Continuous-Variable Quantum Teleportation of Entangled Coherent States

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.

A scheme of teleporting a superposition of coherent states |α⟩ and | − α⟩ using a beam splitter and two phase shifters was proposed by van Enk and Hirota (2001 Phys. Rev. A 64 022313). The authors concluded that the probability for successful teleportation is 1/2. In this paper, it is shown that the authors' scheme can be altered slightly so as to obtain an almost perfect teleportation for an appreciable value of |α|2. For |α|2 = 5, the minimum of average fidelity, which is the minimum of the sum of the product of probability of occurrence of any case, and the corresponding fidelity is less than 1 by a quantity ∼10−4. We also discuss the effect of decoherence on teleportation fidelity. We find that if no photons are counted in both final outputs, the minimum assured fidelity is still non-zero except when there is no decoherence and the information is an even coherent state. For non-zero photon counts, minimum assured fidelity decreases with an increase in |α|2 for low noise. For high noise, however, it increases, attains a maximum value and then decreases with |α|2. The average fidelity depends appreciably on the information for low values of |α|2 only.

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 quantum teleportation as it gives the optimal fidelity of teleportation less than the classical limit 2/3.

Based on the coherent entangled state |α,x⟩ we introduce the squeezed entangled state (SES). Then wepropose a teleportation protocol for the SES by usingEinstein–Podolsky–Rosen entangled state |η⟩as a quantum channel. The calculation is greatly simplified by virtue of theSchmidt decompositions of both |α,x⟩ and|η⟩. Any bipartite states that can be expandedin terms of |α,x⟩ may be teleported in thisway due to the completeness of |α,x⟩.

In this paper, we propose an optical scheme to almost completely teleport a two-mode four-component entangled coherent state in terms of optical devices such as nonlinear Kerr media, beam splitters, phase shifters and photon detectors. Different from those previous schemes in which exact photon number discrimination is needed, in our scheme one only needs to make ‘yes’ and ‘no’ measurements upon the photon numbers in related modes. This scheme can also be understood as an entanglement swapping protocol.

We propose photonic schemes for the distribution and reconstruction of a two-qubit entangled state using a hybrid entangled state under a noisy quantum channel. First, to generate a hybrid entangled state correlated with polarizations and time-bins, we employ a quantum dot (QD)-cavity system (nonlinear optical gate) and linear optical devices to implement controlled operation. These schemes can achieve the distribution and reconstruction of a two-qubit entangled state from hybrid entanglement by utilizing only linear optical devices without a QD-cavity system (i.e., a nonlinear optical device) for users who want to share an entangled state under a noisy quantum channel. For a feasible realization of the proposed schemes, we analyze the interaction between the photons and QD-cavity system and demonstrate the experimental conditions under which the reliable performance of the QD-cavity system is achieved.

In this paper, we propose an optical scheme to generate four-mode W-type entangled coherent states (ECSs) in free travelling optical fields by using a single-photon source, coherent state sources, beam splitters, photodetectors and cross-Kerr media. Our scheme consists of a symmetric optical setup in which there are two Mach–Zehnder interferometers in which each arm contains a cross-Kerr medium. We calculate the average fidelity of generated W-type ECSs, the success probability of producing four-mode W-type ECSs and the average fidelity of the generated four-mode W-type ECSs. It is indicated that our protocol is nearly deterministic.

New approach to the fidelity of quantum teleportation based on the entangled state generated by beam splitter

The quantum correlations between the output signal, the output idler and the reflected pump fields generated by non-degenerate optical parametric oscillator operating above the oscillation threshold are theoretically calculated with the semi-classical formulae. According to the multipartite entanglement criteria for the continuous variables, proposed by P. van Loock and A. Furusawa, the calculated results prove the existence of the quantum correlations between the amplitude and the phase quadrature for the three optical fields, i. e. they form a tripartite entangled state. We numerically calculate the dependence of the entanglement on the physical parameters of the optical oscillator and find the optimum operating conditions of the oscillator to produce the three-color tripartite entangled state, which provide the direct references for the design of the continuous variable multipartite entanglement generation systems.

We analyze entanglement properties of entangled coherent state (ECS), |α, 0〉1,2 + |0, α〉1,2, with and without photon losses. By separating the coherent state into , we derive exact results of the logarithmic negativity EN, which quantifies the degree of entanglement between the two bosonic modes. Without particle losses, EN = 1 for the N00N state; while for the ECS, EN increases from 0 to 1 as |α|2 → ∞. In the presence of photon losses, we find that the ECS with large enough photon number is more robust than that of the N00N state. An optimal ECS is obtained by maximizing EN with respect to |α|2.

Universal multiport interferometers that can be programmed to perform any unitary or linear transformation turn into an important building block for both classical and quantum photonics. These interferometers typically utilize the mathematical framework of U(2) unitary matrix decomposition techniques and comprise a mesh of 2 × 2 beam splitters and phase shifters. All of them are, however, inherently fidelity limited as their U(2)‐based deployment approach leads to imbalanced path losses without supporting any fidelity restoration mechanism. Herein, a novel Universal Generalized Mach–Zehnder Interferometer (UGMZI) architecture is presented that migrates from U(2) decomposition techniques and adopts a recursive U(N) decomposition, exploiting cascaded size‐augmenting N N beam splitters and phase shifters. The design can natively support fidelity restoration and safeguard absolute fidelity, while outperforming the state‐of‐the‐art designs also with respect to phase‐error‐induced fidelity performance properties. Finally, it is demonstrated that its fidelity restoration properties turn the design into the optimal architecture for constructing any real/complex‐valued matrix via the singular value decomposition (SVD) scheme.

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.

We propose a scheme for generation of three-mode W-type entangled coherent states (ECSs) in free-travelling optical fields by using a single-photon source, coherent state sources, beam splitters, photodetectors, and three-mode cross-Kerr media. The scheme consists of a Mach-Zehnder interferometer (MZI) in which each arm contains a cross-Kerr medium. We calculate the success probability of the generated W-type ECSs, and the total success probability is unity under the ideal conditions.

A new bipartite coherent-entangled state is introduced in the two-mode Fock space, which exhibits the properties of both a coherent state and an entangled state. The set of coherent-entangled states makes up a complete and partly nonorthogonal representation. A simple experimental scheme to produce the coherent-entangled state using an asymmetric beamsplitter is proposed. Some applications of the coherent-entangled state in quantum optics are also presented.

We demonstrate that two independent spin-1/2 Ising-Heisenberg trimer chains provide an effective platform for the quantum teleportation of any entangled two-qubit state through the quantum communication channel formed by two Heisenberg dimers. The reliability of this quantum channel is assessed by comparing the concurrences, which quantify a strength of the bipartite entanglement of the initial input state and the readout output state. Additionally, we rigorously calculate quantities fidelity and average fidelity to evaluate the quality of the teleportation protocol depending on temperature and magnetic field. It is evidenced that the efficiency of quantum teleportation of arbitrary entangled two-qubit state through this quantum communication channel can be significantly enhanced by moderate magnetic fields. This enhancement can be attributed to the magnetic-fielddriven transition from a quantum antiferromagnetic phase to a quantum ferrimagnetic phase, which supports realization of a fully entangled quantum channel suitable for efficient quantum teleportation. The polymeric trimer chains Cu3(P2O6OH)2 are proposed as an experimental resource of this quantum communication channel, which provides an efficient platform for realization of the quantum teleportation up to moderate temperatures 40 K and extremely high magnetic fields 80 T.