement is proposed by repeatedly performing number-conserving generalized superposition of products (GSP) operation, i.e., saa†+ta†am with s2+t2=1, on each modes of even entangled coherent state (EECS). Both Einstein–Podolsky–Rosen (EPR) correlation and concurrence are used as the measures for describing entanglement. It is found that both single-mode and two-mode-symmetric GSP operations can be used for the entanglement improvement. In particular, for the optimal EPR correlation, the GSP-EECS with two-mode-symmetric first-order operations presents a better performance for the entanglement improvement than the cases of high-order GSP operations. Compared to several special non-Gaussian operations, including photon subtraction-then-addition (PSTA) (s=0) and photon-addition-then-subtraction (PATS) (s=1), it is shown that the entanglement of GSP-EECS is always superior to those of both PSTA-EECS and PATS-EECS at a small amplitude level. When the GSP-EECS is used as the entangled resource for teleportation, our optimal teleportation fidelity presents the best performance.

Certifying position-momentum entanglement at telecommunication wavelengths

The successful employment of high-dimensional quantum correlations and its integration in telecommunication infrastructures is vital in cutting-edge quantum technologies for increasing robustness and key generation rate. Position-momentum Einstein-Podolsky-Rosen (EPR) entanglement of photon pairs are a promising resource of such high-dimensional quantum correlations. Here, we experimentally certify EPR correlations of photon pairs generated by spontaneous parametric down-conversion (SPDC) in a nonlinear crystal with type-0 phase-matching at telecommunication wavelength for the first time. To experimentally observe EPR entanglement, we perform scanning measurements in the near- and far-field planes of the signal and idler modes. We certify EPR correlations with high statistical significance of up to 45 standard deviations. Furthermore, we determine the entanglement of formation of our source to be greater than one, indicating a dimensionality of greater than 2. Operating at telecommunication wavelengths around 1550 nm, our source is compatible with today’s deployed telecommunication infrastructure, thus paving the way for integrating sources of high-dimensional entanglement into quantum-communication infrastructures.

Improvement of entanglement via catalytic quantum scissors

We theoretically investigate the generation of a novel non-Gaussian entangled state by using two single-photon catalytic quantum scissors (CQS) on an input two-mode squeezed vacuum state, and derive the effective operator of the CQS which is closely associated with the transmittance of beam splitters. The output state of this setup composes of the zero-, single- and two-photon entangled states. The results show that both larger success probability of achieving such event and higher fidelity between the input and output states can be attained by taking appropriate parameters of the transmittance and the initial squeezing parameters. Moreover, the entanglement properties of the generated non-Gaussian entangled state are discussed in terms of the degree of entanglement, the Einstein–Podolsky–Rosen (EPR) correlation and the two-mode squeezing effect. Our simulation results indicate that, in the small initial squeezing levels, there are always two improved areas of entanglement at the low and high transmittance ranges, respectively. Comparing to the improved areas of the entanglement, we find that both EPR correlation and two-mode squeezing effect rather than the entanglement degree are more rigorous in the measurement of the improved entanglement. These results show that the CQS operation is able to efficiently enhance the entanglement, which may be useful for the continuous-variable quantum communication.

Can orthogonalization enhance the EPR correlation and the teleportation fidelity of a two-mode squeezed vacuum?

For the first time, to the best of our knowledge, based on a two-mode squeezed vacuum (TMSV), we introduce photon-added orthogonal TMSVs and photon-subtracted orthogonal TMSVs via multiphoton addition a † k b † l and multiphoton subtraction a k b l ( k , l are arbitrary integers). As a comparison, we also consider photon-added TMSVs and photon-subtracted TMSVs. We theoretically analyze Einstein–Podolsky–Rosen (EPR) correlation and teleportation fidelity for all these two-mode states. Our results indicate that orthogonalization cannot enhance EPR correlation and teleportation fidelity, at least so far.

Analysis of necessary and sufficient conditions for quantum teleportation with non-Gaussian resources

Recent theoretical and experimental advances have demonstrated advantages of using non-Gaussian optical resources compared to the Gaussian ones in the context of quantum teleportation (QT), an important quantum information processing task. From both theoretical and experimental points of view the question of which attributes of the resources, besides entanglement, render them useful for QT is an important one. In this paper, we examine the question of whether two well-studied attributes of optical resources, viz., squeezed vacuum affinity (SVA) and Einstein-Podolsky-Rosen (EPR) correlation are necessary and/or sufficient for QT. The specific class of non-Gaussian resources that we have considered for this purpose are the two-mode entangled states generated by mixing nonclassical inputs with vacuum at the beam splitter (BS). Our analytical results show that SVA is not always nonzero and hence it cannot be considered to be a genuine attribute. Our numerical results show that there exist some BS-generated entangled states that do not give QT in spite of being EPR correlated, implying that EPR correlation is not sufficient for QT. In conjunction with the earlier observation in the literature to the effect that EPR correlation is not necessary for QT, our results lead to the conclusion that in general, EPR correlation is neither necessary nor sufficient for QT. Our results leave the question open as to what attributes, in general, may be necessary and/or sufficient for QT.

Information-theoretic aspects of Werner states

In a seminal study of quantum states with Einstein–Podolsky–Rosen correlations (entanglement) admitting a hidden-variable model (Werner, 1989), Werner introduced the dichotomy of entanglement/separability and devised a family of highly symmetric states, now termed the Werner states, some of which exhibit entanglement but no Bell nonlocality. It turns out that the Werner states have a rich structure of correlations and constitute a paradigm which has played an innovative role in both theoretical and experimental explorations of quantum information. Given the theoretical significance and wide applications of the Werner states, here we first give a concise review of information contents of the Werner states, and then present an information-theoretic characterization of them in terms of the Wigner–Yanase skew information: The Werner states are identified as the states with the minimum quantum uncertainty with respect to a natural family of observables (i.e., the generators of the diagonal unitary group). For this purpose, we introduce a measure of quantum uncertainty which is of independent interest in studying asymmetry, coherence, and uncertainty, and reveal its fundamental properties. We further identify the Bell triplet states as the opposite states of the Werner states in the sense that they have the maximal amount of quantum uncertainty. Analogously, we provide a similar characterization of the isotropic states as the minimum quantum uncertainty states with respect to a closely related family of operators.

Quantum entanglement and teleportation in superposition of multiple-photon-added two-mode squeezed vacuum state

In this paper, a new state called superposition of multiple-photon-added two-mode squeezed vacuum state (SMPA-TMSVS) is introduced by adding the multiple photons to both modes of a two-mode squeezed vacuum state (TMSVS). We explicitly investigate the degree of quantum entanglement, the Einstein–Podolsky–Rosen (EPR) correlation and the quantum steering in the SMPA-TMSVS. The results show in the SMPA-TMSVS that the degree of entanglement and the EPR correlation can be enhanced by nonlocal adding photons to a TMSVS. The quantum steering appears in the SMPA-TMSVS in case the superposition of single-photon addition [Formula: see text], in which mode [Formula: see text] can steer mode [Formula: see text]. By using the SMPA-TMSVS as an entangled resource, the quantum teleportation process is studied in detail based on the Vaidman–Braunstein–Kimble (VBK) protocol.

Role of EPR correlation in Gaussian quantum teleportation

Quantum teleportation (QT) plays a central role in state-of-the-art information science and technology that necessitates proper characterization of the resources. While entanglement is known to be necessary, condition of sufficiency for QT still remains an open question. Here, we partially answer this question in light of Einstein-Podolsky-Rosen (EPR) correlation. In the case of input coherent state, we provide an analytic proof that with a general two-mode Gaussian entangled resources EPR correlation is sufficient for QT. For a relatively restricted set of Gaussian states, however bigger than that of the symmetric states, we further show that EPR correlation is both necessary and sufficient. On the other hand, in the case of Gaussian pure input, our numerical results hint that EPR correlation mostly appears to be a necessary condition only. However, the necessary and/or sufficient condition for QT of a Gaussian mixed input state, apart from the entanglement, still remains an open question.

Nonclassicality and entanglement properties of non-Gaussian entangled states via a superposition of number-conserving operations

We theoretically investigate the nonclassicality and entanglement properties of non-Gaussian entangled states generated by using a number-conserving generalized superposition of products (GSP), i.e., $$\left( saa^{\dag }+ta^{\dag }a\right) ^{m}$$ with $$s^{2}+t^{2}=1$$ on each mode of an input two-mode squeezed coherent (TMSC) state. The simulation results show that, compared to the typical two-mode squeezed vacuum state, the usage of small coherent amplitude is conductive to offering an opportunity for not only effectively enhancing the nonclassicality in terms of antibunching effect and Wigner function, but also significantly improving the entanglement quantified by Einstein–Podolsky–Rosen correlation and Hillery–Zubairy correlation. For the increase of the number of operations, the region of both the existing antibunching effect and the improved entanglement decreases, but this region of the improved teleportation fidelity and the negative distribution of the Wigner function is on the increase. Under an ideal Braunstein and Kimble teleportation protocol, when the generated states are treated as an entangled resource, the optimal teleportation fidelity can be achieved by taking a suitable squeezing parameter and the number of operations for the optimal choices of s. In order to highlight the advantages of the use of the GSP-embedded TMSC, under the same parameters, we also make a comparison about the performances of both the entanglement and the fidelity for different non-Gaussian entangled states, involving the photon-subtracted-then-added TMSC states and the photon-added-then-subtracted TMSC states. It is found that in the regime of small squeezing values, both of the entanglement and the fidelity for the generated states can perform better than the other cases.

Continuous‐Variable Entanglement and Wigner‐Function Negativity via Adding or Subtracting Photons

AbstractThe performance of adding or subtracting photons on two‐mode squeezed thermal states via examining the Einstein–Podolsky–Rosen (EPR) correlation, the Hillery–Zubairy (HZ) correlation, the fidelity of teleportation, and the negativity of Wigner function is theoretically investigated. The normalization factors and the teleportation fidelity are related to Jacobi polynomials, and the (evolved) Wigner functions are simply associated with two‐variable Hermite polynomials. Compared with the original squeezed thermal states, the EPR correlation and the teleportation fidelity can be enhanced by photon subtraction and basically weakened by photon addition symmetric operations, but they cannot be enhanced for both photon addition and subtraction asymmetric cases. Also, HZ correlation can provide a better option relative to the EPR correlation in detecting the entanglement, and the fidelity for teleporting a squeezed state with a large squeezing can also be enhanced via photon addition symmetric operations, in contrast to teleporting a coherent state. Additionally, the nonclassicality is discussed in terms of the negativity of the (evolved) Wigner functions, which shows that photon addition and subtraction and the squeezing cannot restrain the deteriorate of nonclassicality, and the evolved Wigner functions become Gaussian (corresponding to vacuum) with long decay times as a result of amplitude decay.

Finite-dimensional quantum states generated by conditional measurements on beam splitters

In this work, the basic idea of the quantum scissors (QS) device is slightly modified to generate finite-dimensional quantum states by means of conditional measurements on beam splitters (BSs). It turns out that a QS device with two single-photon inputs and two single-photon detections is just a projection operator composed of the vacuum state, one-photon state, and two-photon state, depending upon the transmission coefficients of BSs. As the most general example, we consider the squeezed coherent state as the input state and derive the analytical expression of the output state. Its nonclassical characteristics are analyzed in detail by means of the average photon number, intensity gain, and Wigner function. In addition, we extend this technique to the two-mode squeezed vacuum state (TMSVS). The resulting state is just the generalized Bell state, containing only the twin vacuum, twin one-photon, and twin two-photon components, whose entanglement properties are quantified by the von Neumann entropy and Einstein–Podolsky–Rosen correlation. The results show that the entanglement of the truncated TMSVS is stronger than that of TMSVS within a certain range of squeezing parameter and transmissivity.

Entanglement properties of a tunable non-Gaussian quantum state by virtue of multi-photon conditional measurement

In this work, we present a theoretical scheme for generating a new kind of tunable non-Gaussian entangled state, by means of beam splitters and multi-photon conditional measurement with two-mode squeezed vacuum state (TMSVS) inputs. The output state is proven to be two-variable Hermite polynomial excited squeezed vacuum states, whose success probability of detection relates to the Jacobi polynomials. We then mainly study the entanglement properties of the output state for the symmetric case quantified by the von Neumann entropy and Einstein–Podolsky–Rosen correlation. It is shown that the entropy of entanglement is valid for verifying the improvement of entanglement within a certain range of squeezing parameter and transmissivity, and the resulting state case may possess a stronger correlation than the initial TMSVS by increasing the transmissivity or photon number of detection. In addition, the violation of the Clauser–Horne–Shimony–Holt (CHSH) inequality for the output state is also evaluated in terms of Wigner representation in phase space. It is found that the negative region of Wigner function distribution becomes more visible with the increase of the photon number of detection, and the degree of the violation of the CHSH inequality significantly increases as the photon number of detection for the symmetrical case increases. The resulting state with highly nonclassical characteristics will provide a useful application in the fields of quantum information processing.

Measurement-induced nonclassical state from two-mode squeezed vacuum states via beam splitter and its entanglement properties

A theoretical scheme of generating a new kind of two-mode non-Gaussian entangled state is presented by means of beam splitters (BSs) and conditional measurement. Here, after detecting photon numbers at the output port of each BS with two kinds of two-mode squeezed vacuum-state inputs, the output state is proved to be two-variable Hermite polynomial excited squeezed vacuum states. Its success probability of detection, namely, normalization factor, is derived in compact expression related to the Jacobi polynomials. Based on the general expression of expectation value, the statistical properties are discussed by exploring the cross-correlation function and anti-bunching effect. The entanglement properties are also investigated by using the Shchukin–Vogel criteria and Einstein–Podolsky–Rosen correlation. The results show that the entanglement of the output state can be enhanced with the increasing photon detection number under the condition of simultaneously detecting the same photon number at the two output ports, which may have good potential for applications in the field of quantum information processing.

Improvement of the entanglement properties for entangled states using a superposition of number-conserving operations

The non-Gaussian operation, which can be easily implemented by current techniques, is an effective way for the improvement of the continuous-variable entanglement. Here, we theoretically propose a scheme for generating a number-conserving two-mode generalized superposition of products (TM-GSP) state by performing the -order GSP operations i.e. on an input two-mode squeezed vacuum (TMSV) state. Then, the entanglement properties of the TM-GSP state are analyzed detailedly by means of logarithmic negative, Einstein–Podolsky–Rosen (EPR) correlation and two-mode squeezing property. It is shown that, in contrast to the TMSV case, for the optimal choices of s1 and s2, the entanglement properties of the TM-GSP state can be improved by using symmetric GSP operations () and single-side GSP operations . Furthermore, the fidelity effect is also considered when the TM-GSP state is used as the entangled resource under the Braunstein and Kimble scheme. In terms of the optimal teleportation fidelity, it is found that the effect of the single GSP operation is equivalent to that of the case . This phenomenon also exists in logarithmic negative, EPR correlation and two-mode squeezing property. These results show that the prepared TM-GSP state may provide a well application in the fields of quantum information processing.

Properties of two-mode squeezed Laguerre-polynomial-excited vacuum state generated by conditional measurement

We theoretically put forward a scheme to generate a new kind of the non-Gaussian state—two-mode squeezed Laguerre-polynomial-excited vacuum state (TMS-LPEVs) by using two beam splitters and conditional measurements with two kinds of TMS states inputs. It is interesting that the squeezed Bell state can be considered as a special case of TMS-LPEVs. Then we further examine its properties according to the entanglement entropy, the Einstein–Podolsky–Rosen correlation and the squeezing degree. It is found that for small auxiliary squeezing parameter r and high transmissivity, the entanglement entropy can be enhanced by single-photon measurement. When optimized over transmissivity, multiphoton measurements are beneficial to the improvement of the squeezing property and the teleportation fidelity in the region of larger λ accompanied by small auxiliary squeezing. More significantly, one can use a smaller squeezing parameter r to realize the improvements of the entanglement and the teleportation fidelity. These results may provide guidance for the implementation of experiments in quantum information and quantum computation.

Experimental test of the irreducible four-qubit Greenberger-Horne-Zeilinger paradox

Bell's theorem shows a profound contradiction between local realism and quantum mechanics on the level of statistical predictions. It does not involve directly Einstein-Podolsky-Rosen (EPR) correlations. The paradox of Greenberger-Horne-Zeilinger (GHZ) disproves directly the concept of EPR elements of reality, based on the EPR correlations, in an all-versus-nothing way. A three-qubit experimental demonstration of the GHZ paradox was achieved nearly twenty years ago, and followed by demonstrations for more qubits. Still, the GHZ contradictions underlying the tests can be reduced to three-qubit one. We show an irreducible four-qubit GHZ paradox, and report its experimental demonstration. The reducibility loophole is closed. The bound of a three-setting per party Bell-GHZ inequality is violated by $7\sigma$. The fidelity of the GHZ state was around $81\%$, and an entanglement witness reveals a violation of the separability threshold by $19\sigma$.

Einstein–Podolsky–Rosen correlation and continuous-variable quantum teleportation for the non-Gaussian entangled state with coherent component

We investigate the role of the coherent displacements in the entanglement and the quantum teleportation when PS-TMSCs considered as an entangled resource. We find that the scheme of asymmetric photon-subtraction operation and the displacement parameters involving in the two-mode squeezed coherent state (TMSCs) will decrease the EPR correlation and the fidelity of the coherent teleportation. While the EPR correlation and the fidelity of the coherent teleportation can be effectively enhanced by the symmetric photon subtraction. In addition, the improvement increases with the number of the symmetric operations in small-squeezing regime.

Lorentz symmetry breaking effects on relativistic EPR correlations

Lorentz symmetry breaking effects on relativistic EPR (Einstein-Podolsky-Rosen) correlations are discussed. From the modified Maxwell theory coupled to gravity, we establish a possible scenario of the Lorentz symmetry violation and write an effective metric for the Minkowski spacetime. Then, we obtain the Wigner rotation angle via the Fermi-Walker transport of spinors and consider the WKB ((Wentzel-Kramers-Brillouin) approximation in order to study the influence of Lorentz symmetry breaking effects on the relativistic EPR correlations.

Continuous-variable quantum teleportation with non-Gaussian entangled states generated via multiple-photon subtraction and addition

We theoretically analyze the Einstein-Podolsky-Rosen (EPR) correlation, the quadrature squeezing, and the continuous-variable quantum teleportation when considering non-Gaussian entangled states generated by applying multiple-photon subtraction and multiple-photon addition to a two-mode squeezed vacuum state (TMSVs). Our results indicate that in the case of the multiple-photon-subtracted TMSVs with symmetric operations, the corresponding EPR correlation, the two-mode squeezing degree, the sum squeezing, and the fidelity of teleporting a coherent state or a squeezed vacuum state can be enhanced for any squeezing parameter r and these enhancements increase with the number of subtracted photons in the low-squeezing regime, while asymmetric multiple-photon subtractions will generally reduce these quantities. For the multiple-photon-added TMSVs, although it holds stronger entanglement, its EPR correlation, two-mode squeezing, sum squeezing, and the fidelity of a coherent state are always smaller than that of the TMSVs. Only when considering the case of teleporting a squeezed vacuum state does the symmetric photon addition make somewhat of an improvement in the fidelity for large-squeezing parameters. In addition, we analytically prove that a one-mode multiple-photon-subtracted TMSVs is equivalent to that of the one-mode multiple-photon-added one. And one-mode multiple-photon operations will diminish the above four quantities for any squeezing parameter r.