Framework for classifying logical operators in stabilizer codes

Journal Article · Sat May 15 00:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.81.052302· OSTI ID:21408781

Yoshida, Beni; Chuang, Isaac L ^[1]

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1. Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)

Entanglement, as studied in quantum information science, and nonlocal quantum correlations, as studied in condensed matter physics, are fundamentally akin to each other. However, their relationship is often hard to quantify due to the lack of a general approach to study both on the same footing. In particular, while entanglement and nonlocal correlations are properties of states, both arise from symmetries of global operators that commute with the system Hamiltonian. Here, we introduce a framework for completely classifying the local and nonlocal properties of all such global operators, given the Hamiltonian and a bipartitioning of the system. This framework is limited to descriptions based on stabilizer quantum codes, but may be generalized. We illustrate the use of this framework to study entanglement and nonlocal correlations by analyzing global symmetries in topological order, distribution of entanglement, and entanglement entropy.

• OSTI ID: 21408781
• Journal Information: Physical Review. A, Vol. 81, Issue 5; Other Information: DOI: 10.1103/PhysRevA.81.052302; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
CORRELATIONS
ENTROPY
HAMILTONIANS
QUANTUM ENTANGLEMENT
QUANTUM INFORMATION
SYMMETRY
TOPOLOGY
INFORMATION
MATHEMATICAL OPERATORS
MATHEMATICS
PHYSICAL PROPERTIES
QUANTUM OPERATORS
THERMODYNAMIC PROPERTIES