Related papers: Optimal trace-distance bounds for free-fermionic s…
Gaussian states of bosonic quantum systems enjoy numerous technological applications and are ubiquitous in nature. Their significance lies in their simplicity, which in turn rests on the fact that they are uniquely determined by two…
In this paper, we propose a novel truncation method for determining the trace distance between two Gaussian states in fermionic systems. For two fermionic Gaussian states, characterized by their correlation matrices, we consider the von…
Free-fermionic states, also known as matchgates or Gaussian states, are a fundamental class of quantum states due to their efficient classical simulability and their crucial role across various domains of Physics. With the advent of quantum…
The exploration of tomography of bosonic Gaussian states is presumably as old as quantum optics, but only recently, their precise and rigorous study have been moving into the focus of attention, motivated by technological developments. In…
We give an efficient algorithm that learns a non-interacting fermion state, given copies of the state. For a system of $n$ non-interacting fermions and $m$ modes, we show that $O(m^3 n^2 \log(1/\delta) / \epsilon^4)$ copies of the input…
Quantum state tomography, aimed at deriving a classical description of an unknown state from measurement data, is a fundamental task in quantum physics. In this work, we analyse the ultimate achievable performance of tomography of…
The experimental realization of increasingly complex quantum states underscores the pressing need for new methods of state learning and verification. In one such framework, quantum state tomography, the aim is to learn the full quantum…
Continuous-variable quantum systems are central to quantum technologies, with Gaussian states playing a key role due to their broad applicability and simple description via first and second moments. Distinguishing Gaussian states requires…
Measuring the distinguishability between quantum states is a basic problem in quantum information theory. In this paper, we develop optimal quantum algorithms that estimate both the trace distance and the (square root) fidelity between pure…
We study two-state discrimination in chaotic quantum systems. Assuming that one of two $N$-qubit pure states has been randomly selected, the probability to correctly identify the selected state from an optimally chosen experiment involving…
Solving interacting fermionic quantum many-body problems as they are ubiquitous in quantum chemistry and materials science is a central task of theoretical and numerical physics, a task that can commonly only be addressed in the sense of…
The effect of boundaries on the bulk properties of quantum many-body systems is an intriguing subject of study. One can define a boundary effect function, which quantifies the change in the ground state as a function of the distance from…
In the paper of F.A. Mele, A.A. Mele, L. Bittel, J. Eisert, V. Giovannetti, L. Lami, L. Leone, S.F.E. Oliviero, ArXiv:2405.01431, estimates for the trace-norm distance between two quantum Gaussian states in terms of the mean vectors and…
Trace distance and infidelity (induced by square root fidelity), as basic measures of the closeness of quantum states, are commonly used in quantum state discrimination, certification, and tomography. However, the sample complexity for…
Topological phases of matter remain a focus of interest due to their unique properties -- fractionalisation, ground state degeneracy, and exotic excitations. While some of these properties can occur in systems of free fermions, their…
A fundamental task in quantum information is to approximate a pure quantum state in terms of sparse states or, for a bipartite system, states of bounded Schmidt rank. The optimal deterministic approximation in each case is straightforward,…
In this work, we initiate the study of Hamiltonian learning for positive temperature bosonic Gaussian states, the quantum generalization of the widely studied problem of learning Gaussian graphical models. We obtain efficient protocols,…
Continuous-variable systems enable key quantum technologies in computation, communication, and sensing. Bosonic Gaussian states emerge naturally in various such applications, including gravitational-wave and dark-matter detection. A…
We investigate $(k_1,k_2)$-extendibility of fermionic Gaussian states, a property central to quantum correlations and approximations of separability. We show that these states are $(k_1,k_2)$-extendible if and only if they admit a fermionic…
We consider the geometry of quantum states associated with different classes of random matrix Hamiltonians, in particular ensembles that show integrability to chaotic transition in terms of the nearest neighbour energy level spacing…