Adrian Alexandrescu, Diethard Schiller
The $s$-ordered phase-sum and phase-difference distributions are considered for Bell-like superpositions of two-mode coherent states. The distributions are sensitive, respectively, to the sum and difference of the phases of the entangled coherent states. They show loss of information about the entangled state and may take on negative values for some orderings $s$.
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Entangled SU(2) and SU(1,1) coherent states are developed as superpositions of multiparticle SU(2) and SU(1,1) coherent states. In certain cases, these are coherent states with respect to generalized su(2) and su(1,1) generators, and multiparticle parity states arise as a special case. As a special example of entangled SU(2) coherent states, entangled binomial states are introduced and these entangled binomial states enable the contraction from entangled SU(2) coherent states to entangled harmonic oscillator coherent states. Entangled SU(2) coherent states are discussed in the context of pairs…
Quantum nonlocality is tested for an entangled coherent state, interacting with a dissipative environment. A pure entangled coherent state violates Bell's inequality regardless of its coherent amplitude. The higher the initial nonlocality, the more rapidly quantum nonlocality is lost. The entangled coherent state can also be investigated in the framework of $2\times2$ Hilbert space. The quantum nonlocality persists longer in $2\times2$ Hilbert space. When it decoheres it is found that the entangled coherent state fails the nonlocality test, which contrasts with the fact that the decohered enta…
Introducing classical fields, we can transfer entanglement completely from discrete qubits into entangled coherent state. The entanglement also can be retrieved from the continuous-variable state of the cavities to the atomic qubits. Via postselection measure, atomic entangled state and entangled coherent state can be mutual transformed fully.
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In this paper, we propose a scheme to produce pure and macroscopical entangled coherent state. When a three-level ''V'' configuration atom interacts with a doubly reasonant cavity, under the strong classical driven condition, entangled coherent state can be generated from vacuum fields. An analytical solution for this system under the presence of cavity losses is also given.
We suggest an entanglement purification scheme for mixed entangled coherent states using 50-50 beam splitters and photodetectors. This scheme is directly applicable for mixed entangled coherent states of the Werner type, and can be useful for general mixed states using additional nonlinear interactions. We apply our scheme to entangled coherent states decohered in a vacuum environment and find the decay time until which they can be purified.
We propose a feasible scheme to realize the optical entanglement of single-photon-added coherent state (SPACS) and show that, besides the Sanders entangled coherent state, the entangled SPACS also leads to new forms of hybrid entanglement of quantum Fock state and classical coherent state. We probe the essential difference of two types of hybrid entangled state (HES). This HES provides a novel link between the discrete- and the continuous-variable entanglement in a natural way.
This Letter verifies the potential of several classes of entangled coherent state in well known quantum metrology which includes detection of classical external force, and shows that there is a class of entangled coherent state for the external force detection system without the quantum limit in the detection of the light. In the case of the precision measurement of continuos parameter like phase measurement, the entangled coherent state with perfect entanglement does not provide remarkable benefit, but we provide a concrete example that certain class of entangled coherent state gives a remark…
We give an analytical result for the quantum Fisher information of entangled coherent States in a lossy Mach-Zehnder Interferometer recently proposed by J. Joo et al. [Phys. Rev. Lett. 107, 083601(2011)]. For small loss of photons, we find that the entangled coherent state can surpass the Heisenberg limit. Furthermore, The formalism developed here is applicable to the study of phase sensitivity of multipartite entangled coherent states.
In this paper, we present a scheme to generate an entangled coherent state by considering a three-level Λ- type atom interacting with a two-mode cavity driven by classical fields. The two-mode entangled coherent state can be obtained under large detuning conditions. Considering the cavity decay, an analytical solution is deduced.
In this paper, we propose a method to generate entangled coherent states between two spatially separated atomic Bose-Einstein condensates (BECs) via the technique of the electromagnetically induced transparency (EIT). Two strong coupling laser beams and two entangled probe laser beams are used to make two distant BECs be in EIT states and to generate an atom-photon entangled state between probe lasers and distant BECs. The two BECs are initially in un-entangled product coherent states while the probe lasers are initially in an entangled state. Entangled states of two distant BECs can be create…
We propose a simple scheme for the quantum teleportation of both bipartite and multipartite entangled coherent states with the successful probability 1/2. The scheme is based on only linear optical devices such as beam splitters and phase shifters, and two-mode photon number measurements. The quantum channels described by multipartite maximally entangled coherent states are readily made by the beam splitters and phase shifters.
We present an improved phase estimation scheme employing entangled coherent states and demon- strate that the states give the smallest variance in the phase parameter in comparison to NOON, BAT and "optimal" states under perfect and lossy conditions. As these advantages emerge for very modest particle numbers, the optical version of entangled coherent state metrology is achievable with current technology.
An entangled two-mode coherent state is studied within the framework of $2\times 2$ dimensional Hilbert space. An entanglement concentration scheme based on joint Bell-state measurements is worked out. When the entangled coherent state is embedded in vacuum environment, its entanglement is degraded but not totally lost. It is found that the larger the initial coherent amplitude, the faster entanglement decreases. We investigate a scheme to teleport a coherent superposition state while considering a mixed quantum channel. We find that the decohered entangled coherent state may be useless for qu…
We study the entanglement of entangled coherent states in vacuum environment by employing the entanglement of formation and propose a scheme to probabilistically teleport a coherent superposition state via entangled coherent states, in which the amount of classical information sent by Alice is restricted to one bit. The influence of decoherence due to photon absorpation is considered. It is shown that decoherence can improve the mean fidelity of probabilistic teleportation in some situations.
A new entangled quantum state is introduced by applying local coherent superposition (ra^+ +ta) of photon subtraction and addition to each mode of even entangled coherent state (EECS) and the properties of entanglement are investigated. It is found that the Shchukin-Vogel inseparability, the degree of entanglement and the average fidelity of quantum teleportation of the EECS can be improved due to the coherent superposition operation. The effects of improvement by coherent superposition operation are better than those by single (a^+) and two-photon (a^+ b^+) addition operations under a small r…
We study GHZ-type and W-type three-mode entangled coherent states. Both the types of entangled coherent states violate Mermin's version of the Bell inequality with threshold photon detection (i.e., without photon counting). Such an experiment can be performed using linear optics elements and threshold detectors with significant Bell violations for GHZ-type entangled coherent states. However, to demonstrate Bell-type inequality violations for W-type entangled coherent states, additional nonlinear interactions are needed. We also propose an optical scheme to generate W-type entangled coherent st…
We investigate the violation of non-local realism using entangled coherent states (ECS) under nonlinear operations and homodyne measurements. We address recently proposed Leggett-type inequalities, including a class of optimized incompatibility ones and thoroughly assess the effects of detection inefficiency.
In this paper, We investigate three-mode photon-added Greenberger-Horne-Zeilinger (GHZ) entangled coherent states by repeatedly operating the photon-added operator on the GHZ entangled coherent states. The product of two Laguerre polynomials is demonstrated to be connected to the normalizing constant. The influence of the operation on the non-classical and non-Gaussian behavior of the GHZ entangled coherent states is investigated. Sub-Poissonian statistics, such as Mandel's parameter and the negativity of the Wigner function, show that non-classical properties can enhance GHZ entangled coheren…
We introduce the entangled coherent state representation, which provides a powerful technique for efficiently and elegantly describing and analyzing quantum optics sources and detectors while respecting the photon number superselection rule that is satisfied by all known quantum optics experiments. We apply the entangled coherent state representation to elucidate and resolve the longstanding puzzles of the coherence of a laser output field, interference between two number states, and dichotomous interpretations of quantum teleportation of coherent states.
We present experimental schemes to prepare the three-cavity GHZ-type and \emph{W}-type entangled coherent states in the context of dispersive cavity quantum electrodynamics. The schemes can be easily generalized to prepare the GHZ-type and \emph{W}-type entangled coherent states of $n$-cavity fields. The discussion of our schemes indicates that it can be realized by current technologies.
We investigate an optimal distance of two components in an entangled coherent state for quantum phase estimation in lossy interferometry. The optimal distance is obtained by an economical point, representing the quantum Fisher information that we can extract per input energy. Maximizing the formula of the quantum Fisher information over an input mean photon number, we show that, as the losses of the interferometer increase, it can be more beneficial to prepare an initially entangled coherent state that is less entangled. This represents that the optimal distance of the two-mode components decr…
In this contribution, a generalized protocol of quantum teleportation is suggested to investigate the possibility of remotely transfer unknown multiparities entangled coherent state. A theoretical technique is introduced to generate maximum entangled coherent states which are used as quantum channels. We show that the mean photon number plays a central role on the fidelity of the transferred information. The noise parameter can be considered as a control parameter only for small values of the mean photon number.
We microscopically model the decoherence dynamics of entangled coherent states under the influence of vacuum fluctuation. We derive an exact master equation with time-dependent coefficients reflecting the memory effect of the environment, by using the Feynman-Vernon influence functional theory in the coherent-state representation. Under the Markovian approximation, our master equation recovers the widely used Lindblad equation in quantum optics. We then investigate the non-Markovian entanglement dynamics of the quantum channel in terms of the entangled coherent states under noise. Compared wit…
Using Entangled Generalized Coherent States for Photonic Quantum Metrology
本文提出在光子量子计量学中引入纠缠广义相干态（EGCS）以改进参数估计，该方案展现出超越经典和海森堡极限的灵敏度，优于纠缠相干态和NOON态，并给出了实验生成该态的方案。
We proposed two linear optics based entanglement concentration protocols (ECPs) to obtain maximally entangled 4-mode Cluster-type entangled coherent state (ECS) from less (partially) entangled Cluster-type ECS. The first ECP is designed using a superposition of single-mode coherent state with two unknown parameters, whereas the second ECP is obtained using a superposition of single-mode coherent state and a superposition of two-mode coherent state with four unknown parameters. The success probabilities have been calculated for both the ECPs. Necessary quantum circuits enabling future experimen…
We consider the problem of bi-directional controlled quantum teleportation of information encoded in phase opposite coherent state among two distant partners Alice and Bob, with the consent of controller, Charlie. We use five-mode cluster-type entangled coherent state as the quantum resource to achieve this task. The scheme uses linear optical devices such as beam splitter, phase shifters, and photon counters. We have shown that for moderately large coherent amplitude, near-perfect bi-directional controlled teleportation can be obtained in terms of the average fidelity of teleportation.
We show how entangled qubits can be encoded as entangled coherent states of two-dimensional centre-of-mass vibrational motion for two ions in an ion trap. The entangled qubit state is equivalent to the canonical Bell state, and we introduce a proposal for entanglement transfer from the two vibrational modes to the electronic states of the two ions in order for the Bell state to be detected by resonance fluorescence shelving methods.
Entangled coherent states are useful for various applications in quantum information processing but they are are sensitive to loss. We propose a scheme to generate distributed entangled coherent states over a lossy environment in such a way that the fidelity is independent of the losses at detectors heralding the generation of the entanglement. We compare our scheme with a previous one for the same purpose [Ourjoumtsev {\em et al.}, Nat. Phys. {\bf 5} 189 (2009)] and find parameters for which our new scheme results in superior performance.
Bell's and Mermin's inequalities, entangled coherent states and unitary operators
该研究利用幺正位移算符分析纠缠相干态的Bell与Mermin不等式，发现Mermin不等式接近最大违背，结果与既有文献一致。
We compare effects of decoherence and detection inefficiency on entangled coherent states (ECSs) and entangled photon pairs (EPPs), both of which are known to be particularly useful for quantum information processing (QIP). When decoherence effects caused by photon losses are heavy, the ECSs outperform the EPPs as quantum channels for teleportation both in fidelities and in success probabilities. On the other hand, when inefficient detectors are used, the teleportation scheme using the ECSs suffers undetected errors that result in the degradation of fidelity, while this is not the case for the…
We study the evolution of entangled coherent states of the two quantized electromagnetic fields under dissipation. Characteristic time scales for the decay of the negativity are found in the case of large values of the phase space distance among the states of each mode. We also study how the entanglement emerges among the reservoirs.
By combining the beam splitter and the Fresnel transform, a protocol is proposed to generate a new entangled state representation, called the intermediate coherent-entangled state (ICES) representation. The properties, such as eigenvalue equation, completeness relation and orthogonal relation, are investigated. The conjugate state representation of the ICES and the Schmidt decomposing of the ICES are also discussed. As applications, a new squeezing operator and some operator identities by using the ICES are obtained.
We propose a scheme for generating multipartite entangled coherent states via entanglement swapping, with an example of a physical realization in ion traps. Bipartite entanglement of these multipartite states is quantified by the concurrence. We also use the $N$--tangle to compute multipartite entanglement for certain systems. Finally we establish that these results for entanglement can be applied to more general multipartite entangled nonorthogonal states.
In Xu and Kuang (\textit{J. Phys. A: Math. Gen.} 39 (2006) L191), the authors claim that, for single-mode excited entangled coherent states $| Ψ_{\pm}(α,m)>$, \textquotedblleft the photon excitations lead to the decrease of the concurrence in the strong field regime of $| α| ^{2}$ and the concurrence tends to zero when $| α| ^{2}\to \infty$". This is wrong.
We present the cluster-type entangled coherent states (CTECS) and discuss their properties. A cavity QED generation scheme using suitable choices of atom-cavity interactions, obtained via detunings adjustments and the application of classical external fields, is also presented. After the realization of simple atomic measurements, CTECS representing nonlocal electromagnetic fields in separate cavities can be generated.
We consider a resonant bichromatic excitation of N trapped ions that generates displacement and squeezing in their collective motion conditioned to their ionic internal state, producing eventually Scrhodinger cat states and entangled squeezing. Furthermore, we study the case of tetrachromatic illumination or producing the so called entangled coherent states in two motional normal modes.
We review entangled coherent state research since its first implicit use in 1967 to the present. Entangled coherent states are important to quantum superselection principles, quantum information processing, quantum optics, and mathematical physics. Despite their inherent fragility they have produced in a conditional propagating-wave quantum optics realization. Fundamentally the states are intriguing because they are entanglements of the coherent states, which are in a sense the most classical of all states of a dynamical system.
We introduce two types of two-mode excited entangled coherent states (TMEECSs) $|Ψ_{\pm}(α,m,n)>$, study their entanglement characteristics, and investigate the influence of photon excitations on quantum entanglement. It is shown that for the state $|Ψ_{+}(α,m,n)>$ the two-mode photon excitations affect seriously entanglement character while the the state $|Ψ_{-}(α,m,n)>$ is always a maximally entangled state. We show how such states can be produced by using cavity QED and quantum measurements. It is found that the entanglement amount of the TMEECSs is larger than that of the single-mode excit…
The so-called quasi-Bell entangled coherent states in a thermal environment are studied. In the analysis, we assume thermal noise affects only one of the two modes of each state. First the matrix representation of the density operators of the quasi-Bell entangled coherent states in a thermal environment is derived. Secondly we investigate the entanglement property of one of the quasi-Bell entangled coherent states with thermal noise. At that time a lower bound of the entanglement of formation for the state is computed. Thirdly the minimax discrimination problem for two cases of the binary set …
A new kind of tripartite coherent-entangled state (CES) $\ket{β,γ, x}_{μντ}$ is proposed, which exhibits the properties of both coherence and entanglement. We investigate its completeness and orthogonality, and find it can make up a representation of tripartite CES. A protocol for generating the tripartite CES is proposed using asymmetric beam splitter. Applications of the tripartite CES in quantum optics are also presented.
We propose a simple scheme to generate an arbitrary photon-added coherent state of a travelling optical field by using only a set of degenerate parametric amplifiers and single-photon detectors. Particularly, when the single-photon-added coherent state (SPACS) is observed by following, e.g., the novel technique of Zavatta \emph{$et al.$} (Science 306, 660 (2004)), we also obtain the generalized optical entangled $W$ state. Finally, a qualitative analysis of possible losses in our scheme is given.
We report on the experimental generation of an entangled state with a spectrally pure heralded single-photon state and a weak coherent state. By choosing group-velocity matching in the nonlinear crystal, our system for producing entangled photons was 60 times brighter than that in the earlier experiment [Phys. Rev. Lett. 90, 240401 (2003)], with no need of bandpass filters. This entanglement system is useful for quantum information protocols that require indistinguishable photons from independent sources.
We find that a bipartite quantum state is entangled if and only if it is quantum coherent with respect to complete bases of states in the corresponding system that are distinguishable under local quantum operations and classical communication. The corresponding minimal quantum coherence is the entanglement of formation. Connections to the relative entropy of entanglement and quantum coherence, and generalizations to the multiparty case are also considered.
The concatenated Greenberger-Horne-Zeilinger (C-GHZ) state is a new type of multipartite entangled state, which has potential application in future quantum information. In this paper, we propose a protocol of constructing arbitrary C-GHZ entangled state approximatively. Different from the previous protocols, each logic is encoded in the coherent state. This protocol is based on the linear optics, which is feasible in experimental technology. This protocol may be useful in quantum information based on the C-GHZ state.
We describe a new method of coherent optical control of internal dynamics of atomic collisions by means of two correlated light beams having entangled polarizations. We show that if excitation of a colliding pair of atoms is by two photons having entangled polarizations, it is possible to redirect the output fragments of the collision into certain channels with a selected type of internal transition symmetry. The transition symmetry is defined in the body-fixed coordinate frame which has random and originally unknown orientation in space.
A recent work [1] proposed a type of cluster entangled coherent states and its generation. Here we present an alternative experimental arrangement for its generation in bimodal QED cavities. The scheme employs a single two-level atom that interacts dispersively with cavity modes initially prepared in coherent states. The fidelity and success probability of the state preparation are obtained considering the influence of atomic velocity spread and atomic efficiency detection.
When a superposition $(|α>-|-α>)$ of two coherent states with opposite phase falls upon a 50-50 beamsplitter, the resulting state is entangled. Remarkably, the amount of entanglement is exactly 1 ebit, irrespective of $α$, as was recently discovered by O. Hirota and M. Sasaki. Here we discuss decoherence properties of such states and give a simple protocol that teleports one qubit encoded in Schrödinger cat states
We propose a particular encoding for bipartite entangled states derived from multipartite cluster-type entangled coherent states (CTECSs). We investigate the effects of amplitude damping on the entanglement content of this bipartite state, as well as its usefulness as a quantum channel for teleportation. We find interesting relationships among the amplitude of the coherent states constituting the CTECSs, the number of subsystems forming the logical qubits (redundancy), and the extent to which amplitude damping affects the entanglement of the channel. For instance, in the sense of sudden death …
We review and compare Bell-state measurement and quantum teleportation schemes using linear optics with three different types of resources, i.e., two-photon pairs, entangled coherent states and hybrid entangled states. Remarkably, perfect teleportation with linear optics is possible in principle based on a hybrid approach that combines two-photon pairs and entangled coherent states. It turns out that hybrid approach allows to perform Bell-state measurement and local Pauli operations in a deterministic way, while it requires photon number resolving measurements.
We proposed two entanglement concentration protocols (ECPs) to obtain maximally entangled Greenberger-Horne-Zeilinger (GHZ)-type entangled coherent state (ECS) from the corresponding partially entangled GHZ-type ECSs. We obtained the first ECP using a partially entangled GHZ-type ECS assisted with a superposition of single-mode coherent state, however the second ECP is designed using two copies of partially entangled GHZ-type ECSs. The success probabilities have also been calculated and discussed for both the ECPs. We have further compared the success probabilities of our first ECP for 3-mode …
Two-mode photon-added entangled coherent states and their entanglement properties
本文研究对纠缠相干态进行局域光子添加后形成的双模光子添加纠缠相干态，利用纠缠熵和准概率函数分析其纠缠与统计性质，证明光子添加可提高纠缠量。
An example is given of an interaction that produces an infinite amount of entanglement in an infinitely short time, but only a finite amount in longer times. The interaction arises from a standard Kerr nonlinearity and a 50/50 beamsplitter, and the initial state is a coherent state. For certain finite interaction times multi-dimensional generalizations of entangled coherent states are generated, for which we construct a teleportation protocol. Similarities between probabilistic teleportation and unambiguous state discrimination are pointed out.
A practical source of high fidelity entangled photons is desirable for quantum information applications and exploring quantum physics. Semiconductor quantum dots have recently been shown to conveniently emit entangled light when driven electrically, however the fidelity was not optimal. Here we show that the fidelity is not limited by decoherence, but by coherent interaction with nuclei. Furthermore we predict that on 100μs timescales, strongly enhanced fidelities could be achieved. This insight could allow tailoring of quantum logic to operate using quantum dots in the fault tolerant regime.
A new kind of tripartite non-symmetric coordinate coherent-entangled state (TNCCES) $ | β,γ,x >$ is proposed which exhibits the properties of both coherence and entanglement and makes up a new quantum mechanical representation.We investigate some properties of TNCCES such as completeness and orthogonality which prove it is just a tripartite complete continuous coordinate base. A protocol for generating TNCCES is proposed using asymmetric beam splitter. And in application of TNCCES, we find its corresponding Wigner operator and carry out its marginal distribution form; further a new tripartite …
We propose a deterministic scheme for teleporting an unknown qubit through continuous-variable entangled states in superconducting circuits. The qubit is a superconducting two-level system and the bipartite quantum channel is a photonic entangled coherent state between two cavities. A Bell-type measurement performed on the hybrid state of solid and photonic states brings a discrete-variable unknown electronic state to a continuous-variable photonic cat state in a cavity mode. This scheme further enables applications for quantum information processing in the same architecture of circuit-QED suc…
We study an asymmetric form of two-mode entangled coherent state (ECS), where the two local amplitudes have different values, for testing the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality. We find that the asymmetric ECSs have obvious advantages over the symmetric form of ECSs in testing the Bell-CHSH inequality. We further study an asymmetric strategy in distributing an ECS over a lossy environment and find that such a scheme can significantly increase violation of the inequality.
In this paper, we introduce a controllable method for producing two and three-mode entangled coherent states (ECS's) using atom-field interaction in cavity QED and beam splitter. The generated states play central roles in linear optics, quantum computation and teleportation. We especially focus on qubit, qutrit and qufit like ECS's and investigate their entanglement by concurrence measure. Moreover, we illustrate decoherence properties of ECS's due to noisy channels, using negativity measure. At the end the effect of noise on monogamy inequality is discussed.
By exploiting a system of three distant cavities, we propose a scheme for constructing tripartite entangled coherent GHZ and W states which are robust due to the photon losses in the cavities. Each of cavities is doped with a semiconductor quantum dot. By the dynamics, the excitonic modes of quantum dots are enabled to exhibit entan-gled coherent GHZ and W states. Apart from the exciton losses, the master equation approach shows that when the populations of the field modes in the cavities are negli-gible the destruction of entanglement due to decoherence arises from photon losses, is effective…
We demonstrate several new results for the nonlinear interferometer, which emerge from a formalism which describes in an elegant way the output field of the nonlinear interferometer as two-mode entangled coherent states. We clarify the relationship between squeezing and entangled coherent states, since a weak nonlinear evolution produces a squeezed output, while a strong nonlinear evolution produces a two-mode, two-state entangled coherent state. In between these two extremes exist superpositions of two-mode coherent states manifesting varying degrees of entanglement for arbitrary values of th…
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