Alice and Bob through a quantum mirror

Abstract

A quantum mirror is a device whose optical response, that is, transmission and reflection, can be controlled by a single qubit. Here, we propose the use of quantum mirrors as nodes in quantum networks. Propagating coherent states mediate the interaction between the control qubits of each quantum mirror. This allows implementing quantum teleportation, quantum state transfer, and entanglement swapping with success probability and average fidelity exponentially approaching unity as the average photon number increases. Furthermore, we show that quantum teleportation exhibits robustness against known sources of error, such as optical path phase difference, photon loss, and reduced quantum mirror reflectivity, presenting a promising alternative towards long-distance quantum communication.

Figures (4)

• Figure 1: (a) Schematic representation of a quantum mirror (QM) interacting with two optical modes. Yellow (purple) states denote transmission (reflection) conditioned on the control atom state $\left|0\right\rangle$ ($\left|1\right\rangle$). (b) Quantum circuit for the teleportation protocol between the control atoms of two QMs. Two optical modes (red) propagate from Bob to Alice, becoming entangled with Bob's control atom upon interaction. The modes then interact with Alice's QM, after which her system is measured. The measurement outcomes are classically communicated to Bob, who applies the appropriate operations to reconstruct the state initially prepared by Alice.
• Figure 2: Average teleportation fidelity $\bar{\mathcal{F}}_{\delta}^{(\alpha)}$ as a function of $\delta$, the phase difference between optical modes, and $|\alpha|^2$, the average number of photons in the propagating field. Area enclosed by the dashed blue lines describe a parameter region where $\bar{\mathcal{F}}_{\delta}^{(\alpha)}$ is greater than 0.95. Area enclosed by the dashed red lines describe a parameter region where $\bar{\mathcal{F}}_{\delta}^{(\alpha)}$ is greater than 0.66, the classical threshold.
• Figure 3: Average teleportation fidelity $\bar{\mathcal{F}}_{\eta}^{(\alpha)}$ as a function of $\eta$, the channel's transmission efficiency, and $|\alpha|^2$, the average number of photons in the propagating field. The area below the dashed line describes a parameter region with average fidelity greater than: 0.95 (blue), 0.80 (purple) and 0.66 (red). The right-hand blue labels indicate the corresponding fiber lengths in kilometers (km) for select values of $\eta$, specially corresponding to the maximum average fidelities achieved along the dashed lines, considering a realistic and state-of-the-art loss rate of $\gamma=6.3\text{kHz}$. Color scale as in Fig. \ref{['fig:delta']}.
• Figure 4: Average fidelities for errors in the amplitude $r$ and phase $\phi_r$ of reflection coefficients, presented for two different input field amplitudes: $\alpha=1.75$ and $\alpha=4$. Panels (a) and (b) depict the impact of errors in the Bob's quantum mirror. Panels (c) and (d) illustrate the effect of errors, assuming no phase errors, for both QMs.