Related papers: Optimal discrimination between real and complex qu…
We introduce a new notion of a sufficient subalgebra for quantum states: a subalgebra is 2- sufficient for a pair of states $\{\rho_0,\rho_1\}$ if it contains all Bayes optimal tests of $\rho_0$ against $\rho_1$. In classical statistics,…
The area of property testing tries to design algorithms that can efficiently handle very large amounts of data: given a large object that either has a certain property or is somehow "far" from having that property, a tester should…
We describe a quantum scheme to ``color-code'' a set of objects in order to record which one is which. In the classical case, N distinct colors are required to color-code N objects. We show that in the quantum case, only N/e distinct…
Different observers do not have to agree on how they identify a quantum system. We explore a condition based on algorithmic complexity that allows a system to be described as an objective "element of reality". We also suggest an…
Quantum Information Theory, the standard formalism used to represent information contained in quantum systems, is based on complex Hilbert spaces (CQT). It was recently shown that it predicts correlations in quantum networks which cannot be…
Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some…
We provide a detailed analysis of the question: how many measurement settings or outcomes are needed in order to identify a quantum system which is constrained by prior information? We show that if the prior information restricts the system…
The simulation of quantum effects requires certain classical resources, and quantifying them is an important step in order to characterize the difference between quantum and classical physics. For a simulation of the phenomenon of…
This paper is a review of our recent work on three notorious problems of non-relativistic quantum mechanics: realist interpretation, quantum theory of classical properties and the problem of quantum measurement. A considerable progress has…
We propose a test of quantum contextuality for a single three-level system that uses nine projective measurements. It has a form of an inequality that has to be satisfied by any non-contextual theory and which is violated by any quantum…
In this perspective we discuss verification of quantum devices in the context of specific examples, formulated as proposed experiments. Our first example is verification of analog quantum simulators as Hamiltonian learning, where the input…
We introduce a protocol addressing the conformance test problem, which consists in determining whether a process under test conforms to a reference one. We consider a process to be characterized by the set of end-product it produces, which…
The problem of discriminating with minimum error between two mixed quantum states is reviewed, with emphasize on the detection operators necessary for performing the measurement. An analytical result is derived for the minimum probability…
One of the key tasks in physics is to perform measurements in order to determine the state of a system. Often, measurements are aimed at determining the values of physical parameters, but one can also ask simpler questions, such as "is the…
The hypothesis of quantum self-interference is not directly observable, but has at least three necessary implications. First, a quantum entity must have no less than two open paths. Second, the size of the interval between any two…
The quantum decision theory is examined in its simplest form of two-condition two-choice setting. A set of inequalities to be satisfied by any quantum conditional probability describing the decision process is derived. Experimental data…
A core principle of quantum theory is that non-orthogonal quantum states cannot be perfectly distinguished with single-shot measurements. However, it is possible to exclude a subset of non-orthogonal states without error in certain…
Quantum hypothesis testing (QHT) provides an effective method to discriminate between two quantum states using a two-outcome positive operator-valued measure (POVM). Two types of decision errors in a QHT can occur. In this paper we focus on…
There are fundamental limits to the accuracy with which one can determine the state of a quantum system. I give an overview of the main approaches to quantum state discrimination. Several strategies exist. In quantum hypothesis testing, a…
Quantum sensing is commonly described as a constrained optimization problem: maximize the information gained about an unknown quantity using a limited number of particles. Important sensors including gravitational-wave interferometers and…