Related papers: An invitation to the sample complexity of quantum …

We propose a sampling-based simulation for fault-tolerant quantum error correction under coherent noise. A mixture of incoherent and coherent noise, possibly due to over-rotation, is decomposed into Clifford channels with a quasiprobability…

Standard approaches to quantum statistical inference rely on measurements that induce a collapse of the wave function, effectively consuming the quantum state to extract information. In this work, we investigate the fundamental limits of…

Quantum computers are now on the brink of outperforming their classical counterparts. One way to demonstrate the advantage of quantum computation is through quantum random sampling performed on quantum computing devices. However, existing…

By repeated trials, one can determine the fairness of a classical coin with a confidence which grows with the number of trials. A quantum coin can be in a superposition of heads and tails and its state is most generally a density matrix.…

We consider sequential hypothesis testing between two quantum states using adaptive and non-adaptive strategies. In this setting, samples of an unknown state are requested sequentially and a decision to either continue or to accept one of…

In this work, we show that reconstructing a sparse signal from quantized compressive measurement can be achieved in an unified formalism whatever the (scalar) quantization resolution, i.e., from 1-bit to high resolution assumption. This is…

Although there are many ideas for the formulations of statistical hypothesis testing, we consider that the likelihood ratio test is the most reasonable and orthodox. However, it is not handy, and thus, it is not usual in elementary books.…

This work studies post-training parameter quantization in large language models (LLMs). We introduce quantization with incoherence processing (QuIP), a new method based on the insight that quantization benefits from $\textit{incoherent}$…

I propose a general quantum hypothesis testing theory that enables one to test hypotheses about any aspect of a physical system, including its dynamics, based on a series of observations. For example, the hypotheses can be about the…

Determining the presence of a potential optical source in the interest region is important for an imaging system and can be achieved by using hypothesis testing. The previous studies assume that the potential source is completely…

Fast, reliable logical operations are essential for realizing useful quantum computers. By redundantly encoding logical qubits into many physical qubits and using syndrome measurements to detect and correct errors, one can achieve low…

We address the issue of reducing the resource required to compute information-theoretic quantum correlation measures like quantum discord and quantum work deficit in two qubits and higher dimensional systems. We show that determination of…

Recently, it is well recognized that hypothesis testing has deep relations with other topics in quantum information theory as well as in classical information theory. These relations enable us to derive precise evaluation in the…

Martingale concentration inequalities constitute a powerful mathematical tool in the analysis of problems in a wide variety of fields ranging from probability and statistics to information theory and machine learning. Here we apply…

In the asymptotic theory of quantum hypothesis testing, the minimal error probability of the first kind jumps sharply from zero to one when the error exponent of the second kind passes by the point of the relative entropy of the two states…

Quantum learning from state samples is often benchmarked in a fixed-budget paradigm, relating error to a prescribed number of copies. We instead adopt a stopping-time viewpoint: in minimal-feedback learning, the learning completion can be…

Quantum hypothesis testing is a central task in the entire field of quantum information theory. Understanding its ultimate limits will give insight into a wide range of quantum protocols and applications, from sensing to communication.…

Quantum hypothesis testing is one of the most basic tasks in quantum information theory and has fundamental links with quantum communication and estimation theory. In this paper, we establish a formula that characterizes the decay rate of…

In this paper we present a new approach for testing QM against the realism aspect of hidden variable theory (HVT). We consider successive measurements of non-commuting operators on a input spin $s$ state. The key point is that, although…

Quantum computing promises polynomial and exponential speedups in many domains, such as unstructured search and prime number factoring. However, quantum programs yield probabilistic outputs from exponentially growing distributions and are…