We devise and examine two procrustean entanglement concentration schemes using Quantum Non- Demolition (QND) interaction Hamiltonians in the continuous variable regime, applicable for light, for atomic ensembles or in a hybrid setting. We thus expand the standard entanglement distillation toolbox to the use of a much more general, versatile and experimentally feasible interaction class. The first protocol uses Gaussian ancillary modes and a non-Gaussian post-measurement, the second a non-Gaussian ancillary mode and a Gaussian post-measurement. We explicitly calculate the density matrix elements of the non-Gaussian mixed states resulting from these protocols using an elegant Wigner-function based method in a numerically efficient manner. We then quantify the entanglement increase calculating the Logarithmic Negativity of the output state and discuss and compare the performance of the protocols.
This paper presents simulations of the state vector dynamics for a pair of atomic samples which are being probed by phase shift measurements on an optical beam passing through both samples. We show how measurements, which are sensitive to different atomic components, serve to prepare states which are close to being maximally entangled.
We propose a new scheme and protocol for quantum teleportation of a single-mode field state, based on entanglement produced by quantum non-demolition interaction. We show that the recently attained results in QND technique allow to perform the teleportation in quantum regime. We also show that applying QND coupling to squeezed fields will significantly improve the quality of teleportation for a given degree of squeezing.
We present a quantum circuit that implements a non-demolition measurement of complementary single- and bi-partite properties of a two-qubit system: entanglement and single-partite visibility and predictability. The system must be in a pure state with real coefficients in the computational basis, which allows a direct operational interpretation of those properties. The circuit can be realized in many systems of interest to quantum information.
A simple and efficient quantum non-demolition measurement (QND) scheme is proposed in which the arrival of a signal photon is detected without affecting the qubit state. The proposed QND scheme functions even if the ancillary photon is replaced with weak light composed of vacuum and one-photon states. Although the detection scheme is designed for entanglement sharing applications, it is also suitable for general purification of a single photon state.
We present a protocol for probing the state of a quantum system by its resonant coupling and entanglement with a meter system. By continuous measurement of a time evolving meter observable, we infer the evolution of the entangled systems and, ultimately, the state and dynamics of the system of interest. The photon number in a cavity field is thus resolved by simulated monitoring of the time dependent excited state population of a resonantly coupled two-level system, and we propose to regard this as an extension of quantum non-demolition measurements with potential applications in quantum metro…
We propose a feasible scheme to create $n$-party ($n\geq 2$) polarization-entangled photon states in a controllable way. The scheme requires only single-photon sources, single-photon quantum non-demolition measurement (SP-QNDM) and simple linear optical elements, usually with high perfections. The SP-QNDM acts as a non-destructive projection measurement onto the wanted entangled states and filters out the unwanted terms. Our scheme in fact realizes entanglement of non-interacting photons; the interaction occurs only implicitly in the optical elements and SP-QNDM. We also briefly consider purif…
Planar squeezed states, i.e. quantum states which are squeezed in two orthogonal spin components, have recently attracted attention due to their applications in atomic interferometry and quantum information [Q. Y. He et al, New J. Phys. 14, 093012 (2012)]. While canonical variables such as quadratures of the radiation field can be squeezed in at most one component, simultaneous squeezing in two orthogonal spin components can be achieved due to the angular momentum commutation relations. We present a novel scheme for planar squeezing via quantum non-demolition (QND) measurements in spin-1 syste…
We describe an entanglement purification protocol to generate maximally entangled states with high efficiencies from two-mode squeezed states or from mixed Gaussian continuous entangled states. The protocol relies on a local quantum non-demolition measurement of the total excitation number of several continuous variable entangled pairs. We propose an optical scheme to do this kind of measurement using cavity enhanced cross--Kerr interactions.
We study entanglement creation over global distances based on a quantum repeater architecture that uses low-earth orbit satellites equipped with entangled photon sources, as well as ground stations equipped with quantum non-demolition detectors and quantum memories. We show that this approach allows entanglement creation at viable rates over distances that are inaccessible via direct transmission through optical fibers or even from very distant satellites.
Single-photon detection is an essential component in many experiments in quantum optics, but remains challenging in the microwave domain. We realize a quantum non-demolition detector for propagating microwave photons and characterize its performance using a single-photon source. To this aim we implement a cavity-assisted conditional phase gate between the incoming photon and a superconducting artificial atom. By reading out the state of this atom in single shot, we reach an internal photon detection fidelity of 71%, limited by the coherence properties of the qubit. By characterizing the cohere…
Photon detectors are an elementary tool to measure electromagnetic waves at the quantum limit and are heavily demanded in the emerging quantum technologies such as communication, sensing, and computing. Of particular interest is a quantum non-demolition (QND) type detector, which projects the quantum state of a photonic mode onto the photon-number basis without affecting the temporal or spatial properties. This is in stark contrast to conventional photon detectors which absorb a photon to trigger a `click' and thus inevitably destroy the photon. The long-sought QND detection of a flying photon…
We use a quantum non-demolition measurement to generate a spin squeezed state and to create entanglement in a cloud of 10^5 cold cesium atoms, and for the first time operate an atomic clock improved by spin squeezing beyond the projection noise limit in a proof-of-principle experiment. For a clock-interrogation time of 10 μ\s the experiments show an improvement of 1.1 dB in the signal-to-noise ratio, compared to the atomic projection noise limit.
We introduce an entanglement-depth criterion optimized for planar quantum squeezed (PQS) states. It is connected with the sensitivity of such states for estimating an arbitrary, not necessarily small phase. We compare numerically our criterion with the well-known extreme spin squeezing condition of Sørensen and Mølmer [Phys. Rev. Lett. 86, 4431 (2001)] and show that our condition detects a higher depth of entanglement when both planar spin variances are squeezed below the standard quantum limit. We employ our theory to monitor the entanglement dynamics in a PQS state produced via quantum non-d…
We show that far field diffraction image of spontaneously scattered Stokes photons can be used for detection of spin entanglement and for metrology of fields gradients in cold atomic ensembles. For many-body states with small or maximum uncertainty in spin-excitation number, entanglement is simply witnessed by the presence of a sharp diffraction peak or dip. Gradient vector of external fields is measured by the displacement of a diffraction peak due to inhomogeneous spin precessions, which suggests a new possibility for precision measurement beyond the standard quantum limit without entangleme…
We present a protocol for increasing the entanglement between two atomic ensembles based on applying an approximate atom-light beamsplitter transformation to both ensembles. The effective asymmetric atom-light beamsplitter is created via a double-pass quantum non-demolition interaction between polarized light and a spin polarized atomic ensemble, derived from the linearised dipole interaction. The entanglement concentration protocol itself uses the procrustean method, similar to that first devised for light by Browne et al [2003 Phys Rev A 67 062320] and includes photon counting after the inte…
An entanglement concentration scheme for unknown atomic entanglement states is proposed via entanglement swapping in cavity QED. Because the interaction used here is a large-detuned one between two driven atoms and a quantized cavity mode, the effects of the cavity decay and thermal field have been eliminated. These advantages can warrant the experimental feasibility of the current scheme.
We introduce a simple, experimentally realisable, entanglement manipulation protocol for exploring mixed state entanglement. We show that for both non-maximally entangled pure, and mixed polarisation-entangled two qubit states, an increase in the degree of entanglement and purity, which we define as concentration, is achievable.
We present two method for optimal entanglement concentration from pure entangled states by local actions only. However a prior knowledge of the Schmidt coefficients is required. The first method is optimally efficient only when a finite ensemble of pure entangled states are available whereas the second method realizes the single pair optimal concentration probability. We also propose an entanglement assisted method which is again optimally efficient even for a single pair. We also discuss concentrating entanglement from N-partite cat like states.
We construct a Universal Quantum Entanglement Concentration Gate (QEC-Gate). Special times operations of QEC-Gate can transform a pure 2-level bipartite entangled state to nearly maximum entanglement. The transformation can attain any required fidelity with optimal probability by adjusting concentration step. We also generate QEC-Gate to the Schmidt decomposable multi-partite system.
We propose an entanglement concentration scheme which uses only the effects of quantum statistics of indistinguishable particles. This establishes the fact that useful quantum information processing can be accomplished by quantum statistics alone. Due to the basis independence of statistical effects, our protocol requires less knowledge of the initial state than most entanglement concentration schemes. Moreover, no explicit controlled operation is required at any stage.
Different procedures have been developed in order to recover entanglement after propagation over a noisy channel. Besides a certain amount of noise, entanglement is completely lost and the channel is called entanglement breaking. Here we investigate both theoretically and experimentally an entanglement concentration protocol for a mixed three-qubit state outgoing from a strong linear coupling of two-qubit maximally entangled polarization state with another qubit in a completely mixed state. Thanks to such concentration procedure, the initial entanglement can be probabilistically recovered. Fur…
We investigate entanglement concentration of continuous-variable Gaussian states by local single-photon subtractions combined with local Gaussian operations. We first analyze the local squeezing-enhanced entanglement concentration protocol proposed very recently by Zhang and van Loock [e-print: arXiv:1103.4500 (2011)] and discuss the mechanism by which local squeezing before photon subtraction helps to increase the entanglement of the output state of the protocol. We next show that a similar entanglement improvement can be achieved by using local coherent displacements instead of single-mode s…
Entanglement concentration from many copies of unknown pure states is discussed, and we propose the protocol which not only achieves entropy rate, but also produces the perfect maximally entangled state. Our protocol is induced naturally from symmetry of $n$-tensored pure state, and is optimal for all the protocols which concentrates entanglement from unknown pure states, in the sense of failure probability. In the proof of optimality, the statistical estimation theory plays a key role, for concentrated entanglement gives a natural estimate of the entropy of entanglement.
In quantum information theory, it is widely believed that entanglement concentration for bipartite pure states is asymptotically reversible. In order to examine this, we give a precise formulation of the problem, and show a trade-off relation between performance and reversibility, which implies the irreversibility of entanglement concentration. Then, we regard entanglement concentration as entangled state compression in an entanglement storage with lower dimension. Because of the irreversibility of entanglement concentration, an initial state can not be completely recovered after the compressi…
General formulas of entanglement concentration are derived by using an information-spectrum approach for the i.i.d. sequences and the general sequences of partially entangled pure states. That is, we derive general relations between the performance of the entanglement concentration and the eigenvalues of the partially traced state. The achievable rates with constant constraints and those with exponential constraints can be calculated from these formulas.
We propose two probabilistic entanglement concentration schemes for a single copy of two-mode squeezed vacuum state. The first scheme is based on the off-resonant interaction of a Rydberg atom with the cavity field while the second setup involves the cross Kerr interaction, auxiliary mode prepared in a strong coherent state and a homodyne detection. We show that the continuous-variable entanglement concentration allows us to improve the fidelity of teleportation of coherent states.
We consider asymptotic convertibility of an arbitrary sequence of bipartite pure states into another by local operations and classical communication (LOCC). We adopt an information-spectrum approach to address cases where each element of the sequences is not necessarily in tensor power of a bipartite pure state. We derive necessary and sufficient conditions for the LOCC convertibility of one sequence to another in terms of spectral entropy rates of entanglement of the sequences. Based on these results, we also provide simple proofs for previously known results on the optimal rates of entanglem…
We investigate the concentration of multi-party entanglement by focusing on simple family of three-partite pure states, superpositions of Greenberger-Horne-Zeilinger states and singlets. Despite the simplicity of the states, we show that they cannot be reversibly concentrated by the standard entanglement concentration procedure, to which they seem ideally suited. Our results cast doubt on the idea that for each N there might be a finite set of N-party states into which any pure state can be reversibly transformed. We further relate our results to the concept of locking of entanglement of forma…
We demonstrate a general weak measurement model which allows Gaussian preserving entanglement concentration of the two mode squeezed vacuum. The power of this simple and elegant protocol is through the constraints it places on possible ancilla states and measurement strategies that will allow entanglement concentration. In particular, it is shown how previously discovered protocols of this kind emerge as special examples of the general model described here. Finally, as evidence of its utility, we use it to provide another novel example of such a protocol.
The concatenated Greenberger-Horne-Zeiglinger (C-GHZ) state which is a new type of logic-qubit entanglement has attracted a lot of attentions recently. We present a feasible entanglement concentration protocol (ECP) for logic-qubit entanglement. This ECP is based on the linear optics, and it does not know the initial coefficients of the less-entangled C-GHZ state. This protocol can be extended to arbitrary C-GHZ state. This protocol may be useful in future quantum information processing tasks.
The ability to accumulate and retrieve entanglement in the fields of two remote cavities with pairs of two-level atoms is discussed. It is shown that this transfer and retrieval can be indeed ideal with a resonant interaction. The case of initial non-maximally entangled atomic pairs is also considered. This leads to the possibility of concentrating entanglement into a single pair at the retrieval stage. A teleportation protocol based on the same setup is presented. This makes possible teleportation with built-in entanglement concentration.
Deterministic extraction of Bell pairs from a finite number of partially entangled pairs is discussed. We derive the maximum number of Bell pairs that can be obtained with probability 1 by local operations and classical communication. It is proved that the optimal deterministic concentration needs only a two-pair collective manipulation in each step, and that a collective manipulation of all entangled pairs is not necessary. Finally, this scheme reveals an entanglement measure for the deterministic concentration.
We study the back action on a coupled multiple-qubit system induced by a quantum cavity probe in a non-demolition quantum measurement scheme. The exact quantum state stochastic Schrödinger equation is derived to systematically investigate the dynamics of quantum entanglement of the multiple-qubit system inside the cavity probe. Although quantum entanglement cannot be directly measured through experiments, the back action on quantum entanglement in the multi-qubit system is witnessed by applying the exact quantum state stochastic equations. Our results demonstrate that the analysis on the sensi…
In this work, we perform a series of phonon counting measurement with different methods in a 3-mode optomechanical system, and we compare the difference of the entanglement after measurement. In this article we focus on the two cases: imperfect measurement and on-off measurement. We find that whatever measurement you take, the entanglement will increase. The size of entanglement enhancement is the largest in perfect measurement, second in the imperfect measurement, and it is not obvious in the on-off measurement. We are sure that the more precise measurement information, the larger entanglemen…
We propose a scheme for concentrating nonmaximally pure and mixed polarization-entangled state of individual photon pairs. The scheme uses only simple linear optical elements and may be feasible within current optical technology.
We present two groups of practical entanglement concentration protocols (ECPs) for optical hybrid entangled state (HES). In the first group, it contains two ECPs and both ECPs do not need to know the initial coefficients of the less-entangled state. The second group contains three ECPs and they need to know the initial coefficients. It is shown that the yield of the entanglement concentration in the second group is greater than the first group. Moreover, some protocols are based on the linear optics and can be easily realized under current experiment condition. These protocols may be useful in…
We propose a Procrustean entanglement concentration scheme for continuous variable states inspired by the scheme proposed in Fiurasek et. al. Phys. Rev. A 67, 022304, (2003). We show that the eight-port homodyne measurement of Fiurasek et. al. Phys. Rev. A 67, 022304, (2003) can be replaced by a balanced homodyne measurement with the advantage of providing a success criterion that allows Alice and Bob to determine if entanglement concentration was achieved. In addition, it facilitates a straightforward and feasible experimental implementation.
We report a practical non-postselection entanglement concentration scheme in which a maximally entangled Bell-state photon pair is produced from two pairs of partially (or non-maximally) entangled photons. Since this scheme is built only upon linear optical elements and does not require photon-number resolving detectors, it has immediate applications in experimental implementations of various quantum information protocols which require two-photon Bell-states.
We present an indirect two-qubit parity meter in planar circuit quantum electrodynamics, realized by discrete interaction with an ancilla and a subsequent projective ancilla measurement with a dedicated, dispersively coupled resonator. Quantum process tomography and successful entanglement by measurement demonstrate that the meter is intrinsically quantum non-demolition. Separate interaction and measurement steps allow commencing subsequent data qubit operations in parallel with ancilla measurement, offering time savings over continuous schemes.
Enhancement of entanglement enhancement is necessary for most quantum communication protocols many of which are defined in Hilbert spaces larger than two. In this work we present the experimental realization of entanglement concentration of orbital angular momentum entangled photons produced in the spontaneous parametric down-conversion process which have been shown to provide a source for higher dimensional entanglement. We investigate the specific case of three dimensions and the possibility of generating different entangled states out of an initial state. The results presented here are of i…
For a pure state $ψ$ on a composite system $\mathcal{H}_A\otimes\mathcal{H}_B$, both the entanglement cost $E_C(ψ)$ and the distillable entanglement $E_D(ψ)$ coincide with the von Neumann entropy $H(\mathrm{Tr}_{B}ψ)$. Therefore, the entanglement concentration from the multiple state $ψ^{\otimes n}$ of a pure state $ψ$ to the multiple state $Φ^{\otimes L_n}$ of the EPR state $Φ$ seems to be able to be reversibly performed with an asymptotically infinitesimal error when the rate ${L_n}/{n}$ goes to $H(\mathrm{Tr}_{B}ψ)$. In this paper, we show that it is impossible to reversibly perform the ent…
We propose an entanglement beam splitter (EBS) using a quantum-dot spin in a double-sided optical microcavity. In contrast to the conventional optical beam splitter, the EBS can directly split a photon-spin product state into two constituent entangled states via transmission and reflection with high fidelity and high efficiency (up to 100 percent). This device is based on giant optical circular birefringence induced by a single spin as a result of cavity quantum electrodynamics and the spin selection rule of trion transition (Pauli blocking). The EBS is robust and it is immune to the fine stru…
We present a nonlocal entanglement concentration scheme for reconstructing some maximally entangled multipartite states from partially entangled ones by exploiting cross-Kerr nonlinearities to distinguish the parity of two polarization photons. Compared with the entanglement concentration schemes based on two-particle collective unitary evolution, this scheme does not require the parties to know accurately information about the partially entangled states--i.e., their coefficients. Moreover, it does not require the parties to possess sophisticated single-photon detectors, which makes this proto…
We develop an improvement to the weak laser pulse BB84 scheme for quantum key distribution, which utilizes entanglement to improve the security of the scheme and enhance its resilience to the photon-number-splitting attack. This protocol relies on the non-commutation of photon phase and number to detect an eavesdropper performing quantum non-demolition measurement on number. The potential advantages and disadvantages of this scheme are compared to the coherent decoy state protocol.
We report the generation of a macroscopic singlet state in a cold atomic sample via quantum non-demolition (QND) measurement induced spin squeezing. We observe 3 dB of spin squeezing and detect entanglement of up to $5.5\times10^5 $ atoms with $5σ$ statistical significance using a generalized spin squeezing inequality. The degree of squeezing implies at least 50% of the atoms have formed singlets, while the response to a magnetic field gradient indicates entanglement bonds at all length scales, a characteristic of quantum spin liquids.
We propose an optimal nonlocal entanglement concentration protocol (ECP) for multi-photon systems in a partially entangled pure state, resorting to the projection measurement on an additional photon. One party in quantum communication first performs a parity-check measurement on her photon in an N-photon system and an additional photon, and then she projects the additional photon into an orthogonal Hilbert space for dividing the original $N$-photon systems into two groups. In the first group, the N parties will obtain a subset of $N$-photon systems in a maximally entangled state. In the second…
Entanglement enhancement is a key task for quantum technologies. This operation performed on states produced by parametric down-conversion sources has been the object of several recent experimental investigations. In particular, conditional preparation by photon-subtraction has been shown to improve the entanglement of these states. Here we analyse the role played by non-Gaussian and Gaussian measurements in more general entanglement concentration operations performed on a pair of two-mode squeezed vacua. We find stringent requirements for achieving an improved entanglement enhancement by meas…
We present an entanglement concentration protocol for electrons based on their spins and their charges. The combination of an electronic polarizing beam splitter and a charge detector functions as a parity check device for two electrons, with which the parties can reconstruct maximally entangled electron pairs from those in a less-entanglement state nonlocally. This protocol has a higher efficiency than those based on linear optics and it does not require the parties to know accurately the information about the less-entanglement state, which makes it more convenient in a practical application …
Quantum technologies use entanglement to outperform classical technologies, and often employ strong cooling and isolation to protect entangled entities from decoherence by random interactions. Here we show that the opposite strategy - promoting random interactions - can help generate and preserve entanglement. We use optical quantum non-demolition measurement to produce entanglement in a hot alkali vapor, in a regime dominated by random spin-exchange collisions. We use Bayesian statistics and spin-squeezing inequalities to show that at least $1.52(4)\times 10^{13}$ of the $5.32(12) \times 10^{…
Consider entanglement concentration schemes that convert n identical copies of a pure state into a maximally entangled state of a desired size with success probability being close to one in the asymptotic limit. We give the distillable entanglement, the number of Bell pairs distilled per copy, as a function of an error exponent, which represents the rate of decrease in failure probability as n tends to infinity. The formula fills the gap between the least upper bound of distillable entanglement in probabilistic concentration, which is the well-known entropy of entanglement, and the maximum att…
We propose two alternative entanglement concentration protocols (ECPs) using the Faraday rotation of photonic polarization. Through the single-photon input-output process in cavity QED, it is shown that the maximally entangled atomic (photonic) state can be extracted from two partially entangled states. The distinct feature of our protocols is that we can concentrate both atomic and photonic entangled states via photonic Faraday rotation, and thus they may be universal and useful for entanglement concentration in the experiment. Furthermore, as photonic Faraday rotation works in low-$Q$ caviti…
We report a novel Bell-state synthesizer in which an interferometric entanglement concentration scheme is used. An initially mixed polarization state from type-II spontaneous parametric down-conversion becomes entangled after the interferometric entanglement concentrator. This Bell-state synthesizer is universal in the sense that the output polarization state is not affected by spectral filtering, crystal thickness, and, most importantly, the choice of pump source. It is also robust against environmental disturbance and a more general state, partially mixed$-$partially entangled state, can be …
Entanglement is a unique nature of quantum theory and has tremendous potential for application. Nevertheless, the complexity of quantum entanglement grows exponentially with an increase in the number of entangled particles. Here we introduce a quantum state concentration scheme which decomposes the multipartite entangled state into a set of bipartite and tripartite entangled states. It is shown that the complexity of the entanglement induced by the large number of particles is transformed into the high dimensions of bipartite and tripartite entangled states for pure quantum systems. The result…
We study entanglement concentration of continuous variable Gaussian states by local photon subtractions enhanced by coherent displacements. Instead of the previously considered symmetric two-mode squeezed vacuum states, we investigate the protocol for input states in the form of split single-mode squeezed vacuum, i.e., states obtained by mixing a single-mode squeezed vacuum with a vacuum state on a beam splitter, which is an experimentally highly relevant configuration. We analyze two scenarios in which the displacement-enhanced photon subtraction is performed either only on one, or on both of…
We present an entanglement concentration protocols (ECPs) for less-entangled W state with quantum-dot and microcavity coupled system. The present protocol uses the quantum nondemolition measurement on the spin parity to construct the parity check gate. Different from other ECPs, this less-entangled W state with quantum-dot and microcavity coupled system can be concentrated with the help of some single photons. The whole protocol can be repeated to get a higher success probability. It may be useful in current quantum information processing.
We propose an optimal entanglement concentration protocol (ECP) for nonlocal N-electron systems in a partially entangled pure state, resorting to charge detection and the projection measurement on an additional electron. For each nonlocal N-electron system, one party in quantum communication, say Alice first entangles it with an additional electron, and then she projects the additional electron into an orthogonal basis for dividing the N-electron systems into two groups. In the first group, the N parties obtain a subset of $N$-electron systems in a maximally entangled state directly. In the se…
We present an optimal entanglement concentration ECP for an arbitrary less-entangled W state. By two of the parties say Alice and Charlie performing one parity check measurements, they can obtain the maximally entangled W state with a certain probability. Otherwise, they can obtain another lesser-entangled W state with another probability, which can be used to reconcentrated into a maximally entangled W state. By iterating this ECP several times, it has the maximal success probability. This ECP maybe an optimal one and is useful in current quantum information processing.
Multi-photon states from parametric down-conversion can be entangled both in polarization and photon number. Maximal high-dimensional entanglement can be concentrated from these states via photon counting. This makes them natural candidates for quantum key distribution, where the presence of more than one photon per detection interval has up to now been considered as undesirable. We propose a simple multi-photon protocol for the case of low losses and point out the robustness of the entanglement under photon loss.
We analytically obtain the maximum probability of converting a finite number of copies of an arbitrary two-qubit pure state to a single copy of a maximally entangled two-qubit pure state via entanglement assisted local operations and classical communications using a two-qubit catalyst state. We show that the optimal catalyst for this transformation is always more entangled than the initial state but any two-qubit state can act as a (non-optimal) catalyst. Interestingly, the entanglement of the optimal two-qubit catalyst state is shown to decrease with that of the initial state. Entanglement as…
