# Quantum-to-Classical Coexistence: Wavefunction Decay Kinetics, Photon Entanglement, and Q-Bits

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## Abstract

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## 1. Introduction

- i.
- Elucidating the formulation of the stochastic quantum hydrodynamic equation of motion as a consequence of fluctuations in spacetime curvature originating from the noisy background of gravitational waves (dark energy).
- ii.
- Exploring the path integral approach to comprehend quantum stochastic dynamics, which describes the progression of quantum superposition states and potentially their transition to stable configurations.
- iii.
- Describing stationary quantum state configurations in the presence of noise and establishing their correspondence with standard quantum mechanical states.
- iv.
- Defining the circumstances under which the zero noise “deterministic” case aligns with conventional quantum mechanics.
- v.
- Identifying the criteria that lead to the emergence of classical behavior within extensive-scale systems.
- vi.
- Generalizing the uncertainty principles within the context of fluctuating quantum systems.
- vii.
- Investigating quantum entanglement, wave function decay, and the measurement process.
- viii.
- Comparing the measurement process as defined by the stochastic quantum hydrodynamic model with the perspectives of decoherence theory and the Copenhagen interpretation of quantum mechanics.
- ix.
- Examine experiments involving entangled photons within the context of finite time decay kinetics of wave functions.
- x.
- Extension of quantum coherence to macroscopic distances to build a system with a large number of Q-bits

## 2. The Quantum Potential Fluctuations Induced by the Background of Stochastic Gravitational Waves

- The virtual mass density fluctuations own the wave function ${\psi}_{vac}$ and density $|{\psi}_{vac}{|}^{2}$
- The associated energy density $E$ (of the spacetime background fluctuations) is proportional to $|{\psi}_{vac}{|}^{2}$
- The virtual mass ${m}_{vac}$ is defined by the identity $E={m}_{vac}{c}^{2}|{\psi}_{vac}{|}^{2}$;
- The virtual mass does not interact with the mass of the physical system (since the gravity is sufficiently weak to be ignored).

## 3. The Schrodinger-Langevin Equation from Stochastic Madelung Quantum Hydrodynamics

## 4. The Quantum Path Integral Motion Equation in the Presence of Stochastic Noise

#### 4.1. Evolution of Quantum Superposition of States Submitted to Stochastic Noise

#### 4.2. General Features of Relaxation of the Quantum Superposition of States

## 5. Emerging Classical Mechanics on Large Size Systems

#### 5.1. Lindemann Constant for Quantum Lattice-to-Classical Fluid Transition

#### 5.2. Fluid–Superfluid ${}^{4}\mathrm{He}$ Transition

#### 5.3. The Coarse-Grained Approach

#### 5.4. Measurement Process and the Finite Distance of Quantum Entanglement

#### 5.5. Minimum Measurement Uncertainty of Quantum Systems in Fluctuating Spacetime Backgrounds

#### 5.6. The Noisy Quantum Hydrodynamic Theoryl and the Decoherence Approach

#### 5.7. The SQHM and the Copenhagen Foundations of Quantum Mechanics

- i.
- need for real decoupling at the initial and final state of the measure between the system and the measuring apparatus and
- ii.
- utilization of classical experimental equipment for the collection and treatment of data.

#### 5.8. Stochastic Quantum Hydrodynamics, EPR Paradox and Completeness of Quantum Mechanics

- i.
- Classical reality emerges at the macroscopic level, persisting as a preexisting reality before measurement.
- ii.
- The measurement process is feasible in a classical macroscopic world, because we can have independent systems, namely the system and the measuring apparatus.
- iii.
- Determinism is acknowledged within standard quantum mechanics under the condition of zero noise.
- iv.
- Locality and causality are achieved at the macroscopic scale, where quantum nonlocal domains condense to punctual domains.
- v.
- The maximum light speed of the propagation of information aligns with quantum uncertainty.

## 6. Measurement of Photon Entanglement on Large Distances

- i.
- The quantum potential interaction propagates at the speed of light;
- ii.
- The quantum potential has a spatial extension equal to the physical length $\lambda \mathit{qu}.$

#### 6.1. The Quantum Potential Range of Photon Interactions

#### 6.2. Discussion

## 7. Extending Quantum Coherence to Obtain a Large Number of Entangled Q-Bits

## 8. Conclusions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Quantum Mechanics as an Imaginary Time Stochastic Process

## Appendix B. Stochastic Generalization of the Madelung Quantum Hydrodynamic Model

## Appendix C. The Markovian Noise Approximation in the Presence of the Quantum Potential

## Appendix D. Harmonic Oscillator Eigenstates in Fluctuating Spacetime

## Appendix E. Quantum Decoupling of the Measuring Apparatus at the Initial and Final Times

## Appendix F. The Nonlocal Quantum Potential Length of Interaction of the Photon

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