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

Graduate texts in physics

Quantum Mechanics for Qubit Systems

Masahito Hayashi, Satoshi Ishizaka, Akinori Kawachi, Gen Kimura, Tomohiro Ogawa

Published Aug 22, 2014• 0 citations
Publisher
DOI
10.1007/978-3-662-43502-1_2

Related papers

QUANTUM MECHANICS OF QUBITS

WORLD SCIENTIFIC eBooks•Jul 21, 2019•0 citations

The ZX-calculus is complete for stabilizer quantum mechanics

Miriam Backens

The ZX-calculus is a graphical calculus for reasoning about quantum systems and processes. It is known to be universal for pure state qubit quantum mechanics (QM), meaning any pure state, unitary operation and post-selected pure projective measurement can be expressed in the ZX-calculus. The calculus is also sound , i.e. any equality that can be derived graphically can also be derived using matrix mechanics. Here, we show that the ZX-calculus is complete for pure qubit stabilizer QM, meaning any equality that can be derived using matrices can also be derived pictorially. The proof relies on bringing diagrams into a normal form based on graph states and local Clifford operations.

arXiv:1307.7025•New Journal of Physics•Sep 17, 2014•122 citations

PT -Symmetric Qubit-System States in the Probability Representation of Quantum Mechanics

Vladimir N. Chernega, Margarita A. Man’ko, Vladimir I. Man’ko

PT-symmetric qubit-system states are considered in the probability representation of quantum mechanics. The new energy eigenvalue equation for probability distributions identified with qubit and qutrit states is presented in an explicit form. A possibility to test PT-symmetry and its violation by measuring the probabilities of spin projections for qubits in three perpendicular directions is discussed.

Symmetry•Oct 16, 2020•6 citations

Quantum Mechanics and Quantum Computing

WORLD SCIENTIFIC eBooks•Oct 13, 2022•1 citation

Quantum Mechanics With Applications

David B. Beard, G. B. Beard, Garrison Sposito

Physics Today•Jan 1, 1971•4 citations

Understanding quantum entanglement: Qubits, rebits and the quaternionic approach

Josep Amengual i Batle, Angel Ricardo Plastino, M. Casas +1 more

It has been recently pointed out by Caves, Fuchs, and Rungta [1] that real quantum mechanics (that is, quantum mechanics defined over real vector spaces [2–5]) provides an interesting foil theory whose study may shed some light on just which particular aspects of quantum entanglement are unique to standard quantum theory and which are more generic over other physical theories endowed with this phenomenon. Following this work, some entanglement properties of two-rebit systems are discussed and a comparison with the basic properties of two-qubit systems, i.e., the systems described by standard complex quantum mechanics, is made. The use of quaternionic quantum mechanics as applied to the phenomenon of entanglement is also discussed.

arXiv:quant-ph/0603060•Optics and Spectroscopy•May 1, 2003•17 citations
The ZX-calculus is a graphical calculus for reasoning about quantum systems and processes. It is known to be universal for pure state qubit quantum mechanics (QM), meaning any pure state, unitary operation and post-selected pure projective measurement can be expressed in the ZX-calculus. The calculus is also sound , i.e. any equality that can be derived graphically can also be derived using matrix mechanics. Here, we show that the ZX-calculus is complete for pure qubit stabilizer QM, meaning any equality that can be derived using matrices can also be derived pictorially. The proof relies on bringing diagrams into a normal form based on graph states and local Clifford operations.
It has been recently pointed out by Caves, Fuchs, and Rungta [1] that real quantum mechanics (that is, quantum mechanics defined over real vector spaces [2–5]) provides an interesting foil theory whose study may shed some light on just which particular aspects of quantum entanglement are unique to standard quantum theory and which are more generic over other physical theories endowed with this phenomenon. Following this work, some entanglement properties of two-rebit systems are discussed and a comparison with the basic properties of two-qubit systems, i.e., the systems described by standard complex quantum mechanics, is made. The use of quaternionic quantum mechanics as applied to the phenomenon of entanglement is also discussed.