M. A. Nielsen & I. L. Chuang. Quantum Computation and Quantum Information (Cambridge University Press, 2010).

Bennett, C. H. & DiVincenzo, D. P. Quantum information and computation. Nature. 404, 247 (2000).

ADS 
CAS 
PubMed 

Google Scholar
 

Ibrahim, T., Amin, M. E. & Salah, A. On the dynamics of correlations in 2\(\times\)3 Heisenberg chains with inhomogeneous magnetic field. Int. J. Theoret. Phys. 62, 14 (2023).

MathSciNet 

Google Scholar
 

Abdel-Wahab, N., Ibrahim, T., Amin, M. E. & Salah, A. Influence of intrinsic decoherence on quantum metrology of two atomic systems in the presence of dipole-dipole interaction. Optical Quant. Electron. 56, 1 (2024).


Google Scholar
 

Braunstein, S. L. & Kimble, H. J. Teleportation of continuous quantum variables. Phys. Rev. Lett. 80, 869 (1998).

ADS 
CAS 

Google Scholar
 

Milburn, G. & Braunstein, S. L. Quantum teleportation with squeezed vacuum states. Phys. Rev. A 60, 937 (1999).

ADS 
MathSciNet 
CAS 

Google Scholar
 

Ralph, T. C. Continuous variable quantum cryptography. Phys. Rev. A. 61, 010303 (1999).

ADS 
MathSciNet 

Google Scholar
 

Nahla, A. A. & Ahmed, M. Nonclassical properties of asymmetric two two-level atoms interacting with multi-photon quantized field. Int. J. Modern Phys. B 32, 1850250 (2018).

ADS 
CAS 

Google Scholar
 

Jaynes, E. T. & Cummings, F. W. Comparison of quantum and semiclassical radiation theories with application to the beam maser. Proc. IEEE 51, 89 (1963).


Google Scholar
 

Obada, A.-S., Ahmed, M., Faramawy, F. & Khalil, E. Entropy and entanglement of the nonlinear Jaynes-Cummings model. Chin. J. Phys. 42, 79 (2004).


Google Scholar
 

F. J. Garcia-Vidal, C. Ciuti, & T. W. Ebbesen. Manipulating matter by strong coupling to vacuum fields. Science. 373, eabd0336 (2021).

Frisk Kockum, A., Miranowicz, A., De Liberato, S., Savasta, S. & Nori, F. Ultrastrong coupling between light and matter. Nat. Rev. Phys. 1, 19 (2019).


Google Scholar
 

Buck, B. & Sukumar, C. Exactly soluble model of atom-phonon coupling showing periodic decay and revival. Phys. Lett. A 81, 132 (1981).

ADS 

Google Scholar
 

Sukumar, C. & Buck, B. Multi-phonon generalisation of the Jaynes-Cummings model. Phys. Lett. A 83, 211 (1981).

ADS 

Google Scholar
 

J. Larson & T. Mavrogordatos. The Jaynes–Cummings Model and Its Descendants, 2053–2563 (IOP Publishing, 2021).

Fang, M.-F. & Liu, H.-E. Properties of entropy and phase of the field in the two-photon Jaynes-Cummings model with an added kerr medium. Phys. Lett. A 200, 250 (1995).

ADS 

Google Scholar
 

Abdel-Aty, M. Entanglement degree of a three-level atom interacting with pair-coherent states with a nonlinear medium. Laser Phys. 11, 871 (2001).

CAS 

Google Scholar
 

Abdel-Wahab, N. A three-level atom interacting with a single mode cavity field: Different configurations. Physica Scripta 76, 244 (2007).

ADS 
CAS 

Google Scholar
 

Rizk, S.-E.A., Elkhateeb, M. M., Hashem, M. & Obada, A.-S.F. Analytical solution for \(\Xi\)-type qutrit interacting nonlinearly with a cavity field through Kerr-like medium with intrinsic noise present. Modern Phys. Lett. A 39, 2450045 (2024).

MathSciNet 
CAS 

Google Scholar
 

Osman, K. & Ashi, H. Effects of the radiation field on collapse and revival phenomena in a four-level system. Physica A Stat. Mech. Appl. 310, 165 (2002).

ADS 

Google Scholar
 

A. Obada, A. Abu Sitta, & O. Yasin. Three-photon micromasers, Tech. Rep. (International Centre for Theoretical Physics, 1993).

Abdel-Wahab, N. The interaction between a four-level N-type atom and two-mode cavity field in the presence of a Kerr medium. J. Phys. B Atomic Mol. Optical Phys. 40, 4223 (2007).

ADS 
CAS 

Google Scholar
 

Abdel-Wahab, N. H. A moving four-level N-type atom interacting with cavity fields. J. Phys. B Atomic Mol. Optical Phys. 41, 105502 (2008).

AbdelWahab, N. H. On the interaction between a four-level W-type atom and a two-mode cavity field. Nuovo Cimento. B. 125, 173 (2010).


Google Scholar
 

Devi, A., Gunapala, S. D. & Premaratne, M. Coherent and incoherent laser pump on a five-level atom in a strongly coupled cavity-QED system. Phys. Rev. A. 105, 013701 (2022).

ADS 
MathSciNet 
CAS 

Google Scholar
 

Ghosh, S. & Mandal, S. A theoretical analysis on coherent double resonant absorptive lineshape in closely spaced transitions for \(\lambda\)-type five level system. Optics Commun. 284, 376 (2011).

ADS 
CAS 

Google Scholar
 

Kaur, A. et al. The five-level \(\Lambda\)-\(\Xi\) system as an optical switch under different wavelength mismatching regimes, including one due to Rydberg transition. Optik. 223, 165600 (2020).

CAS 

Google Scholar
 

Wang, H. et al. Adiabatic Raman passage via two-photon resonant transitions in a five-level \(\lambda\) system. Optics Commun. 285, 3498 (2012).

ADS 
CAS 

Google Scholar
 

Antón, M., Carreño, F., Calderón, O. G., Melle, S. & Gonzalo, I. Optical switching by controlling the double-dark resonances in a N-tripod five-level atom. Optics Commun. 281, 6040 (2008).

ADS 

Google Scholar
 

Bhattacharyya, D., Ray, B. & Ghosh, P. N. Theoretical study of electromagnetically induced transparency in a five-level atom and application to Doppler-broadened and Doppler-free Rb atoms. J. Phys. B Atomic Mol. Optical Phys. 40, 4061 (2007).

ADS 
CAS 

Google Scholar
 

Abdel-Wahab, N. & Salah, A. Dynamic evolution of double \(\Lambda\) five-level atom interacting with one-mode electromagnetic cavity field. Pramana 89, 87 (2017).

ADS 

Google Scholar
 

Vafafard, A., Sahrai, M., Siahpoush, V., Hamedi, H. R. & Asadpour, S. H. Optically induced diffraction gratings based on periodic modulation of linear and nonlinear effects for atom-light coupling quantum systems near plasmonic nanostructures. Sci. Rep. 10, 16684 (2020).

CAS 
PubMed 
PubMed Central 

Google Scholar
 

Salah, A., Thabet, L., El-Shahat, T., El-Wahab, N. A. & Edin, M. G. A double \(\Lambda\)-five-level moving atom interacting with a two-mode field in the presence of damping and nonlinear Kerr medium. Mod. Phys. Lett. A 37, 2250030 (2022).

ADS 
MathSciNet 
CAS 

Google Scholar
 

Barzanjeh, S., Naderi, M. H. & Soltanolkotabi, M. Generation of motional nonlinear coherent states and their superpositions via an intensity-dependent coupling of a cavity field to a micromechanical membrane. J. Phys. B Atomic Mol. Optical Phys. 44, 105504 (2011).

Cheng, G.-L., Chen, A.-X. & Zhong, W.-X. Generation of three-mode light entanglement via double-channel resonant four-wave mixing. Optics Commun. 284, 4028 (2011).

ADS 
CAS 

Google Scholar
 

Abdel-Aty, M. Influence of a Kerr-like medium on the evolution of field entropy and entanglement in a three-level atom. J. Phys. B Atomic Mol. Optical Phys. 33, 2665 (2000).

ADS 
CAS 

Google Scholar
 

Amin, M., Abdel-Wahab, N. & Taha, M. Influence of a Kerr-like medium and the detuning parameter on the statistical aspects of the intensity-dependent-coupling Hamiltonian. Int. J. Theor. Phys. 43, 411 (2004).


Google Scholar
 

Obada, A.-S., Ahmed, M., Faramawy, F. & Khalil, E. Influence of Kerr-like medium on a nonlinear two-level atom. Chaos Solitons Fractals 28, 983 (2006).

ADS 
CAS 

Google Scholar
 

Hu, M.-L. et al. Quantum coherence and geometric quantum discord. Phys. Rep. 762–764, 1 (2018).

ADS 
MathSciNet 

Google Scholar
 

Ma, Z.-H. et al. Operational advantage of basisindependent quantum coherence. Europhys. Lett. 125, 50005 (2019).

ADS 
CAS 

Google Scholar
 

Wiseman, H. M., Jones, S. J. & Doherty, A. C. Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox. Phys. Rev. Lett. 98, 140402 (2007).

ADS 
MathSciNet 
CAS 
PubMed 

Google Scholar
 

Rahman, A. U., Abd-Rabbou, M. Y., Haddadi, S. & Ali, H. Two-qubit steerability, nonlocality, and average steered coherence under classical dephasing channels. Annalen der Physik 535, 2200523 (2023).

ADS 

Google Scholar
 

Ali, A., Al-Kuwari, S. & Haddadi, S. Trade-off relations of quantum resource theory in Heisenberg models. Physica Scripta. 99, 055111 (2024).

ADS 

Google Scholar
 

A. Ali, S. Al-Kuwari, M. Rahim, M. Ghominejad, H. Ali, & S. Haddadi. A study on thermal quantum resources and probabilistic teleportation in spin-1/2 Heisenberg XYZ+DM+KSEA model under variable Zeeman splitting. Appl. Phys. B. 130 (2024).

Baumgratz, T., Cramer, M. & Plenio, M. B. Quantifying coherence. Phys. Rev. Lett. 113, 140401 (2014).

ADS 
CAS 
PubMed 

Google Scholar
 

Streltsov, A., Adesso, G. & Plenio, M. B. Colloquium: Quantum coherence as a resource. Rev. Mod. Phys. 89, 041003 (2017).

ADS 
MathSciNet 

Google Scholar
 

Li, X.-S. et al. Nonresonant interaction of a three-level atom with cavity fields. I. General formalism and level occupation probabilities. Phys. Rev. A. 36, 5209 (1987).

ADS 
CAS 

Google Scholar
 

A. Salah. Quantum aspects for three-level atom with one mode cavity field (LAP LAMBERT Academic Publishing, 2015).

Abdel-Wahab, N. A four-level atom interacting with a single-mode cavity field: Double \(\Xi\)-configuration. Mod. Phys. Lett. B 22, 2587 (2008).

ADS 
CAS 

Google Scholar
 

Abdel-Wahab, N., Abdel-Khalek, S., Khalil, E., Alshehri, N. & Almalki, F. A deformed model for N-type four-level atom and a single mode field system in the presence of the Kerr medium. Optical Quant. Electronics 54, 334 (2022).


Google Scholar
 

Salah, A., Thabet, L. & El-Shahat, T. & N. Abd El-Wahab. On the interaction between tripod-type four-level atom and one-mode field in the presence of a classical homogeneous gravitational field. Pramana. 94, 1 (2020).

Abdel-Wahab, N., Ibrahim, T. & Amin, M. E. The entanglement of a two two-level atoms interacting with a cavity field in the presence of intensity-dependent coupling regime, atom-atom, dipole-dipole interactions and Kerr-like medium. Quant. Inform. Process. 23, 94 (2024).

ADS 
MathSciNet 

Google Scholar
 

Raddadi, M. H., Nahla, A. A. & Abo-Kahla, D. A. M. Quantized study for asymmetric two two-level atoms interacting with intensity-dependent coupling regime. Indian J. Phys. 97, 1345 (2023).

ADS 
CAS 

Google Scholar
 

Zangi, S., Li, J.-L. & Qiao, C.-F. Entanglement classification of four-partite states under the SLOCC. J. Phys. A Math. Theoret. 50, 325301 (2017).

ADS 
MathSciNet 

Google Scholar
 

Zangi, S., Li, J. L. & Qiao, C.-F. Quantum state concentration and classification of multipartite entanglement. Phys. Rev. A. 97, 012301 (2018).

ADS 
MathSciNet 
CAS 

Google Scholar
 

Seoudy, T. A. & AitChlih, A. Dephasing effects on nonclassical correlations in two-qubit Heisenberg spin chain model with anisotropic spin-orbit interactions. Appl. Phys. B. 130, 62 (2024).

ADS 
CAS 

Google Scholar
 

Li, L.-J., Ming, F., Song, X.-K., Ye, L. & Wang, D. Quantumness and entropic uncertainty in curved space-time. Eur. Phys. J. C 82, 726 (2022).

ADS 
CAS 

Google Scholar
 

Czerwinski, A. Quantifying entanglement of two-qubit Werner states. Commun. Theor. Phys. 73, 085101 (2021).

ADS 
MathSciNet 

Google Scholar
 

Zangi, S. M., Shukla, C., Rahman, A. U. & Zheng, B. Entanglement swapping and swapped entanglement. Entropy 25, 415 (2023).

ADS 
MathSciNet 
PubMed 
PubMed Central 

Google Scholar
 

Ekert, A. K. Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661 (1991).

ADS 
MathSciNet 
CAS 
PubMed 

Google Scholar
 

Pati, A. K. & Braunstein, S. L. Role of entanglement in quantum computation. J. Indian Inst. Sci. 89, 295 (2009).

MathSciNet 

Google Scholar
 

Czerwinski, A. Quantum tomography of entangled qubits by time-resolved single-photon counting with time-continuous measurements. Quant. Inf. Process. 21, 332 (2022).

ADS 
MathSciNet 

Google Scholar
 

Czerwinski, A. & Szlachetka, J. Efficiency of photonic state tomography affected by fiber attenuation. Phys. Rev. A. 105, 062437 (2022).

ADS 
MathSciNet 
CAS 

Google Scholar
 

Haddadi, S. & Bohloul, M. A brief overview of bipartite and multipartite entanglement measures. Int. J. Theor. Phys. 57, 3912 (2018).

MathSciNet 

Google Scholar
 

Abdel-Wahab, N. A, Ibrahim, T. & Amin, M. E. Exploring the influence of intrinsic decoherence on residual entanglement and tripartite uncertainty bound in XXZ Heisenberg chain model. Eur. Phys. J. D 78, 17 (2024).


Google Scholar
 

Wootters, W. K. Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998).

ADS 
CAS 

Google Scholar
 

Zangi, S. M. & Qiao, C.-F. Robustness of 2\(\times\)N\(\times\)M entangled states against qubit loss. Phys. Lett. A. 400, 127322 (2021).

MathSciNet 
CAS 

Google Scholar
 

Zangi, S. M., Wu, J.-S. & Qiao, C.-F. Combo separability criteria and lower bound on concurrence. J. Phys. A Math. Theoret. 55, 025302 (2021).

ADS 
MathSciNet 

Google Scholar
 

Abdel-Wahab, N., Ibrahim, T., Amin, M. E. & Salah, A. Dense coding, non-locality correlations and entanglement for two two-level atoms interacting resonantly with a single mode cavity field in intrinsic decoherence model. Optical Quant. Electron. 56, 728 (2024).

ADS 

Google Scholar
 

A. Rényi, On measures of entropy and information, in Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics, Vol. 4 (University of California Press, 1961) pp. 547–562.

Rahman, A. U., Haddadi, S., Javed, M., Kenfack, L. T. & Ullah, A. Entanglement witness and linear entropy in an open system influenced by FG noise. Quant. Inf. Process. 21, 368 (2022).

ADS 
MathSciNet 

Google Scholar
 

Xiong, W., Jin, D.-Y., Qiu, Y., Lam, C.-H. & You, J. Q. Cross-Kerr effect on an optomechanical system. Phys. Rev. A. 93, 023844 (2016).

ADS 

Google Scholar