Entangled EPR spin pairs can be treated using the statistical ensemble interpretation of quantum mechanics. As such the singlet state results from an ensemble of spin pairs each with its own specific axis of quantization. This axis acts like a quantum mechanical hidden variable. If the spins lose coherence they disentangle into a mixed state that contains classical correlations. In this paper an infinitesimal phase decoherence is introduced to the singlet state in order to reveal more clearly some of the correlations. It is shown that a singlet state has no classical correlations.
In this thesis, we study about three subjects 1- Classical simulation of two spin-$s$ singlet correlations for all $s$ involving spin measurements, 2- Quantum correlations in successive single spin measurements, 3- Non locality without inequality for almost all two-qubit entangled states based on Cabello's non locality argument.
We consider the problem of establishing entangled states of optimal singlet fraction and negativity between two remote parties for every use of a noisy quantum channel and trace-preserving LOCC under the assumption that the parties do not share prior correlations. We show that for a family of quantum channels in every finite dimension $d\geq3$, one-shot optimal singlet fraction and entanglement negativity are attained only with appropriate nonmaximally entangled states. We further show that the generalization of the formula that exactly computes one-shot optimal singlet fraction for qubit chan…
Bipartite entangled quantum states with a positive partial transpose (PPT), i.e., PPT entangled states, are usually considered very weakly entangled. Since no pure entanglement can be distilled from them, they are also called bound entangled. In this paper we present two classes of ($2d\times 2d$)-dimensional PPT entangled states for any $d\ge 2$ which outperform all separable states in metrology significantly. We present strong evidence that our states provide the maximal metrological gain achievable by PPT states for a given system size. When the dimension $d$ goes to infinity, the metrologi…
We demonstrate the possibility of achieving the maximum possible singlet fraction using a entangled mixed two-qubit state as a resource. For this, we establish a tight upper bound on singlet fraction and show that the maximal singlet fraction obtained in \cite{Verstraete} does not attain the obtained upper bound on the singlet fraction. Interestingly, we found that the required upper bound can in fact be achieved using local filtering operations.
Invariant entangled states remain unchanged under simultaneous identical unitary transformations of all their subsystems. We experimentally generate and characterize such invariant two-, four-, and six-photon polarization entangled states. This is done only with a suitable filtering procedure of multiple emissions of entangled photon pairs from a single source, without any interferometric overlaps. We get the desired states utilizing bosonic emission enhancement due to indistinguishability. The setup is very stable, and gives high interference contrasts. Thus, the process is a very likely cand…
Maximally entangled states--a resource for quantum information processing--can only be shared through noiseless quantum channels, whereas in practice channels are noisy. Here we ask: Given a noisy quantum channel, what is the maximum attainable purity (measured by singlet fraction) of shared entanglement for single channel use and local trace preserving operations? We find an exact formula of the maximum singlet fraction attainable for a qubit channel and give an explicit protocol to achieve the optimal value. The protocol distinguishes between unital and nonunital channels and requires no loc…
Spin-entaglement has been proposed and extensively used in the case of correlated triplet pairs which are intermediate states in singlet fission process in select organic semiconductors. Here, we employ quantum process tomography of polarization entangled photon-pairs resonant with the excited state absorption of these states to investigate the nature of the inherent quantum correlations and to explore for an unambiguous proof for the existence of exciton entanglement.
A quantum communication system is proposed that uses polarization-entangled photons and trapped-atom quantum memories. This system is capable of long-distance, high-fidelity teleportation, and long-duration quantum storage.
Recently, an explicit protocol ${\cal E}_0$ for faithfully teleporting arbitrary two-qubit states using genuine four-qubit entangled states was presented by us [Phys. Rev. Lett. {\bf 96}, 060502 (2006)]. Here, we show that ${\cal E}_0$ with an arbitrary four-qubit mixed state resource $Ξ$ is equivalent to a generalized depolarizing bichannel with probabilities given by the maximally entangled components of the resource. These are defined in terms of our four-qubit entangled states. We define the generalized singlet fraction ${\cal G}[Ξ]$, and illustrate its physical significance with several e…
We introduce a spin-orbital entangled (SOE) resonating valence bond (RVB) state on a square lattice of spins-$\frac12$ and orbitals represented by pseudospins-$\frac12$. Like the standard RVB state, it is a superposition of nearest-neighbor hard-core coverings of the lattice by spin singlets, but adjacent singlets are favoured to have perpendicular orientations and, more importantly, an orientation of each singlet is entangled with orbitals' state on its two lattice sites. The SOE-RVB state can be represented by a projected entangled pair state (PEPS) with a bond dimension $D=4$. This represen…
If two separated observers are supplied with entanglement, in the form of $n$ pairs of particles in identical partly-entangled pure states, one member of each pair being given to each observer; they can, by local actions of each observer, concentrate this entanglement into a smaller number of maximally-entangled pairs of particles, for example Einstein-Podolsky-Rosen singlets, similarly shared between the two observers. The concentration process asymptotically conserves {\em entropy of entanglement}---the von Neumann entropy of the partial density matrix seen by either observer---with the yiel…
Dynamical polarization of nuclear spin ensembles is of central importance for magnetic resonance studies, precision sensing and for applications in quantum information theory. Here we propose a scheme to generate long-lived singlet pairs in an unpolarized nuclear spin ensemble which is dipolar coupled to the electron spins of a Nitrogen Vacancy center in diamond. The quantum mechanical back-action induced by frequent spin-selective readout of the NV centers allows the nuclear spins to pair up into maximally entangled singlet pairs. Counterintuitively, the robustness of the pair formation to de…
We present a general theoretical method to generate maximally entangled mixed states of a pair of photons initially prepared in the singlet polarization state. This method requires only local operations upon a single photon of the pair and exploits spatial degrees of freedom to induce decoherence. We report also experimental confirmation of these theoretical results.
Addressing the feasibility of quantum communication with entangled electrons in an interacting many-body environment, we propose an interference experiment using a scattering set-up with an entangler and a beam splitter. It is shown that, due to electron-electron interaction, the fidelity of the entangled singlet and triplet states is reduced by z_F^2 in a conductor described by Fermi liquid theory. We calculate the quasiparticle weight factor z_F for a two-dimensional electron system. The current noise for electronic singlet states turns out to be enhanced (bunching behavior), while it is red…
Theoretical methods for empirical state determination of entangled two-level systems are analyzed in relation to information theory. We show that hidden variable theories would lead to a Shannon index of correlation between the entangled subsystems which is larger that that predicted by quantum mechanics. Canonical representations which have maximal correlations are treated by the use of Schmidt decomposition of the entangled states, including especially the Bohm singlet state and the GHZ entangled states. We show that quantum mechanics does not violate locality, but does violate realism.
We propose a method to dynamically generate and control the flow of spin-entangled electrons, each belonging to a spin-singlet, by means of adiabatic quantum pumping. The pumping cycle functions by periodic time variation of localized two-body interactions. We develop a generalized approach to adiabatic quantum pumping as traditional methods based on scattering matrix in one dimension cannot be applied here. We specifically compute the flow of spin-entangled electrons within a Hubbard-like model of quantum dots, and discuss possible implementations and identify parameters that can be used to c…
Quantum correlation is a fundamental property which distinguishes quantum systems from classical ones, and it is also a fragile resource under projective measurement. Recently, it has been shown that a subsystem in entangled pairs can share nonlocality with multiple observers in sequence. Here we present a new steering scenario where both subsystems are accessible by multiple observers. And it is found that the two qubits in singlet state can be simultaneously steered by two sequential observers, respectively.
We propose and analyze an approach for preparation of high fidelity entanglement and antiferromagnetic states using Rydberg mediated interactions with dissipation. Using asymmetric Rydberg interactions the two-atom Bell singlet is a dark state of the Rydberg pumping process. Master equation simulations demonstrate Bell singlet preparation fidelity $\mcF=0.998$. Antiferromagnetic states are generated on a four spin plaquette in agreement with results found from diagonalization of the transverse field Ising Hamiltonian.
Group theoretic methods to construct all N-particle singlet states by iterative recursion are presented. These techniques are applied to the quantum correlations of four spin one-half particles in their singlet states. Multipartite quantized systems can be partitioned, and their observables grouped and redefined into condensed correlations.
We develop a concept of entanglement percolation for long-distance singlet generation in quantum networks with neighboring nodes connected by partially entangled bipartite mixed states. We give a necessary and sufficient condition on the class of mixed network states for the generation of singlets. States beyond this class are insufficient for entanglement percolation. We find that neighboring nodes are required to be connected by multiple partially entangled states and devise a rich variety of distillation protocols for the conversion of these states into singlets. These distillation protocol…
Bipartite correlations in multi-qubit systems cannot be shared freely. The presence of entanglement or classical correlation on certain pairs of qubits may imply correlations on other pairs. We present a method of characterization of bi-partite correlations in multi-qubit systems using a concept of entangled graphs that has been introduced in our earlier work [M.Plesch and V.Buzek, Phys. Rev. A 67, 012322 (2003)]. In entangled graphs each qubit is represented by a vertex while the entanglement and classical correlations are represented by two types of edges. We prove by construction that any e…
Entanglement concentration requires no classical communication, but the best prior art result for diluting to N copies of a partially entangled state requires an amount of communication on the order of sqrt(N) bits. Our main result is to prove this prior art result optimal up to a constant factor; any procedure for creating N partially entangled states from singlets requires Omega(sqrt(N)) bits of classical communication. Previously not even a constant bound was known for approximate entanglement transforms. We also prove a lower bound on the inefficiency of the process: to dilute singlets to …
We propose and implement a novel scheme for dissipatively pumping two qubits into a singlet Bell state. The method relies on a process of collective optical pumping to an excited level, to which all states apart from the singlet are coupled. We apply the method to deterministically entangle two trapped ${}^{40}\text{Ca}^+$ ions with a fidelity of $93(1)\%$. We theoretically analyze the performance and error susceptibility of the scheme and find it to be insensitive to a large class of experimentally relevant noise sources.
For carrying out many quantum information protocols entanglement must be established in advance between two distant parties. Practically, inevitable interaction of entangled subsystems with their environments during distribution and storage will result in degradation of entanglement. Here we investigate the decoherence of two-qubit entangled states in the local amplitude noise. We show that there exists a set of partially entangled states that are more robust than maximally entangled states in terms of the residual quantum correlation measured by concurrence, fully entangled fraction, and quan…
The stability of two entangled spins dressed by electrons is studied by calculating the scattering phase shifts. The interaction between electrons is interpreted by fully relativistic QED and the screening effect is described phenomenologically in the Debye exponential form $e^{-αr}$. Our results show that if the (Einstein-Podolsky-Rosen-) EPR-type states are kept stable under the interaction of QED, the spatial wave function must be parity-dependent. The spin-singlet state $s=0$ and the polarized state $\frac 1{\sqrt{2}}(\mid +-> -\mid -+>)$ along the z-axis\QTR{bf}{\}give rise to two differe…
We give a classical protocol to exactly simulate quantum correlations implied by a spin $s$ singlet state for the infinite sequence of \textit{integer} spin $s={1,4,13,...}$ satisfying $(2s+1)=3^{n}$,where $n$ is a positive integer.The required amount of communication is found to increase as $log_{3}d^{2}$ where $d=2s+1$ is the dimension of the spin $s$ Hilbert space.
We experimentally prepare a new type of continuous variable genuine four-partite entangled states, the quantum correlation property of which is different from that of the four-mode GHZ and cluster states, and which has not any qubit counterpart to be proposed at present. In the criterion inequalities for the full inseparability of the genuine four-partite entangled states, the amplitude and phase quadrature correlation variances totally consisting of three-party combination from the four entangled modes are involved. The measured correlation variances among the quadratures of the prepared enta…
We in this Letter derive analytic formulas of Bell correlations in terms of quantum probability statistics under the assumption of measuring outcome-independence. For a spin-1/2 singlet state we find analytically that the violations of Bell-type inequalities are really related to the quantum non-local correlations. However, the Bell and Clauser-Horne-Shimony-Holt (CHSH) inequalities are always satisfied for the spin-1 singlet states. More generally the quantum non-locality does not lead to the violation of Bell and CHSH inequalities for the integer-spin singlet since the non-local interference…
We report on a continuous variable analogue of the triplet two-qubit Bell states. We theoretically and experimentally demonstrate a remarkable similarity of two-mode continuous variable entangled states with triplet Bell states with respect to their correlation patterns. Borrowing from the two qubit language, we call these correlations triplet-like.
An experiment is proposed to show that after initial frequency and polarization selection, classical thermal light from two independent sources can be made path-polarization entangled. Such light will show new intensity-intensity correlations involving both path and polarization phases, formally similar to those for four-particle GHZ states. For fixed polarization phases, the correlations reduce to the Hanbury Brown-Twiss phase correlations. It is also shown that these classical correlations violate noncontextuality.
Two separated observers, by applying local operations to a supply of not-too-impure entangled states ({\em e.g.} singlets shared through a noisy channel), can prepare a smaller number of entangled pairs of arbitrarily high purity ({\em e.g.} near-perfect singlets). These can then be used to faithfully teleport unknown quantum states from one observer to the other, thereby achieving faithful transfrom one observer to the other, thereby achieving faithful transmission of quantum information through a noisy channel. We give upper and lower bounds on the yield $D(M)$ of pure singlets ($\ket{Ψ^-}$)…
Bell's theorem teaches us that there are quantum correlations that can not be simulated by just shared randomness (Local Hidden variable). There are some recent results which simulate singlet correlation by using either 1 cbit or a binary (no-signaling) correlation which violate Bell's inequality maximally. But there is one more possible way to simulate quantum correlation by relaxing the condition of independency of measurement on shared randomness. Recently, MJW Hall showed that the statistics of singlet state can be generated by sacrificing measurement independence where underlying distribu…
The derivation of Bell inequalities requires an assumption of measurement independence, related to the amount of free will experimenters have in choosing measurement settings. Violation of these inequalities by singlet state correlations, as has been experimentally observed, brings this assumption into question. A simple measure of the degree of measurement independence is defined for correlation models, and it is shown that all spin correlations of a singlet state can be modeled via giving up a fraction of just 14% of measurement independence. The underlying model is deterministic and no-sign…
By going beyond Hubbard Hamiltonian we reflected correlation effects accurately in the wavefunctions of H2. Using ab initio e-e interaction parameters resulted maximally entangled ground and third excited states. We assigned this maximally entangled character to the nonmagnetic (S=0) property of these states and also the minimally entangled character of the first excited states to its magnetic property. By switching on a magnetic field an entangled state with Sz = 0 can be extracted from a minimally entangled degenerate magnetic state. We suggest that presence of a moderate correlated system a…
Any pure entangled state of two particles violates a Bell inequality for two-particle correlation functions (Gisin's theorem). We show that there exist pure entangled N>2 qubit states that do not violate any Bell inequality for N particle correlation functions for experiments involving two dichotomic observables per local measuring station. We also find that Mermin-Ardehali-Belinskii-Klyshko inequalities may not always be optimal for refutation of local realistic description.
We develop a theoretical model to study the Intensity-Intensity correlation of polarization entangled photons emitted in a biexciton-exciton cascade. We calculate the degree of correlation and show how polarization correlation are affected by the presence of dephasing and energy level splitting of the excitonic states. Our theoretical calculations are in agreement with the recent observation of polarization dependent Intensity-Intensity correlations from a single semiconductor quantum dot [R. M. Stevenson et. al., Nature 439, 179 (2006)] . Our model can be extended to study polarization entang…
The emerging strategy to overcome the limitations of bulk quantum optics consists of taking advantage of the robustness and compactness achievable by the integrated waveguide technology. Here we report the realization of a directional coupler, fabricated by femtosecond laser waveguide writing, acting as an integrated beam splitter able to support polarization encoded qubits. This maskless and single step technique allows to realize circular transverse waveguide profiles able to support the propagation of Gaussian modes with any polarization state. Using this device, we demonstrate the quantum …
We investigate genuinely entangled $N$-qubit states with no $N$-partite correlations in the case of symmetric states. Using a tensor representation for mixed symmetric states, we obtain a simple characterization of the absence of $N$-partite correlations. We show that symmetric states with no $N$-partite correlations cannot exist for an even number of qubits. We fully identify the set of genuinely entangled symmetric states with no $N$-partite correlations in the case of three qubits, and in the case of rank-2 states. We present a general procedure to construct families for an arbitrary odd nu…
We give a classical protocol to exactly simulate quantum correlations implied by a spin-$s$ singlet state for the infinite sequence of spins satisfying $(2s + 1) = 2^{n}$, in the worst-case scenario, where $n$ is a positive integer. The class of measurements we consider here are only those corresponding to spin observables. The required amount of communication is found to be $log_{2}d$ where $d = 2s + 1$ is the dimension of the spin-$s$ Hilbert space.
It is shown that there is no remote action with polarization measurements of photons in singlet state. A model is presented introducing a hidden parameter which determines the polarizer output. This model is able to explain the polarization measurement results with entangled photons. It refutes Bell's Theorem.
The general conclusion of Seevinck and Larsson is that our model exploits the so-called coincidence-time loophole and produces sinusoidal (quantum-like) correlations but does not model the singlet state because it does not violate the relevant Bell inequality derived by Larsson and Gill, since in order to obtain the sinusoidal correlations the probability of coincidences in our model goes to zero. In this reply, we refute their arguments that lead to this conclusion and demonstrate that our model can reproduce results of photon and ion-trap experiments with frequencies of coincidences that are…
We consider a scattering set-up with an entangler and beam splitter where the current noise exhibits bunching behavior for electronic singlet states and antibunching behavior for triplet states. We show that the entanglement of two electrons in the double-dot can be detected in mesoscopic transport measurements. In the cotunneling regime the singlet and triplet states lead to phase-coherent current contributions of opposite signs and to Aharonov-Bohm and Berry phase oscillations in response to magnetic fields. We analyze the Fermi liquid effects in the transport of entangled electrons.
We propose an experimentally feasible scheme for dissipative preparation of tripartite entangled state with atoms separately trapped in an array of three coupled cavities. The combination of coherent driving fields and quantum-jump-based feedback control will drive the system into a non-equilibrium steady state, which has a nearly perfect overlap with the genuine three-atom singlet state. Different control strategies are investigated and the corresponding optimal parameters are confirmed. Moreover, the fidelity of target state is insensitive to detection inefficiencies, and it oversteps 90\% f…
We study the generation of singlets in quantum networks with nodes initially sharing a finite number of partially entangled bipartite mixed states. We prove that singlets between arbitrary nodes in such networks can be created if and only if the initial states connecting the nodes have a particular form. We then generalize the method of entanglement percolation, previously developed for pure states, to mixed states of this form. As part of this, we find and compare different distillation protocols necessary to convert groups of mixed states shared between neighboring nodes of the network into …
In a recent paper [A. Ahanj et al., quant-ph/0603053], we gave a classical protocol to simulate quantum correlations corresponding to the spin $s$ singlet state for the infinite sequence of spins satisfying $2s+1 = 2^{n}$. In the present paper, we have generalized this result by giving a classical protocol to exactly simulate quantum correlations implied by the spin-$s$ singlet state corresponding to all integer as well as half-integer spin values $s$. The class of measurements we consider here are only those corresponding to spin observables, as has been done in the above-mentioned paper. The…
A new pure quantum state, isotropic in spin variables, is defined in an extended spin phase space beyond standard quantum mechanics. It allows to represent the entangled singlet state in separable form. The statistical correlations between Alice and Bob measurements become self correlations between hidden spin values for each particle, together with perfect anti correlation between spin values on the pair. Alice determines through measurement on her particle the value of spin in some direction. Spin in another direction is inferred from Bob measurement on the companion. Bell's inequalities are…
Photon-number correlation measurements are performed on bright squeezed vacuum states using a standard Bell-test setup, and quantum correlations are observed for conjugate polarization-frequency modes. We further test the entanglement witnesses for these states and demonstrate the violation of the separability criteria, which infers that all the macroscopic Bell states, containing typically $10^6$ photons per pulse, are polarization entangled. The study also reveals the symmetry of macroscopic Bell states with respect to local polarization transformations.
Simulation tasks are insightful tools to compare information-theoretic resources. Considering a generalization of usual Bell scenarios where external quantum inputs are provided to the parties, we show that any entangled quantum state exhibits correlations that cannot be simulated using only shared randomness and classical communication, even when the amount and rounds of classical communication involved are unrestricted. We indeed construct explicit Bell-like inequalities that are necessarily satisfied by such classical resources but nevertheless violated by correlations obtainable from entan…
Properties of entangled photon pairs generated in spontaneous parametric down-conversion are investigated in interference experiments. Strong energy correlations are demonstrated in a direct way. If a signal photon is detected behind a narrow spectral filter, then interference appears in the Mach-Zehnder interferometer placed in the route of the idler photon, even if the path difference in the interferometer exceeds the coherence length of the light. Narrow time correlations of the detection instants are demonstrated for the same photon-pair source using the Hong-Ou-Mandel interferometer. Both…
We present an innovative method to address the relation between the purity of type-I polarization entangled states and the spatial properties of the pump laser beam. Our all-optical apparatus is based on a spatial light modulator, and it offers unprecedented control on the spatial phase function of the entangled states. In this way, we demonstrate quantitatively the relation between the purity of the generated state and spatial correlation function of the pump beam.
We present a novel scheme for the generation of entangled states of two spatially separated nitrogen-vacancy (NV) centers with two whispering-gallery-mode (WGM) microresonators, which are coupled either by an optical fiber-taper waveguide, or by the evanescent fields of the WGM. We show that, the steady state of the two NV centers can be steered into a singlet-like state through a dissipative quantum dynamical process, where the cavity decay plays a positive role and can help drive the system to the target state. The protocol may open up promising perspectives for quantum communications and co…
We present a protocol to simulate the quantum correlation implied by non maximally entangled two qubit states, in the worst case scenario. This protocol makes a single use of PR-box and a single use of Millionaire box (M-box). To the best of our knowledge, the resources used in this protocol are weaker than those used in previous protocols and are minimal in the worst case scenario.
