Related papers: Rate-Limited Quantum-to-Classical Optimal Transpor…
In this essay, we discuss the notion of optimal transport on geodesic measure spaces and the associated (2-)Wasserstein distance. We then examine displacement convexity of the entropy functional on the space of probability measures. In…
We determine the rate region of the Gaussian scalar-help-vector source-coding problem under a covariance matrix distortion constraint. The rate region is achieved by a Gaussian achievable scheme. We introduce a novel outer bounding…
Quantum mode parameter estimation determines parameters governing the shape of electromagnetic modes occupied by a quantum state of radiation. Canonical examples, time delays and frequency shifts, underpin radar, lidar, and optical clocks.…
Dissipation in quantum many-body systems provides a more general and experimentally realistic perspective on particle transport than closed quantum systems. In this work, we determine the maximal speed of macroscopic particle transport in…
In this paper, we revisit the sequential source coding framework to analyze fundamental performance limitations of discrete-time stochastic control systems subject to feedback data-rate constraints in finite-time horizon. The basis of our…
Consider the following communication scenario. An encoder observes a stochastic process and causally decides when and what to transmit about it, under a constraint on the expected number of bits transmitted per second. A decoder uses the…
In quantum mechanics, a fundamental law prevents quantum communications to simultaneously achieve high rates and long distances. This limitation is well known for point-to-point protocols, where two parties are directly connected by a…
We investigate the transport of energy, magnetization, etc. in several finite one-dimensional (1D) quantum systems only by solving the corresponding time-dependent Schroedinger equation. We explicitly renounce on any other…
We present a novel method for efficiently computing optimal transport maps and Wasserstein barycenters in high-dimensional spaces. Our approach uses conditional normalizing flows to approximate the input distributions as invertible…
In this thesis, I reflect on quantum instruments that measure the state of pure finite dimensional quantum systems. As the Heisenberg principle dictates, there exists a joint restriction to the information gain and distortion by measurement…
Quantum teleportation is a quantum communication primitive that allows a long-distance quantum channel to be built using pre-shared entanglement and one-way classical communication. However, the quality of the established channel crucially…
We present a noncommutative optimal transport framework for quantum channels acting on von Neumann algebras. Our central object is the Lipschitz cost measure, a transportation-inspired quantity that evaluates the minimal cost required to…
We present a scalable algorithm for solving the transport equation in two and three spatial dimensions for variable grid sizes and discrete velocities on a fault-tolerant universal quantum computer. As a proof of concept of our quantum…
We study the Kimble-Braunstein continuous-variable quantum teleportation with the quantum channel physically realized in the turbulent atmosphere. In this context, we examine the applicability of different strategies preserving the Gaussian…
An important part of the information theory folklore had been about the output statistics of codes that achieve the capacity and how the empirical distributions compare to the output distributions induced by the optimal input in the channel…
We present a full experimental characterization of continuous variable quantum communication channels established by shared entanglement together with local operations and classical communication. The resulting teleportation channel was…
One of the primary goals of information theory is to provide limits on the amount of information it is possible to send through various types of communication channels, and to understand the encoding methods that will allow one to achieve…
We consider channel coding for Gaussian channels with the recently introduced mean and variance cost constraints. Through matching converse and achievability bounds, we characterize the optimal first- and second-order performance. The main…
The efficacy of a communication network hinges upon both its physical architecture and the protocols that are employed within it. In the context of quantum communications, there exists a fundamental rate-loss tradeoff for point-to-point…
An analogue of the quadratic Wasserstein (or Monge-Kantorovich) distance between Borel probability measures on $\mathbf{R}^d$ has been defined in [F. Golse, C. Mouhot, T. Paul: Commun. Math. Phys. 343 (2015), 165-205] for density operators…