Entangled Coherent States Research Articles

Nonlinear optical tomography of q-deformed entangled pair coherent states

We introduce entangled pair coherent states of a noncommutative harmonic oscillator operators associated with a q-deformed oscillator algebra. The definition of two-mode q-deformed operator and the decomposition of its eigenstates in terms of the q-deformed Fock states are obtained. The general solution of the recurrence relation of the first nondeformed quadrature is obtained. The asymptotic behavior of the general solution is studied, a complete expansion is derived, and also representations of the general solution in terms of the Gauss hypergeometric function are given. Also, we prove that the general solution is related to Meixner-Pollaczek orthogonal polynomial and calculate the weight function. The photons number distribution, the second order correlation function and the optical tomogram of the entangled pair coherent states are discussed. The recurrence relation for the first q-deformed quadrature is inferred. We evaluate the eigenstate of the q-deformed quadrature operator and give a numerical study for the optical tomogram of the q-deformed of the entangled pair coherent states. Finally, we show the change of the parameters in the entangled pair coherent states that connected with physical quantities and explain how they affect the format of optimal tomography.

Efficient scheme for creating a W-type optical entangled coherent state.

W-type optical entangled coherent states have important applications in quantum communication. Previous works require performing measurement in the preparation of such W states. We here propose an efficient scheme for creating a W-type optical entangled coherent state without measurement. This scheme employs a setup composed of three microwave cavities and a superconducting flux coupler qutrit. Because no measurement is required, the W state can be generated deterministically. In addition, the system complexity is greatly reduced because of using only one qutrit to couple the three cavities. Numerical analysis shows that within current experimental technology, the W state can be prepared with high fidelity. This scheme is universal and can be extended to create the W-type optical entangled coherent state, by using three microwave or optical cavities coupled via a three-level natural or artificial atom.

Quantum Teleportation via Entangled State of Light in Schwarzschild Black Hole

In this paper, we describe the properties of quantum entanglement and teleportation between Alice and Bob who is freely falling toward the Schwarzschild black hole. To this aim, in the flat Minkowski spacetime before a black hole is formed, Alice and Bob share a two-mode entangled coherent state (ECS) generated by Kerr medium and the beam splitter. We will show that the degree of entanglement decreases with increasing the radius of black hole r. Moreover, the fidelity of quantum teleportation via ECS, as a quantum channel, is also reduced because of the Hawking-Unruh effect.

Optimal entangled coherent states in lossy quantum-enhanced metrology

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 decreases with more loss in the interferometry. Under the constraint of the input mean photon number, we obtain that the optimal entangled coherent state is more robust than a separable coherent state, even in a high photon loss rate. The optimal entangled coherent state preserves quantum advantage over the standard interferometric limit of the separable coherent state. We also show that the corresponding optimal measurement requires correlation measurement bases.

Improving long-distance distribution of entangled coherent state with the method of twin-field quantum key distribution.

The twin-field quantum key distribution (TFQKD) protocol has garnered considerable attention in quantum communication because it overcomes the well-known fundamental limit of the secret key rate without quantum repeaters. In this study, we employ this scheme to demonstrate the long-distance distribution of entangled coherent state (ECS), which has not been addressed in the existing literature. We show a scheme for the distribution of ECS with a yield of η, where η is the total efficiency of the whole transmission link. Compared to the cat-state based scheme, the success probability for fidelity is enhanced by 1.86 to 11.54 times in our new scheme, where the ECS is |ψECS(α = 2.0)〉 and the fixed fidelity (F) ranges from 0.99 to 0.75. The performance of our scheme in the presence of realistic on-off photon detector has also been investigated. Our work provides the application of TFQKD method toward continuous variable entanglement distribution and we believe that its application to other quantum information processing protocols are worth investigation in the near future.

Generation of various classes of entangled states in a two-mode Bose–Einstein condensate under the influence of interatom collisions

In this paper, we generate some new classes of entangled states of a bimodal Bose–Einstein condensate (BEC), a pair of tunnel-coupled BEC, in the presence of two- and three-body elastic as well as mode-exchange collisions. The Hamiltonian of the considered system is very complicated, moreover, it can be fortunately transformed into a simple form using a two-mode displacement operator. After introducing the general form of the time evolved state, various classes of entangled states are generated. Indeed, the influence of different orders of tunneling strengths on the generated entangled states has been studied. Depending on the tunneling strength constants, two-, three- and four-partite entangled states are generated, all of which are superposition states of macroscopic number of BEC atoms. Considering three-particle collision dramatically changes the generated entangled states. Moreover, in particular cases, the resulted states are non-entangled. Also, we show that tunneling and collisional interactions can be manipulated to generate a pair of atomic entangled coherent states (quasi-Bell states). In addition, it is observed that the degree of entanglement for two-partite entangled states can be tuned via the number of BEC atoms, i.e. the corresponding concurrences tend to their maximum value by increasing the atoms in both modes of system.

Nearly maximal violation of the Mermin-Klyshko inequality with multimode entangled coherent states

Entangled coherent states for multiple bosonic modes, also referred to as multimode cat states, not only are of fundamental interest but also have practical applications. The nonclassical correlation among these modes is well characterized by the violation of the Mermin-Klyshko inequality. We here study Mermin-Klyshko inequality violations for such multi-mode entangled states with rotated quantum-number parity operators. It is shown that the Mermin-Klyshko signal obtained with these operators can approach the maximal value even when the average quantum number in each mode is only 1, and the inequality violation exponentially increases with the number of entangled modes. This is in distinct contrast with the framework based on displaced parity operators, with which a nearly maximal Mermin-Klyshko inequality violation requires the size of the cat state to be increased by about 15 times.

Coherent-State-Based Twin-Field Quantum Key Distribution

Large-scale quantum communication networks are still a huge challenge due to the rate-distance limit of quantum key distribution (QKD). Recently, twin-field (TF) QKD has been proposed to overcome this limit. Here, we prove that coherent-state-based TF-QKD is a time-reversed entanglement protocol, where the entanglement generation is realized with entanglement swapping operation via an entangled coherent state measurement. We propose a coherent-state-based TF-QKD with optimal secret key rate under symmetric and asymmetric channels by using coherent state and cat state coding. Furthermore, we show that our protocol can be converted to all recent coherent-state-based TF-QKD protocols by using our security proof. By using the entanglement purification with two-way classical communication, we improve the transmission distance of all coherent-state-based TF-QKD protocols.

Enhancing entanglement of entangled coherent states via a f-deformed photon-addition operation

In this paper, we introduce a new kind of photon-added entangled coherent states (PA-ECSs), by performing repeatedly a f-deformed photon-addition (DPA) operation, $ A^{\dagger}= f(\hat{n}) a^{\dagger}$, on each mode of the entangled coherent states (ECSs), $ \vert\Psi_{\pm}(\alpha)\rangle$. By choosing a particular deformation function $ f(\hat{n})$, we study how the entanglement properties can be enhanced by DPA operation. As a result, we show that both the single and two-mode DPA operation can be used to improve the entanglement of $ \vert\Psi_{+} (\alpha)\rangle$, where the effects of improvement by two-mode DPA operation are more prominent than those by single-mode DPA operation, in any amplitude regime. Moreover, our results show there exists a family of coherent amplitudes $| \alpha |$ such that the two-mode DPA operation preserves the maximal entanglement of the odd ECSs $ \vert\Psi_{-}(\alpha)\rangle$, where the non-deformed photon-addition operation $ a^{\dagger}$ suppresses the entanglement amount. Finally, a theoretical scheme for the physical generation of the introduced states based on a Jaynes-Cummings model with intensity-dependent couplings is proposed.

Nonclassical properties and polarization degree of photon-subtracted entangled nonlinear coherent states

As in two previous papers where nonclassical properties and entanglement dynamics were studied for entangled nonlinear coherent states (ENCS) [D. Afshar and A. Anbaraki, J. Opt. Soc. Am. B 33, 558 (2016).] and for photon-added entangled nonlinear coherent states (PAENCS) [A. Anbaraki, D. Afshar and M. Jafarpour, Eur. Phys. J. Plus 133, 2 (2018).], we study quantum mechanical treatments of photon-subtracted entangled nonlinear coherent states (PSENCS) introduced through applying annihilation operators on the ENCS, where the related nonlinearity functions are assumed to be harmonious. To gain insight into the effectiveness of photon subtracting from ENCS and comparing with the case already discussed as the PAENCS, we present a general analysis of nonclassical properties such as photon statistics and degree of polarization. We also derive the concurrence measure to quantify the entanglement of these states and look for conditions that provide information on whether they become maximally entangled. As a result, we can see that the photon depletion number m plays an important role in nonclassical effects. Especially, depending on whether the photon depletion number m is even or odd, one can observe different nonclassical effects.

Linear optics-based entanglement concentration protocols for cluster-type entangled coherent state

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. The necessary quantum circuits enabling future experimental realizations of the proposed ECPs are provided using linear optical elements. Further, the benefit of the proposed schemes is established in the context of long-distance quantum communication where photon loss is an obstruction.

Superposition of Entangled Coherent States: Physical Realization and Properties

Continuous variable entangled states and especially entangled coherent states have attracted increasing interest in the Geld of quantum information processing. The characteristic features of the superposition of quantum states can be found in the literature. Because of these significant findings, we introduce and investigate a special superposition of multipartite entangled coherent states. We prove that the free-traveling optical field scheme can generate such a superposed state. Using a geometric measure of entanglement, we then investigate the correlation behavior of the superposed state.

Toward a quantum repeater protocol based on the coherent state approach

The aim of this paper is to swap the entanglement between two separate long-distant locations. The well-known entangled coherent states as two-mode continuous-variable states are very interesting in quantum teleportation and entanglement swapping processes. To make our investigation more realistic, by using such entangled states as the building blocks of our quantum repeater protocol, the effect of decoherence on the swapped entanglement is also considered. We explicitly establish our model for four locations; moreover, we find that our model can be extended to 2N locations, where . Consequently, we can introduce this model as a quantum repeater, which is helpful for entanglement swapping to long-enough distances.

Entanglement of a new type of two-mode photon-added entangled coherent state

ABSTRACTWe introduce a new entangled state, which is composed of two photon-added coherent states. We discuss the entanglement of this state by using several sufficient entanglement criteria, such as higher-order entanglement criterion, EPR criterion, SU(1,1) algebra and Cauchy–Schwarz inequality. These criteria reflect some entanglement effects of this new state, but fail to find the degree of entanglement directly. Thus, we use the covariance to measure the entanglement in this state. Our findings show that the degree of entanglement decreases with the increasing of photon-number and the amplitude of the coherent states. One interesting result is that the new entangled state becomes a maximally entangled state when the photon-added number is 1 and the amplitude of the coherent states is zero, which is just one of the four Bell states.

Entangled coherent states created by mixing squeezed vacuum and coherent light

Entangled coherent states are shown to emerge, with high fidelity, when mixing coherent and squeezed vacuum states of light on a beam-splitter. These maximally entangled states, where photons bunch at the exit of a beamsplitter, are measured experimentally by Fock-state projections. Entanglement is examined theoretically using a Bell-type nonlocality test and compared with ideal entangled coherent states. We experimentally show nearly perfect similarity with entangled coherent states for an optimal ratio of coherent and squeezed vacuum light. In our scheme, entangled coherent states are generated deterministically with small amplitudes, which could be beneficial, for example, in deterministic distribution of entanglement over long distances.

One-Mode Wigner Quasi-Probability Distribution Function for Entangled Coherent States Generated by Beam Splitter and Cavity QED

In this paper, we use the displacement operator together with parity operation to construct the superposition of two coherent states. By transmitting this superposition from 50–50 beam splitter the two-mode qubit-like entangled coherent state (ECS) is generated. Moreover, we introduce a controllable method for producing qutrit-like ECS using atom–field interaction in cavity QED and beam splitter. We will show that the distances of peaks of Wigner functions for reduced density matrices of two-mode ECS's are entanglement sensitive and can be witnesses of entanglement. To confirm the results we use concurrence measure to compare bipartite entanglement of ECS's with the behaviour of peaks of Wigner functions. Moreover, we investigate decoherence effects on Wigner function, arising from transmitting ECS's through noisy channels.

Controlled Entanglement Diversion Using GHZ Type Entangled Coherent State

We propose a scheme of controlled entanglement diversion of a bi-partite entangled coherent state using GHZ type entangled coherent state as a resource. The scheme involves only linear optical devices such as phase shifters, beam splitters and photon counters. Average fidelity of diversion is calculated and plotted. It is 2/3 for very small coherent amplitudes and approaches unity for appreciable coherent amplitude.

Generation of superposition coherent states of microwave fields via dissipation of a superconducting qubit with broken inversion symmetry

We present an efficient approach for dissipative generation of quantum superposition states in the microwave resonator, which is coupled to a superconducting qubit. We investigate the situation where the inversion symmetry of potential energy of the qubit is broken, and the strong two-photon nonlinear coupling between qubit and resonator can be realized via the transverse and longitudinal couplings. According to the two-photon dissipation and driving process, the dissipation of a qubit can be utilized to steer the microwave field into a quantum superposition of distinct coherent states, i.e., the Schr\odinger cat state. In addition, we also extend the method to produce an entangled coherent state of two spatially separated resonators. Our scheme is based on quantum reservoir engineering and turns detrimental noise into a resource, which makes it feasible in experimental implementation. The present result may have potential applications in the field of quantum information processing with circuit QED systems.

Quantum Discord for Information Transmission Using Coherent States

We suggest theoretically the possibility to transmit information through a decohering quantum channel employing Glauber’s coherent states. In fact, we study the dynamics of quantum correlations of two-mode entangled bipartite coherent states in the presence of the amplitude damping effect. In addition, we examine the quantum correlations based on quantum discord, which is a powerful key source in quantum information processing.

Influence of atmospheric scintillation on entangled coherent states quantum interferometric radar

Much interest has been aroused in quantum metrology such as quantum interferometric radar, due to its application in sub-Raleigh ranging and remote sensing. Generally, the quantum signal emitted by quantum radar will be affected by atmosphere medium. For instance, both atmospheric loss and atmospheric scintillation seriously affect the sensitivity and resolution of quantum radar. In fact, the effects of atmospheric loss on the sensitivity and resolution of quantum interferometric radar have been investigated thoroughly and completely in the past decades. However, the investigation about the influence of atmospheric scintillation is lacking until now. To realize practical quantum interferometric radar, the perturbation coming from turbulent atmosphere must be considered, thus it is necessary to investigate how the atmospheric scintillation affects the performance of quantum radar.In this paper, the influence of intensity fluctuation which is caused by atmospheric scintillation on the performance of quantum interferometric radar with entangled coherent states (ECS) is thoroughly investigated. We first introduce the physical model of quantum interferometric radar, and the dynamic evolution of quantum light field in atmosphere is obtained by solving the master equation of dissipation channel. Considering the dissipation and fluctuation caused by atmospheric scintillation, we regard the turbulent atmosphere as so-called dissipation-fluctuation channel. Moreover, according to classical statistical theory of turbulence, we derive the explicit expression of probability distribution of transmission coefficient P(T), this probability distribution of transmission cofficient, which is determined by average transmission coefficient TD and scintillation index βD2 plays a crucial role in the studying of atmospheric scintillation.The results of investigation show that atmospheric scintillation leads to the degradation of the sensitivity and resolution of ECS quantum interferometric radar at lower atmospheric loss. Under the higher lossy condition of atmosphere, atmospheric scintillation can greatly enhance the performance of quantum interferometric radar. Furthermore, the critical atmospheric transmission coefficient which determines the lower and higher loss of atmosphere keeps increasing with the increase of average photon number per pulse. Increasing the atmospheric scintillation, rather than introducing noise and degrading the performance of quantum radar, can improve the sensitivity and resolution.This anomalous phenomenon can be explained only by quantum decoherence theory. As is well known, the supersensitivity and super-resolution of quantum radar are based on the nonlocal characteristic of quantum light field, while the dissipation process will induce decoherence that leads to the loss of nonlocal characteristic, and finally degrades the performance of quantum radar. However, there have been several researches indicating that the dissipation-fluctuation channel can alleviate the decoherence effect and maintain the nonlocal characteristic of quantum light field compared with pure dissipation channel. For the evolution of quantum light field in dissipation medium, the loss of amplitude plays a crucial role at a lower loss, while the decoherence will play a dominant role at a higher loss. Consequently, the fluctuation may induce extra noise and degrade the performance of quantum radar at lower loss. For higher loss, the fluctuation can prevent the decoherence process and maintain the quantum characteristic of light field, thus the atmospheric scintillation finally improves the sensitivity and resolution of quantum radar.