The Stokes and anti-Stokes components of the spectrum of resonance fluorescence of a single trapped atom, which originate from the mechanical coupling between the scattered photons and the quantized motion of the atomic center of mass, exhibit quantum correlations which are of two-mode-squeezing type. We study and demonstrate the build-up of such correlations in a specific setup, which is experimentally accessible, and where the atom acts as efficient and continuous source of EPR-entangled, two-mode squeezed light.
Quantum steering inequalities allow to demonstrate the presence of entanglement between two parties when one of the two measurement device is not trusted. In this paper we show that quantum steering can be demonstrated for arbitrary low detection efficiency by using two-qubit non-maximally entangled states. Our result can have important applications in one-sided device-independent quantum key distribution.
We propose a novel scheme for nondistortion quantum interrogation (NQI), defined as an interaction-free measurement which preserves the internal state of the object being detected. In our scheme, two EPR entangled photons are used as the probe and polarization sensitive measurements are performed at the four ports of the Mach-Zehnder interferometer. In comparison with the previous single photon scheme, it is shown that the two photon approach has a higher probability of initial state preserving interrogation of an atom prepared in a quantum superposition. In the case that the presence of the a…
We show that a single, trapped, laser-driven atom in a high-finesse optical cavity allows for the quantum-coherent generation of entangled light pulses on demand. Schemes for generating simultaneous and temporally separated pulse pairs are proposed. The mechanical effect of the laser excitation on the quantum motion of the cold trapped atom mediates the entangling interaction between two cavity modes and between the two subsequent pulses, respectively. The entanglement is of EPR-type, and its degree can be controlled through external parameters. At the end of the generation process the atom is…
We study generation of non-local correlations by atomic interactions in a pair of bi-modal Bose-Einstein Condensates in state-dependent potentials including spatial dynamics. The wave-functions of the four components are described by combining a Fock state expansion with a time-dependent Hartree-Fock Ansatz, so that both the spatial dynamics and the local and non-local quantum correlations are accounted for. We find that despite the spatial dynamics, our protocole generates enough non-local entanglement to perform an EPR steering experiment with two spatially separated con-densates of a few th…
Let an EPR source which generates maximally entangled pairs be located so that it has distances $L_1$ and $L_2$ to two users. After taking into account various effects like loss of photons, deficiencies in the source and detectors, an entangled pair traveling through the channel may loose its perfect correlation due to errors in the channel. How the entanglement of the received pair depends on the above distances and the local properties of the channels used for this transmission? What is the best location of the source if we want to achieve the highest fidelity? What is the threshold distance…
Relativistic bipartite entangled quantum states is studied to show that Nature doesn't favor nonlocality for massive particles in the ultra-relativistic limit. We found that to an observer (Bob) in a moving frame S', the entangled Bell state shared by Alice and Bob appears as the superposition of the Bell bases in the frame S' due to the requirement of the special relativity. It is shown that the entangled pair satisfies the Bell's inequality when the boost speed approaches the speed of light, thus providing a counter example for nonlocality of Einstein-Podolsky-Rosen(EPR) paradox.
We argue that the so-called entangled states in quantum theory are not something exceptional, deserving a special attention in our efforts to understand conceptual foundations of quantum world. They appear by constructing the basis states of a compound system via the basis states of entering subsystems and describe it as a wholeness. While a system is considered as a wholeness, the individual members, forming the entangled state, have no physical meaning. In consequence, there is no physical ground for Einstein, Podolsky and Rosen (EPR) correlations arising in a process of decaying the system,…
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 narrowband photon pairs generated from cold atoms. By using two-photon quantum ghost imaging and ghost interference, we demonstrate explicitly that the narrowband 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-enta…
A local theory with a local correlation is proposed to give an explanation for the contractions in the GHZ-like proofs for Bell's theorem and the violation to Bell's inequality. It agrees with the experimental predictions for the GHZ state of three entangled spins, the Bell state of two entangled spins and one spin state. It is found that the contradiction in the GHZ-like proofs and the violation to Bell's inequality can be attributed to the local correlation.
Recently, Yeo and Chua [Phys. have given an explicit protocol for faithfully teleporting an arbitrary two-qubit state via a genuine four-qubit entangled state, which is not reducible to a pair of Bell states. Here, we present a transformation operator to give the criterion of for faithfully teleporting arbitrary two-qubit states. The theoretical explanations of some quantum channels are given by transformation operators. Furthermore, a new four-qubit entangled state quantum channel is presented.
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 th…
In 1935, Einstein, Podolsky and Rosen (EPR) considered two particles in an entangled state of motion to illustrate why they questioned the completeness of quantum theory. In the past decades, microscopic systems with entanglement in various degrees of freedom have successfully been generated, representing compelling evidence to support the completeness of quantum theory. Today, the generation of an EPR-entangled state of motion of two massive objects of up to the kilogram-scale seems feasible with state-of-the-art technology. Recently, the generation and verification of EPR-entangled mirror mo…
We describe a scheme for entangling mechanical resonators which is efficient also beyond the resolved sideband regime. It employs the radiation pressure force of the squeezed light produced by a degenerate optical parametric oscillator, which acts as a reservoir of quantum correlations (squeezed reservoir), and it is effective when the spectral bandwidth of the reservoir and the fields frequencies are appropriately selected. It allows for the steady state preparation of mechanical resonatrs in entangled EPR states and can be extended to the preparation of many entangled pairs of resonators whi…
A critical reconsideration of the EPR (Einstein-Podolsky-Rosen) paper shows that the EPR argument can be developed without using the concept of `element of physical reality', thus eliminating any philosophical element in the logical chains of the paper. Deprived of its philosophical ornament, the EPR argument plainly reduces to require what quantum mechanics can not do: to assign definite values to two incompatible physical quantities. Hidden variables theories built up according to Bell - type theorems are formulated on the basis of the assumption that the locality condition implies the stati…
By use of Reid's criterion and entropic criterion, we investigate the Einstein-Podolsky-Rosen (EPR) steering for some entangled continuous variable wavefunctions. We find that not all of the entangled states violate Reid's EPR inequality and the entropic inequality, this in turn suggests that both criteria are not necessary and sufficient conditions to detect the EPR steering.
The concept of steering was introduced by Schrodinger in 1935 as a generalization of the EPR paradox for arbitrary pure bipartite entangled states and arbitrary measurements by one party. Until now, it has never been rigorously defined, so it has not been known (for example) what mixed states are steerable (that is, can be used to exhibit steering). We provide an operational definition, from which we prove (by considering Werner states and Isotropic states) that steerable states are a strict subset of the entangled states, and a strict superset of the states that can exhibit Bell-nonlocality. …
Entanglement assistance is known to reduce the quantum communication complexity of evaluating functions with distributed inputs. But does the type of entanglement matter, or are EPR pairs always sufficient? This is a natural question because in several other settings maximally entangled states are known to be less useful as a resource than some partially entangled state. These include non-local games, tasks with quantum communication between players and referee, and simulating bipartite unitaries or communication channels. By contrast, we prove that the bounded-error entanglement-assisted quan…
We study the possibility of testing local realistic theory (LRT), envisioned implicitly by Einstein, Podolsky and Rosen in 1935, based on the Bell inequality for the correlations in the decay modes of entangled K or B-mesons. It is shown that such a test is possible for a restricted class of LRT, despite the passive nature of decay events and/or the non-unitary treatment of the correlations which invalidate the test for general LRT. Unfortunately, the present setup of the KEKB (Belle) experiment, where the coherence of entangled B-mesons has been confirmed recently, does not admit such a test …
A scheme of quantum authentication is presented. Two parties share Einstein-Podolsky-Rosen (EPR) pairs previously as the authentication key which servers as encoder and decoder. The authentication is accomplished with local controlled-NOT operations and unitary rotations. It is shown that our scheme is secure even in the presence of an eavesdropper who has complete control over both classical and quantum channels. Another character of this protocol is that the EPR sources are reusable. The robustness of this protocol is also discussed.
Entanglement, including ``quantum entanglement,'' is a consequence of correlation between objects. When the objects are subunits of pairs which in turn are members of an ensemble described by a wave function, a correlation among the subunits induces the mysterious properties of ``cat-states.'' However, correlation between subsystems can be present from purely non-quantum sources, thereby entailing no unfathomable behavior. Such entanglement arises whenever the so-called ``qubit space'' is not afflicted with Heisenberg Uncertainty. It turns out that all optical experimental realizations of EPR'…
Heisenberg's original uncertainty relation is related to measurement effect, which is different from the preparation uncertainty relation. However, it has been shown that Heisenberg's error-disturbance uncertainty relation can be violated in some cases. We experimentally test the error-tradeoff uncertainty relation by using a continuous-variable Einstein-Podolsky-Rosen (EPR) entangled state. Based on the quantum correlation between the two entangled optical beams, the errors on amplitude and phase quadratures of one EPR optical beam coming from joint measurement are estimated respectively, whi…
We propose a scheme for preparing an EPR state in position and momentum of a pair of distantly-separated trapped atoms. The scheme utilizes the entangled light fields output from a nondegenerate optical parametric amplifier. Quantum state exchange between these fields and the motional states of the trapped atoms is accomplished via interactions in cavity QED.
It is shown that the Einstein, Podolsky and Rosen (EPR) correlations for arbitrary spin-s and the Greenberger, Horne and Zeilinger (GHZ) correlations for three particles can be described by nonlocal joint and conditional quantum probabilities. The nonlocality of these probabilities makes the Bell's inequalities void. A description that exhibits the relation between the randomness and the nonlocality of entangled correlations is introduced. Entangled EPR and GHZ correlations are studied using the Gibbs-Shannon entropy. The nonlocal character of the EPR correlations is tested using the informati…
We propose a scheme to produce the maximally two photon polarization entangled state(EPR state) with single photon sources and the linear optics devices. In particular, our scheme requires the photon detectors only to distinguish the vacuum and non-vacuum Fock number states. A sophisticated photon detector distinguishing one or two photon states is unnecessary.
We analyze optical EPR experimental data performed by Weihs et al in Innsbruck 1997-1998. We show that for some linear combinations of the raw coincidence rates, the experimental results display some anomalous behavior that a more general source state (like non-maximally entangled state) cannot straightforwardly account for. We attempt to explain these anomalies by taking account of the relative efficiencies of the four channels. For this purpose, we use the fair sampling assumption, and assume explicitly that the detection efficiencies for the pairs of entangled photons can be written as a pr…
A model for two entangled systems in an EPR setting is shown to reproduce the quantum-mechanical outcomes and expectation values. Each system is represented by a small sphere containing a point-like particle embedded in a field. A quantum state appears as an equivalence class of several possible particle-field configurations. Contrarily to Bell-type hidden variables models, the fields account for the non-commutative aspects of the measurements and deny the simultaneous reality of incompatible physical quantities, thereby allowing to escape EPR's "completeness or locality" dilemma.
Quantum inseparabilities can be classified into three inequivalent forms: entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Bell-nonlocal states form a strict subset of EPR steerable states which also form a strict subset of entangled states. Recently, EPR steerable states are shown to be fundamental resources for one-sided device-independent quantum information processing tasks and, hence, identification of EPR steerable states becomes important from foundational as well as informational theoretic perspectives. In the present study we propose a new criteria to dete…
We give an introduction to an entangled massive system, specifically the neutral kaon system, which has similarities to the entangled two photon system, but, however, also challenging differences.
We present a scheme for creating quantum entangled atomic states through the coherent spin-exchange collision of a spinor Bose-Einstein condensate. The state generated possesses macroscopic Einstein-Podolsky-Roson correlation and the fluctuation in one of its quasi-spin components vanishes. We show that an elongated condensate with large aspect ratio is most suitable for creating such a state.
A model for two entangled systems in an EPR setting is shown to reproduce the quantum-mechanical outcomes and expectation values. Each system is represented by a small sphere containing a point-like particle embedded in a field. A quantum state appears as an equivalence class of several possible particle-field configurations. Contrarily to Bell-type hidden variables models, the fields account for the non-commutative aspects of the measurements and deny the simultaneous reality of incompatible physical quantities, thereby allowing to escape EPR's ``completeness or locality'' dilemma.
The recently proposed ER=EPR correspondence postulates the existence of wormholes (Einstein-Rosen bridges) between entangled states (such as EPR pairs). Entanglement is famously known to be unobservable in quantum mechanics, in that there exists no observable (or, equivalently, projector) that can accurately pick out whether a generic state is entangled. Many features of the geometry of spacetime, however, are observables, so one might worry that the presence or absence of a wormhole could identify an entangled state in ER=EPR, violating quantum mechanics, specifically, the property of state-i…
In a recent work [Phys. Rev. Lett. {\bf 98}, 140402 (2007)] we defined ``steering'', a type of quantum nonlocality that is logically distinct from both nonseparability and Bell-nonlocality. In the bipartite setting, it hinges on the question of whether Alice can affect Bob's state at a distance through her choice of measurement. More precisely and operationally, it hinges on the question of whether Alice, with classical communication, can convince Bob that they share an entangled state, under the circumstances that Bob trusts nothing that Alice says. We argue that if she can, then this demonst…
In 1935 Schrödinger introduced the terms entanglement and steering in the context of the famous gedanken experiment discussed by Einstein, Podolsky, and Rosen (EPR). Here, we report on a sixfold increase of the observed EPR-steering effect as quantified by the Reid-criterion. We achieved an unprecedented low conditional variance product of about 0.04 < 1, where 1 is the upper bound below which steering is present. The steering effect was observed on an unconditional two-mode-squeezed entangled state that contained a total vacuum state contribution of less than 8%, including detection imperfect…
In this paper we study a two-step version of EPR-B experiment, the Bohm version of the Einstein-Podolsky-Rosen experiment. Its theoretical resolution in space and time enables us to refute the classic "impossibility" to decompose a pair of entangled atoms into two distinct states, one for each atom. We propose a new causal interpretation of the EPR-B experiment where each atom has a position and a spin while the singlet wave function verifies the two-body Pauli equation. In conclusion we suggest a physical explanation of non-local influences, compatible with Einstein's point of view on relativ…
Teleportation of an EPR pair using triplet in state of the Horne-Greenberger-Zeilinger form to two receivers is considered. It needs a three-particle basis for joint measurement. By contrast the one qubit teleportation the required basis is not maximally entangled. It consists of the states corresponding to the maximally entanglement of two particles only. Using outcomes of measurement both receivers can recover an unknown EPR state however one of them can not do it separately. Teleportation of the N-particle entanglement is discussed.
Bell nonlocality and Einstein-Podolsky-Rosen (EPR) steering are every important quantum correlations of a composite quantum system. Bell nonlocality of a bipartite state is a quantum correlation demonstrated by some local quantum measurements, while EPR steering is another form of quantum correlations, observed firstly by Schrodinger in the context of famous EPR paradox. In this paper, we give some remarks on Bell nonlocality and EPR steering of bipartite states, including mathematical definitions and characterizations of these two quantum correlations, the convexity and closedness of the set …
We analyze some aspects of recently performed Franson-type experiments with entangled photon pairs aimed to test Bell's inequalities. We point out that quantum theory leads to the coincidence rate between detectors which includes in fact a dependence on the distance. We study this dependence and obtain that for large distances the correlation function vanishes. Therefore with taking into account the space parts of wave functions of photons for large distances quantum mechanical predictions are consistent with Bell's inequalities. We propose an experimental study of space dependence of correlat…
We propose a scheme for generating two-mode squeezing in high-Q resonators using a beam of atoms with random arrival times, which acts as a reservoir for the field. The scheme is based on four-wave mixing processes leading to emission into two cavity modes, which are resonant with the Rabi sidebands of the atomic dipole transition, driven by a saturating classical field. At steady state the cavity modes are in an Einstein-Podolski-Rosen (EPR) state, whose degree of entanglement is controlled by the intensity and the frequency of the transverse field. This scheme is robust against stochastic fl…
We present the experimental realization of a theoretical effect discovered by Olivares and Paris, in which a pair of entangled optical beams undergoing independent losses can see nonlocal correlations restored by the use of a nonlocal resource correlating the losses. Twin optical beams created in an entangled Einstein-Podolsky-Rosen (EPR) state by an optical parametric oscillator above threshold were subjected to 50% loss from beamsplitters in their paths. The resulting severe degradation of the signature quantum correlations observed between the two beams was then suppressed when another, ind…
We examine Einstein-Podolsky-Rosen's (EPR) steering nonlocality for two realisable Schrodinger cat-type states where a meso/ macroscopic system (called the "cat"-system) is entangled with a spin-$1/2$ system. For large cat-systems, we show that a local hidden state model is near-satisfied, meaning that the cat-system can be consistent with being in a mixture of "dead" and "alive" states despite that it is entangled with the spin system. We justify that a rigorous signature of the Schrodinger cat-type paradox is the EPR-steering of the cat-system and provide two experimental signatures. This le…
Based on total variance of a pair of Einstein-Podolsky-Rosen (EPR) type operators, the generalized EPR entangled states in continuous variable systems are defined. We show that such entangled states must correspond with two-mode squeezing states whether these states are Gaussian or not and whether they are pure or not. With help of the relation between the total variance and the entanglement, the degree of such entanglement is also defined. Through analyzing some specific cases, we see that this method is very convenient and easy in practical application. In addition, an entangled state with n…
We propose a scheme for continuous-variable telecloning with phase-conjugate inputs (PCI). Two cases of PCI telecloning are considered. The first case is where PCI telecloning produces $M$ clones nonlocally and $M$ anticlones locally, or vice versa. This kind of PCI telecloning requires only one EPR (Einstein-Podolsky-Rosen) entangled, two-mode squeezed state as a resource for building the appropriate multi-mode, multipartite entangled state via linear optics. The other case is a PCI telecloning protocol in which both clones and anticlones are created nonlocally. Such a scheme requires two EPR…
The possible connection between EPR correlations and superluminal interactions, as suggested by Bell and Bohm, is discussed using simple and palpable arguments: (a) It is shown how an experiment based on time-like events can allow us to answer the question "Can a measurement performed on one of the photons of an entangled pair change the state of the other?" (b) The theorem on superluminal finite-speed causal influences and superluminal signaling, introduced by Scarani and Gisin, is reexamined. (c) It is shown how faster-than-light interactions and Lorentz transformations might peacefully coex…
We analyse the correlation properties of light in non-linear wave-guides and transmission lines, predict the position-momentum realization of EPR paradox for photon pairs in Kerr-type non-linear photonic circuits, and we show how two-photon entangled states can be generated and detected.
Entanglement of high dimensional states is becoming increasingly important for quantum communication and computing. The most common source of entangled photons is spontaneous parametric down conversion (SPDC), where the degree of frequency and momentum entanglement is determined by the non-linear interaction volume. Here we show that by reducing the length of a highly non-linear material to the micrometer scale it is possible to relax the longitudinal phase matching condition and reach record levels of transverse wavevector entanglement. From a micro-sized layer of lithium niobate we estimate …
It has been shown in earlier works that the vertices of Platonic solids are good measurement choices for tests of EPR-steering using isotropically entangled pairs of qubits. Such measurements are regularly spaced, and measurement diversity is a good feature for making EPR-steering inequalities easier to violate in the presence of experimental imperfections. However, such measurements are provably suboptimal. Here, we develop a method for devising optimal strategies for tests of EPR-steering, in the sense of being most robust to mixture and inefficiency (while still closing the detection loopho…
The sensitivity of laser interferometers used for the detection of gravitational waves (GWs) is limited by quantum noise of light. An improvement is given by light with squeezed quantum uncertainties, as employed in the GW detector GEO600 since 2010. To achieve simultaneous noise reduction at all signal frequencies, however, the spectrum of squeezed states needs to be processed by 100m-scale low-loss optical filter cavities in vacuum. Here, we report on the proof-of-principle of an interferometer setup that achieves the required processed squeezed spectrum by employing Einstein-Podolsky-Rosen …
The two qubit (spin 1/2) singlet state has invariant perfect EPR correlations: if two observers measure {\em any} identical observables the results are always perfectly (anti-)correlated. We show that no such correlations exists in $d\otimes d$ pure or mixed bipartite quantum states if $d\geq3$. This points that two qubit singlets are high-quality quantum information carriers in long distance transmission: their correlations are unaffected by identical random unitary transformations of both qubits. Pairs of entangled qu$d$its, $d>2$, do not have this property. Thus, qu$d$it properties should b…
The Standard Quantum Limit (SQL) in interferometric displacement measurement imposes a restriction on the precision of the measurement due to its quantum back-action noise. This limit can be surpassed over a broad frequency band by injecting squeezed vacuum states with a frequency dependent (FD) quadrature angle into the measurement system. Here, we demonstrate the generation of FD squeezed vacuum states by utilizing Einstein-Podolsky-Rosen (EPR) entangled states. The frequency dependence of the squeezed state can be tuned by conditionally filtering the measurement once the two entangled field…
The measurement of the position-momentum 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 letter, 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, irrespect…
This paper illustrates various aspects of the ER=EPR conjecture.It begins with a brief heuristic argument, using the Ryu-Takayanagi correspondence, for why entanglement between black holes implies the existence of Einstein-Rosen bridges. The main part of the paper addresses a fundamental question: Is ER=EPR consistent with the standard postulates of quantum mechanics? Naively it seems to lead to an inconsistency between observations made on entangled systems by different observers. The resolution of the paradox lies in the properties of multiple black holes, entangled in the Greenberger-Horne-…
