Related papers: Minimum-error discrimination of thermal states
Suppose that the Hamiltonian acting on a quantum system is unknown and one wants to determine what is the Hamiltonian. We show that in general this requires a time $\Delta t$ which obeys the uncertainty relation $\Delta t \Delta H \gtrsim…
Measurements of an object's temperature are important in many disciplines, from astronomy to engineering, as are estimates of an object's spatial configuration. We present the quantum optimal estimator for the temperature of a distant body…
There are two common settings in a quantum-state discrimination problem. One is minimum-error discrimination where a wrong guess (error) is allowed and the discrimination success probability is maximized. The other is unambiguous…
Temperature is a widely used hyperparameter in various tasks involving neural networks, such as classification or metric learning, whose choice can have a direct impact on the model performance. Most of existing works select its value using…
We show a geometric formulation for minimum-error discrimination of qubit states, that can be applied to arbitrary sets of qubit states given with arbitrary a priori probabilities. In particular, when qubit states are given with equal…
It is "conventional wisdom" that the uncertainty of local temperature measurements on equilibrium systems diverges exponentially fast as their temperature $T$ drops to zero. In contrast, some exactly solvable models showcase a more benign…
A measurement strategy is developed for a new kind of hypothesis testing. It assigns, with minimum probability of error, the state of a quantum system to one or the other of two complementary subsets of a set of N given non-orthogonal…
Non-equilibrium states of quantum systems in contact with thermal baths help telling environments with different temperatures or different statistics apart. We extend these studies to a more generic problem that consists in discriminating…
Error probability is a popular and well-studied optimization criterion in discriminating non-orthogonal quantum states. It captures the threat from an adversary who can only query the actual state once. However, when the adversary is able…
Are Gaussian measurements enough to distinguish between Gaussian states? Here, we tackle this question by focusing on the max-relative entropy as an operational distinguishability metric. Given two general multimode Gaussian states, we…
We investigate a state discrimination problem which interpolates minimum-error and unambiguous discrimination by introducing a margin for the probability of error. We closely analyze discrimination of two pure states with general occurrence…
A state discrimination problem in an operational probabilistic theory (OPT) is investigated in diagrammatic terms. It is well-known that, in the case of quantum theory, if a state set has a certain symmetry, then there exists a…
This paper suggests using the configurational temperature $\Tc$ for quantifying how far an active-matter system is from thermal equilibrium. We measure this ``distance'' by the ratio of the systemic temperature $\Ts$ to $\Tc$, where $\Ts$…
Thermometry is a fundamental parameter estimation problem which is crucial in the development process of natural sciences. One way to solve this problem is to the extensive used local thermometry theory, which makes use of the classical and…
Quantum metrology is being gradually studied for weak measurement systems. For weak measurement systems with thermal state pointer, we find that in the displacement space corresponding to imaginary weak values, the maximal QFI after…
Improving the measurement precision of low temperature is significant in fundamental science and advanced quantum technology application. However, the measurement precision of temperature $T$ usually diverges as $T$ tends to 0. Here, by…
We provide a bound on the minimum error when discriminating among quantum states, using the no-signaling principle. The bound is general in that it depends on neither dimensions nor specific structures of given quantum states to be…
We discuss the disturbance by measurements which unambiguously discriminate between given candidate states. We prove that such an optimal measurement necessarily changes distinguishable states indistinguishable when the inconclusive outcome…
We investigate the fundamental and practical precision limits of thermometry in bosonic and fermionic environments by coupling an $N$-level probe to them and continuously monitoring it. Our findings show that the ultimate precision limit,…
In this paper we study the Minimum Error Discrimination problem (MED) for ensembles of linearly independent (LI) states. We define a bijective map from the set of those ensembles to itself and we show that the Pretty Good Measurement (PGM)…