TY - JOUR

T1 - Non-commutative graphs and quantum error correction for a two-mode quantum oscillator

AU - Amosov, G. G.

AU - Mokeev, A. S.

AU - Pechen, A. N.

PY - 2020/2/1

Y1 - 2020/2/1

N2 - An important topic in quantum information is the theory of error correction codes. Practical situations often involve quantum systems with states in an infinite-dimensional Hilbert space, for example, coherent states. Motivated by these practical needs, we develop the theory of non-commutative graphs, which is a tool to analyze error correction codes, to infinite-dimensional Hilbert spaces. As an explicit example, a family of non-commutative graphs associated with the Schrodinger equation describing the dynamics of a two-mode quantum oscillator is constructed and maximal quantum anticliques for these graphs are found.

AB - An important topic in quantum information is the theory of error correction codes. Practical situations often involve quantum systems with states in an infinite-dimensional Hilbert space, for example, coherent states. Motivated by these practical needs, we develop the theory of non-commutative graphs, which is a tool to analyze error correction codes, to infinite-dimensional Hilbert spaces. As an explicit example, a family of non-commutative graphs associated with the Schrodinger equation describing the dynamics of a two-mode quantum oscillator is constructed and maximal quantum anticliques for these graphs are found.

KW - Quantum error correction

KW - Non-commutative graphs

KW - Quantum anticliques

KW - Quantum oscillator

KW - Two-mode field

KW - Coherent states

U2 - 10.1007/s11128-019-2554-5

DO - 10.1007/s11128-019-2554-5

M3 - статья

VL - 19

JO - Quantum Information Processing

JF - Quantum Information Processing

SN - 1570-0755

IS - 3

M1 - 95

ER -