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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

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Published on: May 30, 2014

Coin state properties in quantum walks.

A M C Souza¹, R F S Andrade

¹Departamento de Física, Universidade Federal de Sergipe 49100-000, São Cristovão, Brazil.

Scientific Reports

|June 13, 2013

Summary

This summary is machine-generated.

This study investigates M, the difference between coin states in discrete time quantum walks. Accounting for M enhances information retrieval from quantum walks.

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Area of Science:

Quantum physics
Quantum information science
Condensed matter physics

Background:

Recent experiments measure individual coin components in discrete time quantum walks.
Theoretical studies often overlook these coin components.
Quantum walks are a fundamental model in quantum computation and simulation.

Purpose of the Study:

To investigate the properties of M, the difference between the square moduli of coin states in discrete time quantum walks on a linear chain.
To explore how M influences the information content and dynamics of quantum walks.
To provide a theoretical framework and numerical validation for the role of coin states.

Main Methods:

Derivation of local expectation values in terms of the Fourier transform of the wave function.
Development of a simple analytical expression for the average difference between coin states.
Numerical integration of the dynamical equations in real space to corroborate theoretical findings.

Main Results:

A simple expression for the average difference between coin states (M) is found, dependent on a coin operator angle θ.
Local expectation values exhibit both large and short period modulations.
The quantity M reveals rich patterns not typically considered in standard analyses.

Conclusions:

The quantity M, representing the difference in coin state moduli, offers significant insights into quantum walk dynamics.
Incorporating M enhances the amount of information that can be stored and retrieved from quantum walks.
This work highlights the importance of considering individual coin components for a complete understanding of quantum walks.