Related papers: Generalized quantum Stein's lemma for mixed source…
The simplest example of a quantum information source with memory is a mixed source which emits signals entirely from one of two memoryless quantum sources with given a priori probabilities. Considering a mixed source consisting of a general…
We consider symmetric hypothesis testing in quantum statistics, where the hypotheses are density operators on a finite-dimensional complex Hilbert space, representing states of a finite quantum system. We prove a lower bound on the…
In the problem of composite hypothesis testing, identifying the potential uniformly most powerful (UMP) unbiased test is of great interest. Beyond typical hypothesis settings with exponential family, it is usually challenging to prove the…
We provide a general result for bounding the difference between point probabilities of integer supported distributions and the translated Poisson distribution, a convenient alternative to the discretized normal. We illustrate our theorem in…
Our capacity to process information depends on the computational power at our disposal. Information theory captures our ability to distinguish states or communicate messages when it is unconstrained with unrivaled beauty and elegance. For…
Channel conversion constitutes a pivotal paradigm in information theory and its applications to quantum physics, providing a unified problem setting that encompasses celebrated results such as Shannon's noisy-channel coding theorem. Quantum…
Generalized t-tests are constructed under weaker than normal conditions. In the first part of this paper we assume only the symmetry (around zero) of the error distribution (i). In the second part we assume that the error distribution is a…
We investigate sampling procedures that certify that an arbitrary quantum state on $n$ subsystems is close to an ideal mixed state $\varphi^{\otimes n}$ for a given reference state $\varphi$, up to errors on a few positions. This task makes…
Symmetry plays a crucial role in quantum physics, dictating the behavior and dynamics of physical systems. In this paper, we develop a hypothesis-testing framework for quantum dynamics symmetry using a limited number of queries to the…
We study binary hypothesis testing for i.i.d. observations under a multiplicative context weight. For the optimal weighted total loss, defined as the sum of weighted type-I and type-II losses, we prove the logarithmic asymptotic $$ L_n^* =…
Mutual information is a measure of the dependence between random variables that has been used successfully in myriad applications in many fields. Generalized mutual information measures that go beyond classical Shannon mutual information…
A recent line of work provides new statistical tools based on game-theory and achieves safe anytime-valid inference without assuming regularity conditions. In particular, the framework of universal inference proposed by Wasserman, Ramdas…
For parameter estimation of continuous and discrete distributions, we propose a generalization of the method of moments (MM), where Stein identities are utilized for improved estimation performance. The construction of these Stein-type…
We revisit the fundamental question of simple-versus-simple hypothesis testing with an eye towards computational complexity, as the statistically optimal likelihood ratio test is often computationally intractable in high-dimensional…
We consider asymptotic hypothesis testing (or state discrimination with asymmetric treatment of errors) between an arbitrary fixed bipartite pure state $\ket{\Psi}$ and the completely mixed state under one-way LOCC (local operations and…
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…
Maximum composite likelihood estimation is a useful alternative to maximum likelihood estimation when data arise from data generating processes (DGPs) that do not admit tractable joint specification. We demonstrate that generic composite…
In the simple quantum hypothesis testing problem, upper bound with asymmetric setting is shown by using a quite useful inequality by Audenaert et al, quant-ph/0610027, which was originally invented for symmetric setting. Using this upper…
Coding and testing schemes for binary hypothesis testing over noisy networks are proposed and their corresponding type-II error exponents are derived. When communication is over a discrete memoryless channel (DMC), our scheme combines…
It is common to model random errors in a classical measurement by the normal (Gaussian) distribution, because of the central limit theorem. In the quantum theory, the analogous hypothesis is that the matrix elements of the error in an…