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Preparation information and optimal decompositions for mixed quantum states

Andrei N. Soklakov, Rüdiger Schack

Consider a joint quantum state of a system and its environment. A measurement on the environment induces a decomposition of the system state. Using algorithmic information theory, we define the preparation information of a pure or mixed state in a given decomposition. We then define an optimal decomposition as a decomposition for which the average preparation information is minimal. The average preparation information for an optimal decomposition characterizes the system–environment correlations. We discuss properties and applications of the concepts introduced above and give several examples.Consider a joint quantum state of a system and its environment. A measurement on the environment induces a decomposition of the system state. Using algorithmic information theory, we define the preparation information of a pure or mixed state in a given decomposition. We then define an optimal decomposition as a decomposition for which the average preparation information is minimal. The average preparation information for an optimal decomposition characterizes the system–environment correlations. We discuss properties and applications of the concepts introduced above and give several examples.

arXiv:quant-ph/0002027Journal of Modern OpticsOct 1, 20004 citations

Robust Decomposition of Quantum States

Jonathan E. Moussa

Bulletin of the American Physical SocietyMar 6, 20200 citations

Decompositions in Quantum Mechanics—An Overview

John Harding

Studies in systems, decision and controlJan 1, 20220 citations

Preparation information and optimal decompositions for mixed quantum states

Rudiger Schack Andrei N. Soklakov

Consider a joint quantum state of a system and its environment.A measurement on the environment induces a decomposition of the system state.Using algorithmic information theory, we define the preparation information of a pure or mixed state in a given decomposition.We then define an optimal decomposition as a decomposition for which the average preparation information is minimal.The average preparation information for an optimal decomposition characterizes the system-environment correlations.We discuss properties and applications of the concepts introduced above and give several examples.Consider a joint quantum state of a system and its environment.A measurement on the environment induces a decomposition of the system state.Using algorithmic information theory, we define the preparation information of a pure or mixed state in a given decomposition.We then define an optimal decomposition as a decomposition for which the average preparation information is minimal.The average preparation information for an optimal decomposition characterizes the system-environment correlations.We discuss properties and applications of the concepts introduced above and give several examples.

Journal of Modern OpticsOct 15, 20001 citation

Decomposition of matrix in quantum state control

Hai‐Rui Wei

The relationship between quantum state control and matrix decomposition is reviewed.The matrix decomposition newly applied in quantum information science,i.e.Cartan decomposition based on group theory and cosine-sine decomposition based on numerical linear algebra,is introduced firstly.Then the current research situation and the results in this area are reviewed.These results play important roles in quantum entanglement dynamics,the control of quantum states and optimization of quantum circuit Finally,the Cartan decomposition of a 2-qutrit logic gate is given.The relationship between quantum state control and matrix decomposition is reviewed.The matrix decomposition newly applied in quantum information science,i.e.Cartan decomposition based on group theory and cosine-sine decomposition based on numerical linear algebra,is introduced firstly.Then the current research situation and the results in this area are reviewed.These results play important roles in quantum entanglement dynamics,the control of quantum states and optimization of quantum circuit Finally,the Cartan decomposition of a 2-qutrit logic gate is given.

Chinese Journal of Quantum ElectronicsJan 1, 20080 citations

Decomposition of pure states of quantum register

I. Raptis, Petros Wallden, Romàn R. Zapatrin

The European Physical Journal DSep 7, 20061 citation

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