Related papers: Towards Quantum Universal Hypothesis Testing
Quantum Mechanics (QM) is a quantum probability theory based on the density matrix. The possibility of applying classical probability theory, which is based on the probability distribution function(PDF), to describe quantum systems is…
Identifying symmetries in quantum dynamics, such as identity or time-reversal invariance, is a crucial challenge with profound implications for quantum technologies. We introduce a unified framework combining group representation theory and…
Improved measurement techniques are central to technological development and foundational scientific exploration. Quantum optics relies upon detectors sensitive to non-classical features of light, enabling precise tests of physical laws and…
It is a fundamental prediction of quantum theory that states of physical systems are described by complex vectors or density operators on a Hilbert space. However, many experiments admit effective descriptions in terms of other state…
Annealing approach to quantum tomography is theoretically proposed. First, based on the maximum entropy principle, we introduce classical parameters to combine "quantum models (or quantum states)" given a prior for potentially representing…
Quantum computation has been growing rapidly in both theory and experiments. In particular, quantum computing devices with a large number of qubits have been developed by IBM, Google, IonQ, and others. The current quantum computing devices…
We address a problem of identifying a given pure state with one of two reference pure states, when no classical knowledge on the reference states is given, but a certain number of copies of them are available. We assume the input state is…
We build a general quantum state tomography framework that makes use of machine learning techniques to reconstruct quantum states from a given set of coincidence measurements. For a wide range of pure and mixed input states we demonstrate…
We propose a general method for constructing hypothesis tests and confidence sets that have finite sample guarantees without regularity conditions. We refer to such procedures as "universal." The method is very simple and is based on a…
A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum…
Modern quantum engineering techniques enabled successful foundational tests of quantum mechanics. Yet, the universal validity of quantum postulates is an open question. Here we propose a new theoretical framework of Q-data tests, which…
Hypothesis test plays a key role in uncertain statistics based on uncertain measure. This paper extends the parametric hypothesis of a single uncertain population to multiple cases, thereby addressing a broader range of scenarios. First, an…
Estimating observable expectation values in eigenstates of quantum systems has a broad range of applications and is an area where early fault-tolerant quantum computers may provide practical quantum advantage. We develop a hybrid…
Stochastic models for quantum state reduction give rise to statistical laws that are in many respects in agreement with those of standard quantum measurement theory. Here we construct a counterexample involving a Hamiltonian with degenerate…
We introduce a rigorous and sensitive significance test for hyperuniformity that yields reliable results even from a single sample. Our approach is based on a detailed analysis of the empirical Fourier transform of a stationary point…
Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional condition on its rate of increase compared to the sample size. On the…
Quantum phase classification is a fundamental problem in quantum many-body physics, traditionally approached using order parameters or quantum machine learning techniques such as quantum convolutional neural networks (QCNNs). However, these…
When used in quantum state estimation, projections onto mutually unbiased bases have the ability to maximize information extraction per measurement and to minimize redundancy. We present the first experimental demonstration of quantum state…
As quantum technologies advance, the ability to generate increasingly large quantum states has experienced rapid development. In this context, the verification and estimation of large entangled systems represents one of the main challenges…
In this thesis we study the problem of unambiguously discriminating two mixed quantum states. We first present reduction theorems for optimal unambiguous discrimination of two generic density matrices. We show that this problem can be…