Catalytic Quantum Teleportation

In this work, we address fundamental limitations of quantum teleportation—the process of transferring quantum information using classical communication and preshared entanglement. We develop a new teleportation protocol based upon the idea of using ancillary entanglement catalytically, i.e., without depleting it. This protocol is then used to show that catalytic entanglement allows for a noiseless quantum channel to be simulated with a quality that could never be achieved using only entanglement from the shared state, even for catalysts with a small dimension. On the one hand, this allows for a more faithful transmission of quantum information using generic states and fixed amount of consumed entanglement. On the other hand, this shows, for the first time, that entanglement catalysis provides a genuine advantage in a generic quantum-information processing task. Finally, we show that similar ideas can be directly applied to study quantum catalysis for more general problems in quantum mechanics. As an application, we show that catalysts can activate so-called passive states, a concept that finds widespread application, e.g., in quantum thermodynamics.

Figure 1

The catalytic subroutine that uses a noisy entangled state as a catalyst to enhance entanglement fraction. (a)–(e) describe subsequent steps of the protocol and (f) the final state of the main system and the catalyst. The catalyst remains unchanged as the system is transformed into a state with a higher entanglement fraction.

Figure 2

The catalytic advantage $\eta (\psi )$ in quantum teleportation. The triangle describes the space of all pure states of two qutrits. In particular, each point $\mathit{\lambda }=({\lambda }_1,{\lambda }_2,{\lambda }_3)$ corresponds to a unique (up to local unitaries) state with Schmidt coefficients $\{{\lambda }_i\}$ for $1\le i\le 3$. The red point corresponds to the example from the main text.