Photon-assisted entanglement creation by minimum-error generalized quantum measurements in the strong coupling regime

TL;DR

This work addresses the challenge of generating high-fidelity entanglement between distant material qubits for quantum repeaters by leveraging photon-assisted interactions in the strong coupling regime. It analyzes a Ramsey-type protocol where two three-level systems in spatially separated cavities become entangled with a shared optical field that is transferred through a fiber, and then uses an optimal minimum-error POVM to postselect a Bell state $|Psi^+>_{AB}$ of the qubits. The authors show that, in the strong-coupling limit with near-resonant interaction and large mean photon numbers, the field states correlated with the Bell component become nearly orthogonal at suitably chosen interaction times, yielding fidelity $F_{opt}$ approaching unity and a finite, favorable $P_{Bell}$, even as the system scales. Photon loss and dephasing in the fiber modulate these results, reducing fidelity and success probability and introducing oscillations, yet the framework provides a practical route to high-rate, high-fidelity entanglement for hybrid quantum repeater architectures under realistic conditions.

Abstract

We explore possibilities of entangling two distant material qubits with the help of an optical radiation field in the regime of strong quantum electrodynamical coupling with almost resonant interaction. For this purpose the optimum generalized field measurements are determined which are capable of preparing a two-qubit Bell state by postselection with minimum error. It is demonstrated that in the strong-coupling regime some of the recently found limitations of the non-resonant weak-coupling regime can be circumvented successfully due to characteristic quantum electrodynamical quantum interference effects. In particular, in the absence of photon loss it is possible to postselect two-qubit Bell states with fidelities close to unity by a proper choice of the relevant interaction time. Even in the presence of photon loss this strong-coupling regime offers interesting perspectives for creating spatially well-separated Bell pairs with high fidelities, high success probabilities, and high repetition rates which are relevant for future realizations of quantum repeaters.

Figures (5)

• Figure 1: Schematic representation of photon-assisted entanglement creation: The field state inside cavity $A$ interacts almost resonantly for a short time $\tau$ with the material quantum system inside cavity $A$. The resulting photon state is transferred in a time $T = L/c\gg \tau$ to cavity $B$ by propagation through a connecting optical fiber. ($c$ is the propagation speed in the optical fiber.) By appropriate engineering of the cavity-fiber couplings this quantum state transfer can be achieved perfectly. After this quantum state transfer an analogous second almost resonant short interaction takes place for a time $\tau$. After this Ramsey-type interaction scenario the photon state of cavity $B$ is measured by a minimum-error two-valued positive operator-valued measure (POVM measurement) with measurement results $m\in \{1,0\}$. The measurement result $m=1$ prepares both material quantum systems approximately in a Bell state $|\Psi^+\rangle$ with success probability $P_{Bell}$ and with fidelity $F_{opt}$.
• Figure 2: Dependence of characteristic quantities on the interaction time $\tau$ in the strong coupling limit $\Delta =0$: The success probability for postselecting a Bell state $|\Psi^+\rangle_{AB}$ of Eq.(\ref{['PBell']}) (top); the minimum-error probability of the POVM measurement of the field of Eq.(\ref{['EMin']}) (middle); the fidelity of the postselected Bell state $|\Psi^+\rangle_{AB}$ of Eq.(\ref{['OptFid']}) (bottom).
• Figure 3: Dependence of characteristic quantities on the interaction time $\tau$ in the weak coupling limit $\Delta = 5 \overline{\Omega}_0$: The success probability for postselecting a Bell state $|\Psi^+\rangle_{AB}$ of Eq.(\ref{['PBell']}) (top); the minimum-error probability of the POVM measurement of the field of Eq.(\ref{['EMin']}) (middle); the fidelity of the postselected Bell state $|\Psi^+\rangle_{AB}$ of Eq.(\ref{['OptFid']}) (bottom).
• Figure 4: Fidelity of the postselected Bell state $|\Psi^+\rangle_{AB}$ of Eq.(\ref{['OptFid']}) in the weak coupling limit $\Delta = 5 \overline{\Omega}_0$ for long interaction times: The effects of dephasing lead to an asymptotic increase to unity
• Figure 5: Dependence of characteristic quantities on the propagation time $T$ ( in units of $1/\gamma$) through a lossy optical fiber in the strong coupling limit $\Delta = 0$ for an interaction time $\tau = (23/4) 2\pi/\overline{\Omega}_0$: The success probability for postselecting a Bell state $|\Psi^+\rangle_{AB}$ of Eq.(\ref{['PBell']}) (top); the minimum-error probability of the POVM measurement of the field of Eq.(\ref{['EMin']}) (middle); the fidelity of the postselected Bell state $|\Psi^+\rangle_{AB}$ of Eq.(\ref{['OptFid']}) (bottom).