Entanglement types for two-qubit states with real amplitudes

Perdomo, Oscar; Leyton Ortega, Vicente; Perdomo-Ortiz, Alejandro

doi:10.1007/s11128-021-03025-z

Entanglement types for two-qubit states with real amplitudes

Journal Article · Wed Mar 03 00:00:00 EST 2021 · Quantum Information Processing

DOI:https://doi.org/10.1007/s11128-021-03025-z· OSTI ID:1777764

Perdomo, Oscar ^[1]; Leyton Ortega, Vicente ^[2]; Perdomo-Ortiz, Alejandro ^[3]

Central Connecticut State Univ., New Britain, CT (United States); Rigetti Computing, Berkeley, CA (United States)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Engineering Div.
Zapata Computing Canada, Inc., Toronto, ON (Canada); Univ. College London (United Kingdom). Dept. of Computer Science; Rigetti Computing, Berkeley, CA (United States)

We study the set of two-qubit pure states with real amplitudes and their geometrical representation in the three-dimensional sphere. In this representation, we show that the maximally entangled states—those locally equivalent to the Bell states—form two disjoint circles perpendicular to each other. We also show that taking the natural Riemannian metric on the sphere, the set of states connected by local gates are equidistant to this pair of circles. Moreover, the unentangled or so-called product states are π/4 units away to the maximally entangled states. This is, the unentangled states are the farthest away to the maximally entangled states. In this way, if we define two states to be equivalent if they are connected by local gates, we have that there are as many equivalent classes as points in the interval [0,π/4] with the point 0 corresponding to the maximally entangled states. The point π/4 corresponds to the unentangled states which geometrically are described by a torus. Finally, for every 0

View Accepted Manuscript (DOE)

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1777764

Journal Information:: Quantum Information Processing, Journal Name: Quantum Information Processing Journal Issue: 3 Vol. 20; ISSN 1570-0755

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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