Noise Decoupling for State Transfer in Continuous Variable Systems

TL;DR

A noise decoupling protocol is proposed to manipulate the noise channels generated by linear and quadratic polynomials of creation and annihilation operators, to achieve an identity channel, hence the term noiseDecoupling.

Abstract

We consider a toy model of noise channels, given by a random mixture of unitary operations, for state transfer problems with continuous variables. Assuming that the path between the transmitter node and the receiver node can be intervened, we propose a noise decoupling protocol to manipulate the noise channels generated by linear and quadratic polynomials of creation and annihilation operators, to achieve an identity channel, hence the term noise decoupling. For random constant noise, the target state can be recovered while for the general noise profile, the decoupling can be done when the interventions are fast compared to the noise. We show that the state at the transmitter can be written as a convolution of the target state and a filter function characterizing the noise and the manipulation scheme. We also briefly discuss that a similar analysis can be extended to the case of higher-order polynomial generators. Finally, we demonstrate the protocols by numerical calculations.

Figures (5)

• Figure 1: Schematic of state transfer through a noisy channel with noise decoupling protocols. In (a) it is a generic setup of the problem in which the state $\rho(0)$ is transferred from a transmitter node to the receiver node at the other end of the path $\lambda,$ and the receiver will obtain a state $\rho(\vert\lambda\vert).$ The noise parameter can be described as a complex plane (or more than a single plane) attached to each point on the propagating path, which can be illustrated as a plane orthogonal to the propagating direction. The circle cross symbols depict the insertions of decoupling operators along the path where their locations are denoted by the path length parameter $\ell.$ When the decoupling operators cannot be placed along the communication path, e.g. the transfer of state from a ground station to a satellite in (b), one can adopt a repeating forward-backward method in which two agents transfer the state back and forth and apply decoupling operators before sending at intermediate time steps. The combined transfers can be considered as a single transfer with noise decoupling intervention.
• Figure 2: Numerical demonstration of noise suppression of random displacement. The top row shows the Wigner function of (a) the vacuum state, the initial state at $\ell=0$, (b) the average of $200$ trajectories of the final state in the lack of intervention at $\ell=|\lambda|$, and (c) the average of $200$ trajectories of the final state with the intervention at $\ell=|\lambda|$. Note that the asymmetry in (b) is due to the finite number of trajectories. The dashed circle is a contour for the vacuum state where the Wigner function is at $10$ percent of its maximum. We re-sketched the same circle on (b) and (c) for ease of comparison. (d) shows the Fidelity between the state at $\ell/|\lambda|$ and initial state. Blue color represents fidelity without intervention and green represents intervention. Thin lines are for individual trajectories of noise and the blue(green) thick line shows the average Fidelity without(with) intervention.
• Figure 3: Demonstration of noise suppression of random squeezing noise. The details are the same as Figure \ref{['fig:DisNoise']}.
• Figure 4: Demonstration of noise suppression of combined displacement and squeezing noise. The details are the same as Figure \ref{['fig:DisNoise']}.the
• Figure 5: This shows improvement of fidelity vs. the number of interventions for Squeezing noise (orange squares), Displacement noise (blue circles) and combined displacement and squeezing noise (green triangles). Data points are the result of the simulation and solid lines are logistic curve fit to data.