Related papers: Improved classical shadows from local symmetries i…

We study the estimation of the overlap between two unknown pure quantum states of a finite dimensional system, given $M$ and $N$ copies of each type. This is a fundamental primitive in quantum information processing that is commonly…

In recent years there has been significant interest in understanding the statistical complexity of learning from quantum data under the constraint that one can only make unentangled measurements. While a key challenge in establishing tight…

Verifying uniform conditions over continuous spaces through random sampling is fundamental in machine learning and control theory, yet classical coverage analyses often yield conservative bounds, particularly at small failure probabilities.…

Bayesian shrinkage methods have generated a lot of recent interest as tools for high-dimensional regression and model selection. These methods naturally facilitate tractable uncertainty quantification and incorporation of prior information.…

The ability of quantum computers to directly manipulate and analyze quantum states stored in quantum memory allows them to learn about aspects of our physical world that would otherwise be invisible given a modest number of measurements.…

This paper studies finite-sample set-membership identification for discrete-time bilinear systems under bounded symmetric log-concave disturbances. Compared with existing finite-sample results for linear systems and related analyses under…

A bosonic state is commonly considered nonclassical (or quantum) if its Glauber-Sudarshan $P$ function is not a classical probability density, which implies that only coherent states and their statistical mixtures are classical. We quantify…

Motivated by a similar approach for Born-Oppenheimer molecular dynamics, this paper proposes an extended "shadow" Lagrangian density for quantum states of superfluids. The extended Lagrangian contains an additional field variable that is…

In quantum mechanics, wave functions and density matrices represent our knowledge about a quantum system and give probabilities for the outcomes of measurements. If the combined dynamics and measurements on a system lead to a density matrix…

We analyse orthogonal bases in a composite $N\times N$ Hilbert space describing a bipartite quantum system and look for a basis with optimal single-sided mutual state distinguishability. This condition implies that in each subsystem the…

Building upon a recent analysis of the measurement process in Hamiltonian mechanics, this article investigates the Bayesian epistemology of classical physics -- the landscape of accessible probability distributions over phase space. I prove…

The estimation of high dimensional quantum states is an important statistical problem arising in current quantum technology applications. A key example is the tomography of multiple ions states, employed in the validation of state…

The Schatten-p quasi-norm $(0<p<1)$ is usually used to replace the standard nuclear norm in order to approximate the rank function more accurately. However, existing Schatten-p quasi-norm minimization algorithms involve singular value…

We propose a tomographic protocol for estimating any $ k $-body reduced density matrix ($ k $-RDM) of an $ n $-mode fermionic state, a ubiquitous step in near-term quantum algorithms for simulating many-body physics, chemistry, and…

We explore the role of $\textit{collective measurements}$ on precision in estimation of a single parameter. Collective measurements are represented by observables which commute with all permutations of the probe particles. We show that with…

Spurious couplings and decoherence degrade the performance of solid-state quantum processors, demanding careful design, calibration, and mitigation protocols. These strategies often rely on characterization of the idling processor, but…

There has been a surge of progress in recent years in developing algorithms for testing and learning quantum states that achieve optimal copy complexity. Unfortunately, they require the use of entangled measurements across many copies of…

Schur-Weyl duality is a powerful tool in representation theory which has many applications to quantum information theory. We provide a generalization of this duality and demonstrate some of its applications. In particular, we use it to…

We investigate the role of a statistical complexity measure to assign equilibration in isolated quantum systems. While unitary dynamics preserve global purity, expectation values of observables often exhibit equilibration-like behavior,…

There has been significant interest in understanding how practical constraints on contemporary quantum devices impact the complexity of quantum learning. For the classic question of tomography, recent work tightly characterized the copy…