Analyzing the Decoherence on Biphoton and Schrödinger Cat States through Wigner Function

Simanshu Kumar¹ and Nandan S Bisht^2,

¹Department of Physics, Kumaun University Nainital, S.S.J. Campus, Almora, 263601, Uttarakhand, India

²Department of Physics, Soban Singh Jeena University, S.S.J. Campus, Almora, 263601, Uttarakhand, India

Cite this paper:
Simanshu Kumar and Nandan S Bisht. Analyzing the Decoherence on Biphoton and Schrödinger Cat States through Wigner Function. International Journal of Physics. 2025; 13(3):73-79. doi: 10.12691/ijp-13-3-5

Abstract

This study lights on the phenomenon of quantum decoherence when Biphoton and Schrödinger cat states are evolve. The primary focus of the work is to explore and analyze the phenomenon of decoherence by virtue of the insightful representations on the way of deriving the Wigner function for the considered states. A crucial aspect of this work involves shedding light on the behaviour of Biphoton and Schrödinger cat states with the same spatial modes and similar theoretical tomography. By considering the influence of an external environment, we further extend our exploration of decoherence, aiming to understand how environment as a factor, impact the stability and coherence of these quantum states.

Keywords:
Hong-Ou-Mandel interferometer Wigner function Decoherence Entanglement

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References:

[1]	Bennett, C. H. & DiVincenzo, D. P., Quantum in- information and computation, nature 404, 247–255 (2000).
[2]	Slussarenko, S. & Pryde, G. J., Photonic quantum information processing: A concise review, Applied Physics Reviews 6 (2019).
[3]	Zhang, H., Ji, Z., Wang, H. & Wu, W., Survey on quantum information security, China Communications 16, 1–36 (2019).
[4]	Horodecki, M., Oppenheim, J. & Winter, A., Partial quantum information, Nature 436, 673–676 (2005).
[5]	Knill, E., Quantum computing, Nature 463, 441–443 (2010).
[6]	Walther, P. et al., Experimental one-way quantum computing, Nature 434, 169–176 (2005).
[7]	Gyongyosi, L. & Imre, S., A survey on quantum computing technology, Computer Science Review 31, 51–71 (2019).
[8]	Giovannetti, V., Lloyd, S. & Maccone, L., Quantum metrology, Physical review letters 96, 010401 (2006).
[9]	Giovannetti, V., Lloyd, S. & Maccone, L., Advances in quantum metrology, Nature photonics 5, 222–229 (2011).
[10]	Taylor, M. A. & Bowen, W. P., Quantum metrology and its application in biology, Physics Reports 615, 1–59 (2016).
[11]	Takeuchi, S., Recent progress in single-photon and entangled-photon generation and applications, Japanese Journal of Applied Physics 53, 030101 (2014).
[12]	Oka, H., Two-photon absorption by spectrally shaped entangled photons, Physical Review A 97, 033814 (2018).
[13]	Christandl, M., The structure of bipartite quantum states-insights from group theory and cryptography, arXiv preprint quant-ph/0604183 (2006).
[14]	Nadal, C., Majumdar, S. N. & Vergassola, M., Statistical distribution of quantum entanglement for a random bipartite state, Journal of Statistical Physics 142, 403–438 (2011).
[15]	Masanes, L., All bipartite entangled states are useful for information processing, Physical Review Letters 96, 150501 (2006).
[16]	Schlosshauer, M., Quantum decoherence, Physics Reports 831, 1–57 (2019).
[17]	Hornberger, K., in Entanglement and Decoherence: Foundations and Modern Trends 221–276 (Springer, 2009).
[18]	Zeh, H. D., On the interpretation of measurement in quantum theory, Foundations of Physics 1, 69– 76 (1970).
[19]	Zurek, W. H., Pointer basis of quantum apparatus: Into what mixture does the wave packet collapse?, Physical review D 24, 1516 (1981).
[20]	Zurek, W. H., Environment-induced superselection rules, Physical review D 26, 1862 (1982).
[21]	Hong, C.K., Ou, Z.Y. & Mandel, L., Measurement of subpicosecond time intervals between two photons by interference, Physical review letters 59, 2044 (1987).
[22]	Douce, T. et al., Direct measurement of the biphoton Wigner function through two-photon interference, Scientific reports 3, 3530 (2013).
[23]	Gerrits, T. et al., Spectral correlation measurements at the Hong-Ou-Mandel interference dip, Physical Review A 91, 013830 (2015).
[24]	Harris, S., Oshman, M. & Byer, R., Observation of tunable optical parametric fluorescence, Physical Review Letters 18, 732 (1967).
[25]	Couteau, C., Spontaneous parametric down-conversion, Contemporary Physics 59, 291–304 (2018).
[26]	Kitaeva, G. K. & Penin, A. N., Spontaneous parametric down-conversion, Journal of Experimental and Theoretical Physics Letters 82, 350–355 (2005).
[27]	Boyd, R. W., Gaeta, A. L. & Giese, E., in Springer Handbook of Atomic, Molecular, and Optical Physics 1097–1110 (Springer, 2008).
[28]	Ziane, M. & El Baz, M., in Advances in Quantum Communication and Information 47 (IntechOpen, 2019).
[29]	Wigner, E., On the quantum correction for thermodynamic equilibrium, Physical review 40, 749 (1932).
[30]	Zachos, C., Fairlie, D. & Curtright, T., Quantum mechanics in phase space: an overview with se- selected papers (2005).
[31]	Gerry, C. & Knight, P., Quantum superpositions and Schrödinger cat states in quantum optics, American Journal of Physics 65, 964–974 (1997).
[32]	Schlosshauer, M. A., Decoherence: and the quantum-to-classical transition (Springer Science & Business Media, 2007).
[33]	Kalsoom, H., Ali, M. A., Idrees, M., Agar-wal, P. & Arif, M., New Post Quantum Ana-logues of Hermite–Hadamard Type Inequalities for Interval-Valued Convex Functions, Mathematical Problems in Engineering 2021, 5529650 (2021).
[34]	Hamza, A. E., Shehata, E. M. & Agarwal, P., in Computational Mathematics and Variational Analysis 121–134 (Springer, 2020).
[35]	Walschaers, M., Fabre, C., Parigi, V. & Treps, N., Entanglement and Wigner function negativity of multimode non-Gaussian states, Physical review letters 119,183601 2017).
[36]	Kenfack, A. & Życzkowski, K., Negativity of the Wigner function as an indicator of non- classicality, Journal of Optics B: Quantum and Semiclassical Optics 6, 396 (2004).
[37]	Nedjalkov, M., Querlioz, D, Dollfus, P & Kosina, H., Wigner function approach, Nano-Electronic Devices: Semiclassical and Quantum Transport Modeling, 289–358 (2011).
[38]	Walborn, S., De Oliveira, A., Pádua, S & Monken, C., Multimode hong-ou-mandel interference, Physical review letters 90, 143601 (2003).
[39]	Walborn, S. P., Monken, C., Pádua, S & Ribeiro, P. S., Spatial correlations in parametric down-conversion, Physics Reports 495, 87–139 (2010).
[40]	Singh, R. P., Roychowdhury, S. & Jaiswal, V. K., Non-axial nature of an optical vortex and Wigner function, Optics communications 274, 281–285 (2007).
[41]	Ali, M. A. et al., New quantum boundaries for quantum Simpson’s and quantum Newton’s type inequalities for preinvex functions, Advances in Difference Equations 2021, 64 (2021).
[42]	Wang, S., Liu, C.-X., Li, J. & Wang, Q., Research on the Hong-Ou-Mandel interference with two independent sources, Scientific Reports 9, 3854 (2019).
[43]	Javadi-Abhari, A. et al., Quantum computing with Qiskit, arXiv preprint arXiv: 2405. 08810 (2024).
[44]	Stavenger, T. J. et al., C2qa-bosonic qiskit in 2022 IEEE High Performance Extreme Computing Conference (HPEC) (2022), 1–8.
[45]	Bourassa, J. E. et al., Fast simulation of bosonic qubits via Gaussian functions in phase space, PRX Quantum 2, 040315 2021).
[46]	Younis, E. & Iancu, C., Quantum circuit optimization and transpilation via parameterized circuit instantiation in 2022 IEEE International Conference on Quantum Computing and Engineering (QCE) (2022), 465–475.
[47]	Padgett, M., Orbital angular momentum of single photons: revealing quantum fundamentals, Philosophical Transactions A 382, 20230327 (2024).
[48]	Ji, Z., Zhang, H. & Wang, H., Quantum private comparison protocols with a number of multi-particle entangled states, IEEE Access 7, 44613–44621 (2019).