Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Geometric Phases In Quantum Systems Of Pure And Mixed State

Miran Haider

Published Jan 1, 2017• 0 citations
OpenAlex

Abstract

Note that equations and expressions has been omitted here and is instead presented in the work. This thesis focuses on the geometric phase in pure and mixed quantum states. For the case of a pure q ...

Related papers

GEOMETRIC PHASES OF PURE AND MIXED STATES

Rahul Ravishankar, Jiangfeng Du

The purpose of this article is to review the literature for pure and mixed state geometric phase and also the experimental measurement of the phase using NMR.

COSMOS•May 1, 2006•0 citations

A note on geometric phases

Franco Salmistraro

The usual definition of a geometric phase involves particular conditions on the behaviour of the state vector of a quantum system. We show that they can be removed in some cases by appealing directly to the Schrödinger equation. In this way we obtain an extension of a family of geometric phases previously introduced by us.

Europhysics Letters (EPL)•Jun 15, 1998•0 citations

Geometric Phases for Mixed States in Interferometry

Erik Sjöqvist, Arun Kumar Pati, ARTUR K. EKERT +4 more

We provide a physical prescription based on interferometry for introducing the total phase of a mixed state undergoing unitary evolution, which has been an elusive concept in the past. We define the parallel transport condition that provides a connection form for obtaining the geometric phase for mixed states. The expression for the geometric phase for mixed state reduces to well known formulas in the pure state case when a system undergoes noncyclic and unitary quantum evolution.

arXiv:quant-ph/0005072•Physical Review Letters•Oct 2, 2000•600 citations

Geometriska Faser I Rena Och Blandade Kvantmekaniska System

Haider, Miran

Note that equations and expressions has been omitted here and is instead presented in the work. This thesis focuses on the geometric phase in pure and mixed quantum states. For the case of a pure quantum state, Berry's adiabatic approach (4.1.10) and Aharonov & Anandan's non-adiabatic generalization of Berry's approach (4.2.8) are included in this work. Mixed quantum state involves Uhlmanns approach (5.1.42), which is used extensively in Section 7 and Sjöqvist's et al. approach (5.2.22), used extensively in Section 6. Sjöqvist's approach states that the Uhlmann phase is an observable and provides the experimental groundworkusing an interferometer.􀀀This was later proven, by Du et al.[45] to reproduce experimental data (Figure 19) on page 56. The Uhlmann phase can be used to observe the behaviour of topological kinks. This was tested on 3 models, the Creutz-ladder, the Majorana chain andthe SSU-model. It is found that the Uhlmann phase is split into two regimes with the dividing parameter being the temperature. This temperature is called the critical temperature, Tc. If the temperatureis is below the critical temperature, the Uhlmann phase yields Π and if thetemperature is above the critical temperature, the Uhlmann phase yields zero.

•Jan 1, 2017•0 citations

Geometric phases for nondegenerate and degenerate mixed states

Kuldip Singh, D. M. Tong, Kasturi Basu +2 more

This paper focuses on the geometric phase of general mixed states under unitary evolution. Here we analyze both nondegenerate as well as degenerate states. Starting with the nondegenerate case, we show that the usual procedure of subtracting the dynamical phase from the total phase to yield the geometric phase for pure states, does not hold for mixed states. To this end, we furnish an expression for the geometric phase that is gauge invariant. The parallelity conditions are shown to be easily derivable from this expression. We also extend our formalism to states that exhibit degeneracies. Here with the holonomy taking on a non-Abelian character, we provide an expression for the geometric phase that is manifestly gauge invariant. As in the case of the nondegenerate case, the form also displays the parallelity conditions clearly. Finally, we furnish explicit examples of the geometric phases for both the nondegenerate as well as degenerate mixed states.

arXiv:quant-ph/0304068•Physical Review A•Mar 18, 2003•128 citations

Geometric Phase for entangled Mixed state

H. T. Cui, L. C. Wang, X. X. Yi

This paper has been withdrawn by the author

arXiv:quant-ph/0504139•Apr 19, 2005•0 citations
Note that equations and expressions has been omitted here and is instead presented in the work. This thesis focuses on the geometric phase in pure and mixed quantum states. For the case of a pure quantum state, Berry's adiabatic approach (4.1.10) and Aharonov & Anandan's non-adiabatic generalization of Berry's approach (4.2.8) are included in this work. Mixed quantum state involves Uhlmanns approach (5.1.42), which is used extensively in Section 7 and Sjöqvist's et al. approach (5.2.22), used extensively in Section 6. Sjöqvist's approach states that the Uhlmann phase is an observable and provides the experimental groundworkusing an interferometer.􀀀This was later proven, by Du et al.[45] to reproduce experimental data (Figure 19) on page 56. The Uhlmann phase can be used to observe the behaviour of topological kinks. This was tested on 3 models, the Creutz-ladder, the Majorana chain andthe SSU-model. It is found that the Uhlmann phase is split into two regimes with the dividing parameter being the temperature. This temperature is called the critical temperature, Tc. If the temperatureis is below the critical temperature, the Uhlmann phase yields Π and if thetemperature is above the critical temperature, the Uhlmann phase yields zero.
This paper focuses on the geometric phase of general mixed states under unitary evolution. Here we analyze both nondegenerate as well as degenerate states. Starting with the nondegenerate case, we show that the usual procedure of subtracting the dynamical phase from the total phase to yield the geometric phase for pure states, does not hold for mixed states. To this end, we furnish an expression for the geometric phase that is gauge invariant. The parallelity conditions are shown to be easily derivable from this expression. We also extend our formalism to states that exhibit degeneracies. Here with the holonomy taking on a non-Abelian character, we provide an expression for the geometric phase that is manifestly gauge invariant. As in the case of the nondegenerate case, the form also displays the parallelity conditions clearly. Finally, we furnish explicit examples of the geometric phases for both the nondegenerate as well as degenerate mixed states.