[Paper Review] Non-Markovianity-assisted optimal continuous variable quantum teleportation

Gianpaolo Torre, Fabrizio Illuminati|arXiv (Cornell University)|May 9, 2018

Quantum Information and Cryptography29 references3 citations

TL;DR

This paper demonstrates that non-Markovian quantum channels can significantly enhance continuous-variable quantum teleportation fidelity by inducing a time-dependent phase shift in the two-mode squeezed resource state. By optimizing this phase—dictated by the channel's non-Markovianity—teleportation fidelity approaches unity at finite squeezing and short transit times, enabling near-perfect state transfer in realistic, engineered environments.

ABSTRACT

We study the continuous-variable (CV) quantum teleportation protocol in the case that one of the two modes of the shared entangled resource is sent to the receiver through a Gaussian Quantum Brownian Motion noisy channel. We show that if the channel is engineered in a non-Markovian regime, the information backflow from the environment induces an extra dependance of the phase of the two-mode squeezing of the shared Gaussian entangled resource on the transit time along the channel of the shared mode sent to the receiver. Optimizing over the non-Markovianity dependent phase of the squeezing yields a significant enhancement of the teleportation fidelity. For short enough channel transit times, essentially unit fidelity is achieved at realistic, finite values of the squeezing amplitude for a sufficiently large degree of the channel non-Markovianity.

Motivation & Objective

• To investigate how non-Markovian dynamics in a Gaussian quantum Brownian motion (QBM) channel affects continuous-variable quantum teleportation fidelity.
• To explore whether engineered memory effects in the environment can be leveraged to enhance teleportation performance in realistic, noisy settings.
• To establish a quantitative link between channel non-Markovianity and the optimal phase of the shared entangled resource for maximal fidelity.
• To demonstrate that finite squeezing and short transit times can achieve near-unit fidelity when non-Markovianity is sufficiently large.
• To clarify the role of non-Markovianity measures in optimizing teleportation protocols via phase control of the entangled resource.

Proposed method

• Model the teleportation protocol with one mode of a two-mode squeezed state propagating through a non-Markovian QBM channel using a time-dependent covariance matrix formalism.
• Derive the evolved covariance matrix of the shared resource state under non-Markovian dynamics, incorporating time-dependent phase and decoherence effects via matrices $X(t)$, $Y(t)$, and the symplectic transformation $R^{-1}(t)$.
• Express the teleportation fidelity in terms of the optimized squeezing phase $\phi$, which depends on the channel transit time $\delta\tau$ and the non-Markovianity of the channel.
• Utilize a non-Markovianity measure based on the violation of divisibility in the quantum dynamical map, defined via the negative eigenvalues of the intermediate map's CP condition.
• Compute the logarithmic negativity of the shared resource state to quantify entanglement degradation under non-Markovian noise.
• Optimize the fidelity over the phase $\phi$ as a function of $\delta\tau$ and the channel’s non-Markovianity, derived from the system-bath coupling parameters $\omega_0$ and $\omega_c$.

Experimental results

Research questions

• RQ1 Can non-Markovian dynamics in a noisy channel enhance the fidelity of continuous-variable quantum teleportation?
• RQ2 How does the time-dependent phase of the two-mode squeezed state—induced by channel memory effects—affect teleportation performance?
• RQ3 What is the quantitative relationship between the degree of non-Markovianity and the optimal phase for maximizing fidelity?
• RQ4 Can near-unit fidelity be achieved with finite, realistic squeezing amplitudes under non-Markovian conditions?
• RQ5 How does the non-Markovianity measure based on divisibility violation correlate with the phase-optimized teleportation fidelity?

Key findings

• Non-Markovianity induces a time-dependent phase shift in the two-mode squeezed state's phase, which becomes a tunable parameter for fidelity optimization.
• Optimizing the squeezing phase $\phi$ based on the channel transit time $\delta\tau$ and non-Markovianity leads to a significant enhancement in teleportation fidelity.
• For sufficiently short transit times and high non-Markovianity, teleportation fidelity approaches unity even at finite squeezing amplitudes.
• The fidelity enhancement arises from information backflow in the non-Markovian channel, which counteracts decoherence effects on the shared entangled resource.
• The non-Markovianity measure based on divisibility violation correlates strongly with the optimal phase and fidelity improvement, confirming its relevance for protocol optimization.
• The logarithmic negativity of the shared state remains high under optimized conditions, indicating robust entanglement preservation despite noise.