We consider quantum systems, whose dynamical symmetry groups are semisimple Lie groups, which can be split or decay into two subsystems of the same symmetry. We prove that the only states of such a system that factorize upon splitting are the generalized coherent states. Since Bell's inequality is never violated by the direct product state, when the system prepared in the generalized coherent state is split, no quantum correlations are created. Therefore, the generalized coherent states are the unique Bell states, i.e., the pure quantum states preserving the fundamental classical property of satisfying Bell's inequality upon splitting.
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.
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 …
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…
Non-classical states of light field have been exploited to provide marvellous results in quantum information science. Effectiveness of nonclassical states depends on whether physical parameter as signal is continuous or digital. Here we present an investigation on the potential of quasi Bell state of entangled coherent states in quantum reading of the classical digital memory which was pioneered by Pirandola. This is a typical example of discrete quantum discrimination. We show that the quasi Bell state gives the error free performance in the quantum reading that cannot be obtained by any clas…
We study Bell inequality tests with entanglement between a coherent-state field in a cavity and a two-level atom. In order to detect the cavity field for such a test, photon on/off measurements and photon number parity measurements, respectively, are investigated. When photon on/off measurements are used, at least 50% of detec- tion efficiency is required to demonstrate violation of the Bell inequality. Photon number parity measurements for the cavity field can be effectively performed using ancillary atoms and an atomic detector, which leads to large degrees of Bell violations up to Cirel'son…
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.
Bell state analyzer (BSA) is one of the most crucial apparatus in photonic quantum information processing. While linear optics provide a practical way to implement BSA, it provides unavoidable errors when inputs are not ideal single-photon states. Here, we propose a simple method to deduce the BSA for single-photon inputs using weak coherent pulses. By applying the method to Reference-Frame-Independent Measurement-Device-Independent Quantum Key Distribution, we experimentally verify the feasibility and effectiveness of the method.
The Bell basis, a set of maximally entangled biphoton state, is a critical prerequisite towards quantum information processing, and many quantum applications have highlighted the requirement for the manipulation of high-dimensional Bell basis. While the Bell states can be created by using ingenious single-photon quantum gates, its implementation complexity in higher dimensions is significantly increased. Here we present an elaborate approach to show that the adaptive pump modulation enable the efficient preparation of Bell basis in arbitrary-dimensional Hilbert space. A complete set of four-di…
We analyze effects of squeezing upon superpositions of coherent states (SCSs) and entangled coherent states (ECSs) for Bell-inequality tests. We find that external squeezing can always increase the degrees of Bell violations, if the squeezing direction is properly chosen, for the case of photon parity measurements. On the other hand, when photon on/off measurements are used, the squeezing operation can enhance the degree of Bell violations only for moderate values of amplitudes and squeezing. We point out that a significant improvement is required over currently available squeezed SCSs in orde…
We introduce a complete Bell measurement on atomic qubits based on two photon interactions with optical cavities and discrimination of coherent states of light. The dynamical system is described by the Dicke model for two three-level atoms interacting in two-photon resonance with a single-mode of the radiation field, which is known to effectively generate a non-linear two-photon interaction between the field and two states of each atom. For initial coherent states with large mean photon number, the field state is well represented by two coherent states at half revival time. For certain product…
The coherent-state qubit is a promising candidate for optical quantum information processing due to its nearly-deterministic nature of the Bell-state measurement (BSM). However, its non-orthogonality incurs difficulties such as failure of the BSM. One may use a large amplitude ($α$) for the coherent state to minimize the failure probability, but the qubit then becomes more vulnerable to dephasing by photon loss. We propose a hardware-efficient concatenated BSM (CBSM) scheme with modified parity encoding using coherent states with reasonably small amplitudes ($|α| \lessapprox 2$), which simulta…
A method for performing nonlocal interferometry using phase-entangled macroscopic coherent states is described. The required entanglement can be generated using weak nonlinearities while Bell's inequality can be violated using single photons as a probe. The entanglement is relatively robust against photon loss and Bell's inequality can be violated over a relatively large distance in optical fibers despite the fact that a large number of photons are absorbed in the process.
We present exact analytic formulae which describe the interaction of multistate quantum systems possessing the Majorana and Morris-Shore dynamic symmetries with a train of pulses. The pulse train field can be viewed as repeated interactions of the quantum system with the same field and hence the overall propagator is expressed as the matrix power of the single-pulse propagator. Because of the Majorana and Morris-Shore symmetries the multistate dynamics is characterised by intrinsic two-state features, described by one or more pairs of complex-valued Cayley-Klein parameters. This facilitates th…
In the present article, based on the formalism introduced in [Loubenets, J. Math. Phys. 53, 022201 (2012)], we derive for a pure bipartite quantum state a new upper bound on its maximal violation of general Bell inequalities. This new bound indicates that, for an infinite dimensional pure bipartite state with a finite sum of its Schmidt coefficients, violation of any general Bell inequality is bounded from above by the value independent on a number of settings and a type of outcomes, continuous or discrete, specific to this Bell inequality. As an example, we apply our new general results to sp…
Protocols for probabilistic entanglement-assisted quantum teleportation and for entanglement swapping of material qubits are presented. They are based on a protocol for postselective Bell-state projection which is capable of projecting two material qubits onto a Bell state with the help of ancillary coherent multiphoton states and postselection by balanced homodyne photodetection. Provided this photonic postselection is successful we explore the theoretical possibilities of realizing unit fidelity quantum teleportation and entanglement swapping with $25\%$ success probability. This photon-assi…
Nonlocality, as demonstrated by the violation of Bell inequalities, enables device-independent cryptographic tasks that do not require users to trust their apparatus. In this article, we consider devices whose inputs are spatiotemporal degrees of freedom, e.g. orientations or time durations. Without assuming the validity of quantum theory, we prove that the devices' statistical response must respect their input's symmetries, with profound foundational and technological implications. We exactly characterize the bipartite binary quantum correlations in terms of local symmetries, indicating a fun…
The non-local correlations exhibited when measuring entangled particles can be used to certify the presence of genuine randomness in Bell experiments. While non-locality is necessary for randomness certification, it is unclear when and why non-locality certifies maximal randomness. We provide here a simple argument to certify the presence of maximal local and global randomness based on symmetries of a Bell inequality and the existence of a unique quantum probability distribution that maximally violates it. Using our findings, we prove the existence of N-party Bell test attaining maximal global…
In two recent papers (Phys. Rev. A90 (2014), 062121 and Phys. Rev. A91 (2015), 052110) an interesting method of analyzing the violation of Bell inequalities has been proposed which is based on the theory of finite group representations. We apply here this method to more complicated example of $S_4$ symmetry. We show how the Bell inequality can be related to the symmetries of regular tetrahedron. By choosing the orbits of threedimensional representation of $S_4$ determined by the geometry of tetrahedron we find that the Bell inequality under consideration is violated in quantum theory. The corr…
Quantum superpositions of coherent states are produced both in microwave and optical domains, and are considered realizations of the famous "Schrödinger cat" state. The recent progress shows an increase in the number of components and the number of modes involved. Our work creates a theoretical framework for treatment of multicomponent two-mode Schrödinger cat states. We consider a class of single-mode states, which are superpositions of $N$ coherent states lying on a circle in the phase space. In this class we consider an orthonormal basis created by rotationally-invariant circular states (RI…
The polarization properties of macroscopic Bell states are characterized using three-dimensional quantum polarization tomography. This method utilizes three-dimensional inverse Radon transform to reconstruct the polarization quasiprobability distribution function of a state from the probability distributions measured for various Stokes observables. The reconstructed 3D distributions obtained for the macroscopic Bell states are compared with those obtained for a coherent state with the same mean photon number. The results demonstrate squeezing in one or more Stokes observables.
Spin-exchange collisions in hot vapours are generally regarded as a decoherence mechanism. In contrast, we show that linear and non-linear spin-exchange coupling can lead to the generation of atomic coherence in a Bell-Bloom magnetometer. In particular, we theoretically and experimentally demonstrate that non-linear spin exchange coupling, acting in an analogous way to a wave-mixing mechanism, can create new modes of coherent excitation which inherit the magnetic properties of the natural Larmor coherence. The generated coherences further couple via linear spin-exchange interaction, leading to…
In this paper we present a study of the quantum phase estimation problem employing continuous-variable, entangled squeezed coherent (quasi-Bell) states as probe states. We show that their inherent squeezing and entanglement properties might bring advantages, increasing the precision of phase estimation compared to protocols which employ other continuous variable states e.g., two-mode, entangled coherent states or single-mode, squeezed states. We also analyze the phase estimation process considering: i) a linear (unitary) perturbation, and ii) dissipation, and conclude that the use of entangled…
We suggest implementation of quantum teleportation protocol of unknown qubit beyond Bell states formalism. Hybrid entangled state composed of coherent components that belong to Alice and dual-rail single photon at Bob disposal is used. Nonlinear effect on the teleported state is realized due to peculiarity of interaction of coherent components with discrete variable state on a beam splitter. Bob performs unitary transformation after receiving the appropriate classical information. The protocol is nearly deterministic but the output state is subject to amplitude distortion which reduces the fid…
The characteristics of nonstatic quantum light waves in the coherent state in a static environment is investigated. It is shown that the shape of the wave varies periodically as a manifestation of its peculiar properties of nonstaticity like the case of the Fock-state analysis for a nonstatic wave. A belly occurs in the graphic of wave evolution whenever the wave is maximally displaced in the quadrature space, whereas a node takes place every time the wave passes the equilibrium point during its oscillation. In this way, a belly and a node appear in turn successively. Whereas this change of wa…
We present a detailed analysis of the Bell measurement scheme proposed in [Phys. Rev. Lett. 114, 113603 (2015)] based on a logical qubit using Greenberger-Horne-Zeilinger (GHZ) entanglement of photons. The success probability of the proposed Bell measurement can be made arbitrarily high using only linear optics as the number of photons in a logical qubit increases. We compare our scheme with all the other proposals, using single-photon qubits, coherent-state qubits or hybrid qubits, suggested to enhance the efficiency of the Bell measurement. As a remarkable advantage, our scheme requires only…
Coherent control of reactive atomic and molecular collision processes remains elusive experimentally due to quantum interference-based requirements. Here, with insights from symmetry conditions, a viable method for controlling Penning and Associative ionization in atomic collisions is proposed. Computational applications to He$^*({}^3\text{S})$-Li(${^2\text{S}}$) and Ne$^*{}(^3\text{P}_2$)-Ar($^1\text{S}_0$) show extensive control over the ionization processes under experimentally feasible conditions.
A model of dynamics of quantum correlations of two modes quasi-Bell cat states, based on Glauber coherent states, is considered. The analytic expressions of pairwise entanglement of formation, quantum discord and its geometrized variant are explicitly derived. We analyze the distribution of quantum correlations between the two modes and the environment. We show that, in contrast with squared concurrence, entanglement of formation, quantum discord and geometric quantum discord do not follow the property of monogamy except in some particular situations that we discuss.
We show that the use of probabilistic noiseless amplification in entangled coherent state-based schemes for the test of quantum non locality provides substantial advantages. The threshold amplitude to falsify a Bell-CHSH non locality test, in fact, is significantly reduced when amplification is embedded into the test itself. Such a beneficial effect holds also in the presence of detection-inefficiency. Our study helps in affirming noiseless amplification as a valuable tool for coherent information processing and the generation of strongly non classical states of bosonic systems.
Several families of states such as Werner states, Bell-diagonal states and Dicke states are useful to understand multipartite entanglement. Here we present a [2^(N+1)-1]-parameter family of N-qubit "X states" that embrace all those families, generalizing previously defined states for two qubits. We also present the algebra of the operators that characterize the states and an iterative construction for this algebra, a sub-algebra of su(2^(N)). We show how a variety of entanglement witnesses can detect entanglement in such states. Connections are also made to structures in projective geometry.
We consider a multiphoton Bell-type inequality to study nonlocality in four-mode continuous variable systems, which goes beyond two-photon states and can be applied to mixed as well as states with fluctuating photon number. We apply the inequality to a wide variety of states such as pure and mixed Gaussian states (including squeezed thermal states) and non-Gaussian states. We consider beam splitters as a model for leakage and show that the inequality is able to detect nonclassicality of noisy Gaussian states as well. Finally, we investigate nonlocality in pair-coherent states and entangled coh…
