# Polarimetric Quantum-Strong Correlations with Independent Photons on the Poincaré Sphere

## Abstract

**:**

## 1. Introduction

_{s}+ ω

_{i}= ω

_{p}, the gain- providing medium which generates the spontaneous emission, will also amplify the initially single photons, particularly so in the direction of wavevector matching conditions, even for limited space-time overlap. A phase-pulling effect leading to the phase relation ${\phi}_{s}+{\phi}_{i}={\phi}_{p}+\pi /2$ also occurs, [12] which is capable of countering phase-mismatch. Thus, the commonly assumed one single photon output does not physically happen. At least several photons may be associated with each individual and discrete electronic “click”. A group of photons of the same frequency propagating inside a dielectric medium will follow a straight-line because a photon locally absorbed by a dipole, will be recaptured by the other photons in the group through stimulated emission. Nevertheless, sometimes, only one photon may survive the propagation to reach the photodetector.

## 2. The Shortcomings of the Entangled States of Photons

## 3. Quantum Correlations of Independent Photons

_{A}$\u2a02$$\mathscr{H}$

_{B}.

## 4. Quantum Correlations with Arbitrary Independent Photons on the Poincaré Sphere

- Locality of measurements is supported by the use of single and independent photonic qubits to explain the experimental results of apparently enhanced correlations of outcomes;
- Randomness of experimental parameters stems from the quantum Rayleigh spontaneous emission that generates the projection from the polarization state$\text{}|x\u27e9\text{}$of the input photons to the rotated polarization state $|{\psi}_{k}\u27e9=cos{\phi}_{k}|x\u27e9+sin{\phi}_{k}|y\u27e9$ of Equation (14); and,
- Realism of values carried by the detected photons is indicated by the physical effect of the measuring operators on the detected photons in quantum states of Equation (14). As the expectation values of the product operator $\u27e8{\hat{\sigma}}_{1}{\hat{\sigma}}_{3}\u27e9$ are found to vanish for the pure states of Equation (14) projected onto the measurement Hilbert space, i.e., $\u27e8\psi \left(\phi \right)\left|{\hat{\sigma}}_{3}{\hat{\sigma}}_{1}\right|\psi \left(\phi \right)\u27e9=\u27e8\psi \left(\phi \right)\left|{\hat{\sigma}}_{1}{\hat{\sigma}}_{3}\right|\psi \left(\phi \right)\u27e9=0$ as ${\hat{\sigma}}_{1}{\hat{\sigma}}_{3}|{\psi}_{k}\u27e9={\psi}_{k}\left(\phi +\pi /2\right)\u27e9$, each term of the resulting commutative relation vanishes and we obtain$$\u27e8{\psi}_{k}\left|\left[{\hat{\sigma}}_{1},{\hat{\sigma}}_{3}\right]\right|{\psi}_{k}\u27e9=0$$

## 5. Physical Aspects of Measurements of Independent Photons for Integrated Quantum Photonics

## 6. Conclusions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A. A Summary of Quantum Rayleigh Scattering

_{s}+ ω

_{i}= ω

_{p}, the gain-providing medium which generates the spontaneous emission, will also amplify the initially single photons, particularly so in the direction of wavevector matching conditions, even for a limited space-time overlap. A phase-pulling effect leading to ${\phi}_{s}+{\phi}_{i}={\phi}_{p}+\pi /2$ also occurs [12] which facilitates the parametric amplification. Thus, the commonly assumed one single photon output does not physically happen. At least several photons may be associated with each individual and discrete electronic “click”. A group of photons of the same frequency propagating inside a dielectric medium will follow a straight-line because a photon locally absorbed by a dipole, will be recaptured by the other photons in the group through stimulated emission. Nevertheless, only one photon may survive the propagation to reach the photodetector.

**k**and polarization µ is related to the decay rate ${\gamma}_{s}$ (1/s) of the excited dipole and evaluated as [8]:

**d**denoting the electric dipole moment which is excited by an optical field of the same polarization, and ${\mathit{e}}_{\mathit{k}\mu}$ is the polarization unit vector of the emitted photon, and which is perpendicular to the direction of propagation

**k**. The dielectric constant is $\u03f5$.

## Appendix B. Equal Quantum and Classical Correlations of Polarized Photons

## References

- Moody, G.; Sorger, V.J.; Blumenthal, D.J.; Juodawlkis, P.W.; Loh, W.; Sorace-Agaskar, C.; Jones, A.E.; Balram, K.C.; Matthews, J.C.F.; Laing, A.; et al. 2022 Roadmap on integrated quantum photonics. J. Phys.
**2022**, 4, 012501. [Google Scholar] [CrossRef] - Kok, P.; Lovett, B.W. Introduction to Optical Quantum Information Processing; Cambridge University Press: Cambridge, UK, 2010. [Google Scholar]
- Paneru, D.; Cohen, E.; Fickler, R.; Boyd, R.W.; Karimi, E. Entanglement: Quantum or classical? Rep. Prog. Phys.
**2020**, 83, 064001. [Google Scholar] [CrossRef] [PubMed][Green Version] - Barnett, S.M.; Croke, S. Quantum state discrimination. Adv. Opt. Phot. (AOP)
**2009**, 1, 238–278. [Google Scholar] [CrossRef] - Iannuzzi, M.; Francini, R.; Messi, R.; Moricciani, D. Bell-type polarization experiment with pairs of uncorrelated optical photons. Phys. Lett. A
**2019**, 384, 126200. [Google Scholar] [CrossRef][Green Version] - Louisell, W.H. Quantum Statistical Properties of Radiation; John Wiley & Sons: Hoboken, NJ, USA, 1973. [Google Scholar]
- Marcuse, D. Principles of Quantum Electronics; Academic Press: Cambridge, MA, USA, 1980. [Google Scholar]
- Glauber, R.J.; Lewenstein, M. Quantum optics of dielectric media. Phys. Rev. A
**1991**, 43, 467–491. [Google Scholar] [CrossRef] [PubMed] - Vatarescu, A. The Scattering and Disappearance of Entangled Photons in a Homogeneous Dielectric Medium. In Proceedings of the Rochester Conference on Coherence and Quantum Optics (CQO-11), New York, NY, USA, 4–8 August 2019. [Google Scholar] [CrossRef]
- Vatarescu, A. Photonic coupling between quadrature states of light in a homogeneous and optically linear dielectric medium. J. Opt. Soc. Am. B
**2014**, 31, 1741–1745. [Google Scholar] [CrossRef] - Vatarescu, A. Phase-Sensitive Amplification with Low Pump Power for Integrated Photonics. In Proceedings of the OSA Advanced Photonics Congress, Vancouver, BC, Canada, 18–21 July 2016. [Google Scholar]
- Vatarescu, A. Photonic Quantum Noise Reduction with Low-Pump Parametric Amplifiers for Photonic Integrated Circuits. Photonics
**2016**, 3, 61. [Google Scholar] [CrossRef][Green Version] - Garrison, C.; Chiao, R.Y. Quantum Optics; Oxford University Press: Oxford, UK, 2008. [Google Scholar]
- Griffiths, R.B. Nonlocality claims are inconsistent with Hilbert-space quantum mechanics. Phys. Rev. A
**2020**, 101, 022117. [Google Scholar] [CrossRef][Green Version] - Tipler, F.J. Quantum nonlocality does not exist. Proc. Natl. Acad. Sci. USA
**2014**, 111, 11281–11286. [Google Scholar] [CrossRef] [PubMed] - Hess, K. What Do Bell-Tests Prove? A Detailed Critique of Clauser-Horne-Shimony-Holt Including Counterexamples. J. Mod. Phys.
**2021**, 12, 1219–1236. [Google Scholar] [CrossRef] - Boughn, S. Making Sense of Bell’s Theorem and Quantum Nonlocality. Found. Phys.
**2017**, 47, 640–657. [Google Scholar] [CrossRef][Green Version] - Khrennikov, A. Get Rid of Nonlocality from Quantum Physics. Entropy
**2019**, 21, 806. [Google Scholar] [CrossRef] [PubMed][Green Version] - Kupczynski, M. Closing the Door on Quantum Nonlocality. Entropy
**2018**, 20, 877. [Google Scholar] [CrossRef] [PubMed][Green Version] - Fano, U. Description of States in Quantum Mechanics by Density Matrix and Operator Techniques. Rev. Mod. Phys.
**1957**, 29, 74–93. [Google Scholar] [CrossRef] - Gordon, J.P.; Kogelnik, H. PMD fundamentals: Polarization mode dispersion in optical fibers. Proc. Natl. Acad. Sci. USA
**2000**, 97, 4541–4550. [Google Scholar] [CrossRef] [PubMed][Green Version] - Griffiths, D.J. Introduction to Quantum Mechanics; Prentice Hall: Pearson, GA, USA, 2005. [Google Scholar]
- Vatarescu, A. Instantaneous Quantum Description of Photonic Wavefronts and Applications. Quantum Beam Sci.
**2022**, 6, 29. [Google Scholar] [CrossRef]

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Vatarescu, A.
Polarimetric Quantum-Strong Correlations with Independent Photons on the Poincaré Sphere. *Quantum Beam Sci.* **2022**, *6*, 32.
https://doi.org/10.3390/qubs6040032

**AMA Style**

Vatarescu A.
Polarimetric Quantum-Strong Correlations with Independent Photons on the Poincaré Sphere. *Quantum Beam Science*. 2022; 6(4):32.
https://doi.org/10.3390/qubs6040032

**Chicago/Turabian Style**

Vatarescu, Andre.
2022. "Polarimetric Quantum-Strong Correlations with Independent Photons on the Poincaré Sphere" *Quantum Beam Science* 6, no. 4: 32.
https://doi.org/10.3390/qubs6040032