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Related Experiment Video

Updated: Sep 21, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Quantum Incoherence Based Simultaneously on k Bases.

Pu Wang¹, Zhihua Guo¹, Huaixin Cao¹

¹School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, China.

Entropy (Basel, Switzerland)

|May 28, 2022

Summary

This summary is machine-generated.

This study explores quantum incoherence across multiple bases using matrix theory. Researchers found that the set of incoherent states is identical only if the underlying measurements are the same, with implications for quantum information.

Keywords:

mutually unbiased basis orthonormal basis strong incoherence weak coherence

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Area of Science:

Quantum Information Science
Quantum Foundations
Linear Algebra in Quantum Mechanics

Background:

Quantum coherence is a crucial resource for quantum information processing.
Coherence is a property dependent on the chosen basis for quantum states.
Understanding quantum incoherence is vital for developing robust quantum technologies.

Purpose of the Study:

To analyze quantum incoherence with respect to multiple (k) bases.
To investigate the relationship between sets of incoherent states for different bases.
To introduce and quantify concepts of strong and weak coherence.

Main Methods:

Utilized Matrix Theory methods for analysis.
Defined a correlation function m(e,f) for two orthonormal bases.
Investigated the intersection of incoherent state sets I(e) ∩ I(f).

Main Results:

Proved I(e)=I(f) if and only if rank-one projective measurements are identical.
Established conditions for the intersection I(e) ∩ I(f) beyond the maximally mixed state.
Showed that for mutually unbiased bases, the intersection contains only the maximally mixed state.

Conclusions:

Introduced strong and weak coherence with respect to a set of k bases.
Proposed a measure for weak coherence.
Demonstrated the existence of maximally coherent states for k=2 but not for k=3 in two-qubit systems.