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Entanglement Dynamics of Photon-Added Quasi-Bell Coherent States

Mounaim Hamdoune, Mohammed Daoud A

Published Aug 26, 2025• 0 citations
Publisher

Abstract

Abstract Photon-added coherent states (PACS) represent a critical bridge between classical coherent states and quantum Fock states, exhibiting non-classical properties such as squeezing and sub-Poissonian statistics. In this work, we investigate the entanglement properties of quasi-Bell states constructed from photon-added coherent states, with a focus on the concurrence and entanglement of formation under varying photon excitation numbers m and coherent state amplitudes |α|. By leveraging the mathematical framework of Glauber’s coherent states and Laguerre polynomial normalization, we derive analytical expressions for the overlap between |α, m⟩ and | − α, m⟩, and analyze their suitability for qubit encoding. Our results reveal that for |α| ≥ 2, these states approximate orthogonal logical qubits, while smaller amplitudes exhibit m-dependent entanglement degradation. Numerical simulations demonstrate that entanglement of formation E12 approaches unity for large |α|, independent of m, but diminishes with increasing m in the weak-field regime (|α|2 < 1.5). These findings advance the understanding of photon-added states in quantum information protocols, offering insights into decoherence mitigation and resource-efficient qubit design.

DOI
10.21203/rs.3.rs-7455579/v1

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Abstract Photon-added coherent states (PACS) represent a critical bridge between classical coherent states and quantum Fock states, exhibiting non-classical properties such as squeezing and sub-Poissonian statistics. In this work, we investigate the entanglement properties of quasi-Bell states constructed from photon-added coherent states, with a focus on the concurrence and entanglement of formation under varying photon excitation numbers m and coherent state amplitudes |α|. By leveraging the mathematical framework of Glauber’s coherent states and Laguerre polynomial normalization, we derive analytical expressions for the overlap between |α, m⟩ and | − α, m⟩, and analyze their suitability for qubit encoding. Our results reveal that for |α| ≥ 2, these states approximate orthogonal logical qubits, while smaller amplitudes exhibit m-dependent entanglement degradation. Numerical simulations demonstrate that entanglement of formation E12 approaches unity for large |α|, independent of m, but diminishes with increasing m in the weak-field regime (|α|2 < 1.5). These findings advance the understanding of photon-added states in quantum information protocols, offering insights into decoherence mitigation and resource-efficient qubit design.
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 introduce a class of the photon-added Bell-type entangled coherent states (PABECSs) obtained from Bell-type entangled coherent states by applying creation operators. We investigate their entanglement characteristics by analyzing the entropy of entanglement and discuss the influence of photon excitations on quantum entanglement. It is shown that applying a creation operator can increase the amount of entanglement. We also study the statistical properties of such states by discussing the behavior of the quasi-probability functions graphically. In addition, a possible scheme is presented to produce the PABECSs by using cavity quantum electrodynamics and quantum measurements.
We study the dynamical squeezing of the photon-added coherent state (PACS) due to a time dependence of the frequency of the electromagnetic field oscillator in a cavity or a vibrational frequency of an ion inside an electromagnetic trap. Explicit expressions for the time dependence of various functions characterizing the quantum state, such as the photon distribution, the Wigner function, the mean values and variances of the quadrature components and of the photon number, show that the dynamically squeezed PACS possesses a larger squeezing coefficient than the usual squeezed states. The dynamical squeezing is accompanied by a change of the sub-Poissonian photon statistics to the super-Poissonian one.
Quantum entanglement represents a fundamental resource for quantum information processing, yet the dynamics of multi-photon entangled systems remain inadequately characterized for practical quantum computing applications. This research investigates the generation, manipulation, and characterization of entangled states involving two to eight photons using spontaneous parametric down-conversion techniques. Through theoretical analysis and numerical simulations, we developed a comprehensive framework that quantifies entanglement fidelity, decoherence rates, and Bell inequality violations across various multi-photon configurations. Our findings reveal that entanglement fidelity decreases exponentially with increasing photon number, exhibiting a decay constant of 0.087±0.012 per additional qubit in optical systems. The research demonstrates significant variations in decoherence times across different physical implementations, with ion trap systems maintaining coherence 1.7 times longer than photonic platforms for equivalent qubit numbers. We established mathematical relationships between system parameters and entanglement quality metrics, identifying critical thresholds for fault-tolerant quantum gate operations. The theoretical framework incorporates realistic noise models, environmental coupling mechanisms, and measurement-induced perturbations that affect practical implementations. Our analysis indicates that five-photon entangled states maintain sufficient fidelity (>83.5%) for error-corrected quantum algorithms when decoherence times exceed 75 microseconds. These results provide essential guidelines for designing scalable quantum processors and establishing benchmarks for experimental validation of multi-qubit entanglement protocols.
Entanglment properties of photon-added two-mode entangled coherent states are analyzed and analytical expression of the concurrence entanglement is obtained.The results show that the concurrence of the photon-added entangled coherent states is very sensitive to the superposition phase.Schemes for preparation of photon-added coherent states and photon-added two-mode entangled coherent states are also proposed.The preparation procession of the photon-added coherent states is that the photon-added coherent states are firstly tansformed into a superposition state of coherent state and vacuum state(the superposition coefficient is associated with amplitude of the coherent state),then by applying the interaction of atom inside high-Q cavity with a classical light,finally added coherent states of cavity field is prepared.Preparation of photon-added two-mode entangled coherent states of cavity fields is based on interaction of the flying atom with two cavity fields.
Quantum teleportation has attracted much attention from both theorists and experimenters in the last decade. The emergence of new protocols and their actual implementation have even motivated the development of new quantum optical schemes. A key issue when teleporting a quantum state is establishing the quantum channel between sender and receiver stations, usually done by manipulating an auxiliary bipartite entangled state. The purpose of the present work is to study quantum teleportation processes in which that state is an entangled bipartite photon-added state, and the Adhikari et. al. continuous-variable quantum teleportation protocol is applied. Photon-added states can be generated using different experimental techniques, such as parametric down-conversion in a nonlinear crystal, and conditioned parametric amplification. These states are relevant because they exhibit generalized non-classical features for all orders of creation and annihilation operators, and may even show phase squeezing and sub-Poissonian distribution statistics. We study, the dependence of the fidelity of the teleported states and their photon number statistic as a function of the higher-order squeezing, and the higher-order sub-Poissonian statistic.