We establish the entangling power of a unitary operator on a general finite-dimensional bipartite quantum system with and without ancillas, and give relations between the entangling power based on the von Neumann entropy and the entangling power based on the linear entropy. Significantly, we demonstrate that the entangling power of a general controlled unitary operator acting on two equal-dimensional qudits is proportional to the corresponding operator entanglement if linear entropy is adopted as the quantity representing the degree of entanglement. We discuss the entangling power and operator entanglement of three representative quantum gates on qudits: the SUM, double SUM, and SWAP gates.We establish the entangling power of a unitary operator on a general finite-dimensional bipartite quantum system with and without ancillas, and give relations between the entangling power based on the von Neumann entropy and the entangling power based on the linear entropy. Significantly, we demonstrate that the entangling power of a general controlled unitary operator acting on two equal-dimensional qudits is proportional to the corresponding operator entanglement if linear entropy is adopted as the quantity representing the degree of entanglement. We discuss the entangling power and operator entanglement of three representative quantum gates on qudits: the SUM, double SUM, and SWAP gates.

arXiv:quant-ph/0210156Physical Review AApr 28, 200385 citations

Off-diagonal Geometric Phase of Two-Qubit System

Guo‐Qiang Zhu

International Journal of Theoretical PhysicsAug 17, 20100 citations

Multi-qubit circuits with a simplified entangling gate

Till J. Weinhold, Geoff J. Pryde, Jeremy L. O’Brien +2 more

Dec 5, 20050 citations

Entangling two qudits of arbitrary dimension through light-atomic Faraday interaction

R. Surmay, V. A. Leonov, E. A. Vashukevich

The paper investigates entangling operations acting on two qudits of arbitrary dimension, with one encoded in the states of a spatially multimode optical field, the other in those of atomic collective spin coherence, both carrying orbital angular momentum (OAM). We demonstrate the generation of a wide range of entangling operations within a protocol consisting of two Faraday interactions and a rotation of atomic and light quadratures between them. All generated gates can be represented as rational powers of the d-dimensional gate $SWAP^α_d$ . The probabilities of two-qudit transformations are calculated for various dimensions of the logical space and for different entangling powers of the logical gates.The paper investigates entangling operations acting on two qudits of arbitrary dimension, with one encoded in the states of a spatially multimode optical field, the other in those of atomic collective spin coherence, both carrying orbital angular momentum (OAM). We demonstrate the generation of a wide range of entangling operations within a protocol consisting of two Faraday interactions and a rotation of atomic and light quadratures between them. All generated gates can be represented as rational powers of the d-dimensional gate $SWAP^α_d$. The probabilities of two-qudit transformations are calculated for various dimensions of the logical space and for different entangling powers of the logical gates.

quant-pharXiv:2608.19945Aug 21, 20260 citations

SWAP^α_d

. The probabilities of two-qudit transformations are calculated for various dimensions of the logical space and for different entangling powers of the logical gates.