Enhancing entanglement of entangled coherent states by single-mode coherent superposition of photon subtraction and addition

We introduce a new entangled quantum state generated by applying single-mode coherent superposition of photon subtraction and addition (a^† cos θ + a sin θ)^m to the entangled coherent state |Ψ_±(α,0)〉$|{\Psi }_{\pm }\left(\alpha ,0\right)〉$, and then investigate the entanglement properties affected by coherent superposition operation. It is shown that this operation can be applied to enhance the entanglement of the state |Ψ₊(α,0)〉$|{\Psi }_{+}\left(\alpha ,0\right)〉$. In addition, the effects of the coherent operation is better to improve the entanglement than that of the creation operation (a^†m) for |Ψ₊(α,0)〉$|{\Psi }_{+}\left(\alpha ,0\right)〉$ in a small-amplitude regime and for |Ψ₋(α,0)〉$|{\Psi }_{-}\left(\alpha ,0\right)〉$ in any regime.     

The entanglement properties of non-Gaussian states prepared by photon subtraction from two-mode squeezed thermal states

We analyze the entanglement condition of a new kind of non-Gaussian quantum state, which is prepared by photon number subtraction from the two mode squeezed thermal state. Fock space criterion and Shchukin-Vogel criterion are applied, and they give the same condition which is also that of the input state.     

Gaussian entanglement of symmetric two-mode Gaussian states

A Gaussian degree of entanglement for a symmetric two-mode Gaussian state can be defined as its distance to the set of all separable two-mode Gaussian states. The principal property that enables us to evaluate both Bures distance and relative entropy between symmetric two-mode Gaussian states is the diagonalization of their covariance matrices under the same beam-splitter transformation. The multiplicativity property of the Uhlmann fidelity and the additivity of the relative entropy allow one to finally deal with a single-mode optimization problem in both cases. We find that only the Bures-distance Gaussian entanglement is consistent with the exact entanglement of formation.     

Measurement-based entanglement purification for entangled coherent states

The entangled coherent states (ECSs) have been widely used to realize quantum information processing tasks. However, the ECSs may suffer from photon loss and decoherence due to the inherent noise in quantum channel, which may degrade the fidelity of ECSs. To overcome these obstacles, we present a measurement-based entanglement purification protocol (MBEPP) for ECSs to distill some highquality ECSs from a large number of low-quality copies. We first show the principle of this MBEPP without considering the photon loss. After that, we prove that this MBEPP is feasible to correct the error resulted from the photon loss. Additionally, this MBEPP only requires to operate the Bell state measurement without performing local two-qubit gates on the noisy pairs and the purified high-quality ECSs can be preserved for other applications. This MBEPP may have application potential in the implementation of long-distance quantum communication.     

Two-mode excited entangled coherent states and their entanglement properties

This paper introduces two types of two-mode excited entangled coherent states (TMEECSs) |Ψ_±(α,m,n)>, studies their entanglement characteristics, and investigates the influence of photon excitations on quantum entanglement. It shows that for the state |Ψ₊(α,m,m)> the two-mode photon excitations affect seriously entanglement character while the state |Ψ_-(α,m,m)> is always a maximally entangled state, and shows how such states can be produced by using cavity quantum electrodynamics and quantum measurements. It finds that the entanglement amount of the TMEECSs is larger than that of the single-mode excited entangled coherent states with the same photon excitation number.     

Mode transformations and entanglement relativity in bipartite Gaussian states

A proper choice of subsystems for a system of identical particles e.g., bosons, is provided by second-quantized modes, i.e., creation/annihilation operators. Here we investigate how the entanglement properties of bipartite Gaussian states of bosons change when modes are changed by means of unitary, number conserving, Bogoliubov transformations. This set of “virtual” bipartitions is then finite-dimensionally parametrized and one can quantitatively address relevant questions such as the determination of the minimal and maximal available entanglement. In particular, we show that in the class of bipartite Gaussian states there are states which remain separable for every possible modes redefinition, while do not exist states which remain entangled for every possible modes redefinition.     

Spin squeezing and entanglement via hole-burning in atomic coherent states

We study the generation of spin squeezing via the hole burning of selected Dicke states out of an atomic coherent state prepared for a collection of N two-level atoms or ions. The atoms or ions of the atomic coherent state are not entangled, but the removal of one or more Dicke states generates entanglement, and spin squeezing occurs for some ranges of the relevant parameters. Spin squeezing in a collection of two-level atoms or ions is of importance for precision spectroscopy.     

Quantum Fisher information flow and entanglement in pair coherent states

Realistic quantum systems are the main part of quantum information technology, which causes the rapid destruction of crucial quantum properties. Therefore, the unavoidable interaction between quantum systems, understanding the dynamics of entanglement indicators and finding the correlation between different phenomena may stimulate great interest. In this article the quantum Fisher information and nonlocal correlation between a single qubit and two-mode optical field initially in pair coherent states have investigated. We examine the impact of the qubit motion and intensity dependent function on the flow of quantum Fisher information and quantum entanglement during the time evolution. We discuss the relationship between quantum Fisher information flow and quantum entanglement in the case of moving and unmoving single qubit.     

De-Gaussification by inconclusive photon subtraction

We address conditional de-Gaussiflcation of continuous variable states by inconclusive photon subtraction (IPS) and review in detail its application to the bipartite twin-beam state of radiation. The IPS map in the Fock basis and counterpart in the phase space have been derived. Teleportation assisted by IPS states is analyzed, and the corresponding fidelity is evaluated as a function of the involved parameters. Nonlocality of IPS states is investigated by means of different tests, including displaced parity, homodyne detection, pseudospin, and displaced on/off photodetection. Dissipation and thermal noise and nonunit quantum efficiency are taken into account in the detection stage. We show that the IPS process, for a suitable choice of the involved parameters, improves teleportation fidelity and enhances nonlocal properties.     

Nonclassicality and decoherence of coherent superposition operation of photon subtraction and photon addition on squeezed state

The statistical properties of m-coherent superposition operation (μa+νa⁺)^m on the single-mode squeezed vacuum state (M-SSVS) and its decoherence in a thermal environment have been studied. Converting the M-SSVS to a squeezed Hermite polynomial excitation state, we obtain a compact expression for the normalization factor of M-SSVS, which is the Legendre polynomial of the squeezing parameter. We also derive the explicit expression of Wigner function (WF) of M-SSVS, and find the negative region of WF in phase space. The decoherence effect on this state is then discussed by deriving the time evolution of the WF. Using the negativity of WF, the loss of nonclassicality has been discussed.     

Generic entanglement and standard form for N-mode pure Gaussian states

We investigate the correlation structure of pure N-mode Gaussian resources which can be experimentally generated by means of squeezers and beam splitters, whose entanglement properties are generic. We show that those states are specified (up to local unitaries) by N(N-1)/2 parameters, corresponding to the two-point correlations between any pair of modes. Our construction yields a practical scheme to engineer such generic-entangled N-mode pure Gaussian states by linear optics. We discuss our findings in the framework of Gaussian matrix product states of harmonic lattices, raising connections with entanglement frustration and the entropic area law.     

Quantum entanglement and nonlocality properties of two-mode Gaussian squeezed states

Quantum entanglement and nonlocality properties of a family of two-mode Gaussian pure states have been investigated. The results show that the entanglement of these states is determined by both the two-mode squeezing parameter and the difference of the two single-mode squeezing parameters. For the same two-mode squeezing parameter, these states show larger entanglement than the usual two-mode squeezed vacuum state. The violation of Bell inequality depends strongly on all the squeezing parameters of these states and disappears completely in the limit of large squeezing. In particular, these states can exhibit much stronger violation of local realism than two-mode squeezed vacuum state in the range of experimentally available squeezing values.     

Optical implementation and entanglement distribution in Gaussian valence bond states

We study Gaussian valence bond states of continuous variable systems obtained as the outputs of projection operations from an ancillary space of M infinitely entangled bonds connecting neighboring sites applied at each ofN sites of a harmonic chain. The entanglement distribution in Gaussian valence bond states can be controlled by varying the input amount of entanglement engineered in a (2M+ 1)-mode Gaussian state known as the building block, which is isomorphic to the projector applied at a given site. We show how this mechanism can be interpreted in terms of multiple entanglement swapping from the chain of ancillary bonds, through the building blocks. We provide optical schemes to produce bisymmetric three-mode Gaussian building blocks (which correspond to a single bond, M = 1), and study the entanglement structure in the output Gaussian valence bond states. Finally, the usefulness of such states for quantum communication protocols with continuous variables, like telecloning and teleportation networks, is discussed. The text was submitted by the authors in English.     

Relative entropy as a measure of entanglement for Gaussian states

In this paper, we derive an explicit analytic expression of the relative entropy between two general Gaussian states. In the restriction of the set for Gaussian states and with the help of relative entropy formula and Peres--Simon separability criterion, one can conveniently obtain the relative entropy entanglement for Gaussian states. As an example, the relative entanglement for a two-mode squeezed thermal state has been obtained.     

Maximal entanglement from photon-added nonlinear coherent states via unitary beam splitters

In this paper, we construct photon-added f-deformed coherent states （PAf-DCSs） for nonlinear bosonic fields by discussing Klauder＇s minimal set of conditions required to obtain coherent states. Using this set of nonlinear states, we propose a very useful scheme for generating the maximal amount of entanglement via unitary beam splitters for different strength regimes of the input field α, deformation q and excitation number m. Therefore, the possibility to create highly entangled states and to control the entanglement is proposed. Moreover, the condition for a maximal and separable output beam state is obtained. Finally, we examine the statistical properties of the PAf-DCSs through the Mandel parameter and exploit a connection between this quantity and the behavior variation of the output state entanglement. Our result may open new perspectives in different tasks of quantum information processing.     

Quantum dual signature scheme based on coherent states with entanglement swapping

A novel quantum dual signature scheme, which combines two signed messages expected to be sent to two diverse receivers Bob and Charlie, is designed by applying entanglement swapping with coherent states. The signatory Alice signs two different messages with unitary operations(corresponding to the secret keys) and applies entanglement swapping to generate a quantum dual signature. The dual signature is firstly sent to the verifier Bob who extracts and verifies the signature of one message and transmits the rest of the dual signature to the verifier Charlie who verifies the signature of the other message. The transmission of the dual signature is realized with quantum teleportation of coherent states. The analysis shows that the security of secret keys and the security criteria of the signature protocol can be greatly guaranteed.An extensional multi-party quantum dual signature scheme which considers the case with more than three participants is also proposed in this paper and this scheme can remain secure. The proposed schemes are completely suited for the quantum communication network including multiple participants and can be applied to the e-commerce system which requires a secure payment among the customer, business and bank.     

How to measure squeezing and entanglement of Gaussian states without homodyning

We propose a scheme for measuring the squeezing, purity, and entanglement of Gaussian states of light that does not require homodyne detection. The suggested setup needs only beam splitters and single-photon detectors. Two-mode entanglement can be detected from coincidences between photodetectors placed on the two beams.