arXiv subjects

Hjalmar Rall

Publications and source records attributed to Hjalmar Rall.

4 recordsLinked to original sources

arXiv2026

Gaussian Dynamical Quantum State Tomography

Standard quantum state tomography assumes sufficient control of a system to measure an informationally complete set of observables. Dynamical quantum state tomography (DQST) presents an alternative: given a system with known dynamics and a single fixed observable, it almost always suffices to control only the time at which each i.i.d. copy of the system is measured. This work presents an analogous scheme for tomography of multi-mode Bosonic Gaussian states undergoing Gaussian evolution, using a fixed single-mode homodyne measurement and only assuming control of the time of measurement. I prove that the scheme enables tomography for all discrete homogenous Gaussian evolutions and Gaussian quantum dynamical semigroups except for a null set which includes unitary evolution. When the state is known to be pure, a smaller number of measurement times is shown to be sufficient.

quant-ph↗

arXiv2025

Efficiently Computable Limits on EPR Pair Generation in Quantum Broadcast Channels

We investigate the generation of EPR pairs between three observers in a general causally structured setting, where communication occurs via a noisy quantum broadcast channel. The most general quantum codes for this setup take the form of tripartite quantum channels. Since the receivers are constrained by causal ordering, additional temporal relationships naturally emerge between the parties. These causal constraints enforce intrinsic no-signalling conditions on any tripartite operation, ensuring that it constitutes a physically realizable quantum code for a quantum broadcast channel. We analyze these constraints and, more broadly, characterize the most general quantum codes for communication over such channels. We examine the capabilities of codes that are fully no-signalling among the three parties, positive partial transpose (PPT)-preserving, or both, and derive simple semidefinite programs to compute the achievable entanglement fidelity. We then establish a hierarchy of semidefinite programming converse bounds -- both weak and strong -- for the capacity of quantum broadcast channels for EPR pair generation, in both one-shot and asymptotic regimes. Notably, in the special case of a point-to-point channel, our strong converse bound recovers and strengthens existing results. Finally, we demonstrate how the PPT-preserving codes we develop can be leveraged to construct PPT-preserving entanglement combing schemes, and vice versa.

quant-ph↗

arXiv2025

Quantum tomography from the evolution of a single expectation

We investigate the possibility of performing full quantum tomography based on the homogeneous time evolution of a single expectation value. Remarkably, every non-trivial binary measurement evolved by any quantum channel, except for a null set, in principle enables full quantum state tomography. We show that this remains true when restricted to Lindblad semigroups, although unitary evolution -- even with added simply depolarizing noise -- is insufficient beyond the qubit case, highlighting the necessity of non-trivial noise. We establish an analog of Takens' embedding theorem for quantum channels, which incorporates prior information into the framework. We also provide estimation bounds for finite statistics and analyze the feasibility of recovering an infinite time series of expectation values from a finite one using only spectral properties of the evolution.

math-ph↗

arXiv2024

Demonstration of teleportation across a quantum network code

In quantum networks an important goal is to reduce resource requirements for the transport and communication of quantum information. Quantum network coding presents a way of doing this by distributing entangled states over a network that would ordinarily exhibit contention. In this work, we study measurement-based quantum network coding (MQNC), which is a protocol particularly suitable for noisy intermediate-scale quantum devices. In particular, we develop techniques to adapt MQNC to state-of-the-art superconducting processors and subsequently demonstrate successful teleportation of quantum information, giving new insight into MQNC in this context after a previous study was not able to produce a useful degree of entanglement. The teleportation in our demonstration is shown to occur with fidelity higher than could be achieved via classical means, made possible by considering qubits from a polar cap of the Bloch Sphere. We also present a generalization of MQNC with a simple mapping onto the heavy-hex processor layout and a direct mapping onto a proposed logical error-corrected layout. Our work provides some useful techniques for testing and successfully carrying out quantum network coding.

quant-ph↗