Theory of Quantum Path Entanglement and Interference with Multiplane Diffraction of Classical Light Sources.

Burhan Gulbahar

doi:10.3390/e22020246

Abstract

Quantum history states were recently formulated by extending the consistent histories approach of Griffiths to the entangled superposition of evolution paths and were then experimented with Greenberger–Horne–Zeilinger states. Tensor product structure of history-dependent correlations was also recently exploited as a quantum computing resource in simple linear optical setups performing multiplane diffraction (MPD) of fermionic and bosonic particles with remarkable promises. This significantly motivates the definition of quantum histories of MPD as entanglement resources with the inherent capability of generating an exponentially increasing number of Feynman paths through diffraction planes in a scalable manner and experimental low complexity combining the utilization of coherent light sources and photon-counting detection. In this article, quantum temporal correlation and interference among MPD paths are denoted with quantum path entanglement (QPE) and interference (QPI), respectively, as novel quantum resources. Operator theory modeling of QPE and counterintuitive properties of QPI are presented by combining history-based formulations with Feynman’s path integral approach. Leggett–Garg inequality as temporal analog of Bell’s inequality is violated for MPD with all signaling constraints in the ambiguous form recently formulated by Emary. The proposed theory for MPD-based histories is highly promising for exploiting QPE and QPI as important resources for quantum computation and communications in future architectures.

Highlights

These varying methods include Feynman’s path integral (FPI) formalism [2] as the most fundamental of all inherently including histories, consistent histories approach defined by Griffiths [3,4,5], and the recently formulated entangled histories framework [1] and two-state vector formalism [6,7] while all emphasizing correlations in time as standard quantum mechanical (QM) formalisms without violating
Multiplane diffraction (MPD) design as a simple linear optical system was recently proposed for quantum computing (QC) [8,9] and for modulator design in classical optical communications [10] by exploiting the tensor product structure of quantum temporal correlations as Entropy 2020, 22, 246; doi:10.3390/e22020246
The simplicity of source and detection in MPD setup combined with the highly important promise of the utilization of the tensor product structure of the temporal correlations as quantum resources motivates the definition and study of quantum trajectories or histories in MPD as novel quantum resources. These new resources denoted as quantum path entanglement (QPE) and quantum path interference (QPI) are defined and theoretically modeled in this article in terms of the temporal correlations and interference among the trajectories, respectively, to be exploited for future quantum computing and communications systems

Summary

Introduction

Quantum temporal correlations are analyzed with diverse methods by utilizing histories or trajectories of evolving quantum systems with more recent emphasis on mathematical formulation of the entangled superposition of quantum histories in Reference [1], i.e., denoted with the entangled histories framework.These varying methods include Feynman’s path integral (FPI) formalism [2] as the most fundamental of all inherently including histories, consistent histories approach defined by Griffiths [3,4,5], and the recently formulated entangled histories framework [1] and two-state vector formalism [6,7] while all emphasizing correlations in time as standard quantum mechanical (QM) formalisms without violatingCopenhagen interpretations. The simplicity of source and detection in MPD setup combined with the highly important promise of the utilization of the tensor product structure of the temporal correlations as quantum resources motivates the definition and study of quantum trajectories or histories in MPD as novel quantum resources. These new resources denoted as quantum path entanglement (QPE) and quantum path interference (QPI) are defined and theoretically modeled in this article in terms of the temporal correlations and interference among the trajectories, respectively, to be exploited for future quantum computing and communications systems

Methods

Results

Conclusion