# Informational correlation between two parties of a quantum system: spin-1/2 chains

Informational correlation between two parties of a quantum system: spin-1/2 chains We introduce the informational correlation $$E^{AB}$$ E A B between two interacting quantum subsystems $$A$$ A and $$B$$ B of a quantum system as the number of arbitrary parameters $$\varphi _i$$ φ i of a unitary transformation $$U^A$$ U A (locally performed on the subsystem $$A$$ A ) which may be detected in the subsystem $$B$$ B by the local measurements. This quantity indicates whether the state of the subsystem $$B$$ B may be effected by means of the unitary transformation applied to the subsystem $$A$$ A . Emphasize that $$E^{AB}\ne E^{BA}$$ E A B ≠ E B A in general. The informational correlations in systems with tensor product initial states are studied in more details. In particular, it is shown that the informational correlation may be changed by the local unitary transformations of the subsystem $$B$$ B . However, there is some non-reducible part of $$E^{AB}(t)$$ E A B ( t ) which may not be decreased by any unitary transformation of the subsystem $$B$$ B at a fixed time instant $$t$$ t . Two examples of the informational correlations between two parties of the four-node spin-1/2 chain with mixed initial states are studied. The long chains with a single initially excited spin (the pure initial state) are considered as well. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Informational correlation between two parties of a quantum system: spin-1/2 chains

, Volume 13 (12) – Sep 5, 2014
45 pages

/lp/springer_journal/informational-correlation-between-two-parties-of-a-quantum-system-spin-6gnTbtLzue
Publisher
Springer US
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-014-0811-1
Publisher site
See Article on Publisher Site

### Abstract

We introduce the informational correlation $$E^{AB}$$ E A B between two interacting quantum subsystems $$A$$ A and $$B$$ B of a quantum system as the number of arbitrary parameters $$\varphi _i$$ φ i of a unitary transformation $$U^A$$ U A (locally performed on the subsystem $$A$$ A ) which may be detected in the subsystem $$B$$ B by the local measurements. This quantity indicates whether the state of the subsystem $$B$$ B may be effected by means of the unitary transformation applied to the subsystem $$A$$ A . Emphasize that $$E^{AB}\ne E^{BA}$$ E A B ≠ E B A in general. The informational correlations in systems with tensor product initial states are studied in more details. In particular, it is shown that the informational correlation may be changed by the local unitary transformations of the subsystem $$B$$ B . However, there is some non-reducible part of $$E^{AB}(t)$$ E A B ( t ) which may not be decreased by any unitary transformation of the subsystem $$B$$ B at a fixed time instant $$t$$ t . Two examples of the informational correlations between two parties of the four-node spin-1/2 chain with mixed initial states are studied. The long chains with a single initially excited spin (the pure initial state) are considered as well.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Sep 5, 2014

### References

• Quantum entanglement
Horodecki, R; Horodecki, P; Horodecki, M; Horodecki, K

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