Entanglement types for two-qubit states with real amplitudes
- 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<π/4 the point d corresponds to a disjoint pair of torus. Finally, we also show how this geometrical interpretation allows to clearly see that any pair of two-qubit states with real amplitudes can be connected with a circuit that only has single-qubit gates and one controlled-Z gate.
- 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, Vol. 20, Issue 3; ISSN 1570-0755
- Publisher:
- SpringerCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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