Related papers: On estimates of trace-norm distance between quantu…
The aim of the present note is to show that the method of our paper ArXiv:2408.11400 with minor extra efforts can be extended to obtain upper bounds for the Bures distance between quantum Gaussian states. We argue that these bounds are…
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…
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…
We locate the set of pairs $(\rho_{1},\rho_{2})$ of Gaussian states of a single mode electromagnetic field that exhibit maximal trace distance subject to the energy constraint $\langle a^{\dagger}a \rangle_{\rho_{1}}=\langle a^{\dagger}a…
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…
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…
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…
Quantum state tomography, a fundamental tool for quantum physics, usually requires a number of state copies that scale exponentially with the system size, owing to the intricate quantum correlations between subsystems. We show that, in…
Gaussian states are widely regarded as one of the most relevant classes of continuous-variable (CV) quantum states, as they naturally arise in physical systems and play a key role in quantum technologies. This motivates a fundamental…
Free-fermionic states, also known as fermionic Gaussian states, represent an important class of quantum states ubiquitous in physics. They are uniquely and efficiently described by their correlation matrix. However, in practical…
This paper reviews recent advances in quantum learning theory for continuous-variable (CV) systems. Quantum learning theory investigates how to extract classical information from quantum systems as efficiently as possible. CV systems are…
Distances between quantum states are reviewed within the framework of the tomographic-probability representation. Tomographic approach is based on observed probabilities and is straightforward for data processing. Different states are…
We provide a bound for the trace distance between two quantum states. The lower bound is based on the superfidelity, which provides the upper bound on quantum fidelity. One of the advantages of the presented bound is that it can be…
Given a positive integer k, it is natural to ask for a formula for the distance between a given density matrix (i.e., mixed quantum state) and the set of density matrices of rank at most k. This problem has already been solved when…
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…
In this paper, a new measurement to compare two large-scale graphs based on the theory of quantum probability is proposed. An explicit form for the spectral distribution of the corresponding adjacency matrix of a graph is established. Our…
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…
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 analyze the Uhlmann fidelity of a pair of $n$-mode Gaussian states of the quantum radiation field. This quantity is shown to be the product of an exponential function depending on the relative average displacement and a factor fully…
We propose a new generalization to quantum states of the Wasserstein distance, which is a fundamental distance between probability distributions given by the minimization of a transport cost. Our proposal is the first where the transport…