Related papers: Asymptotic Error Rates in Quantum Hypothesis Testi…
We derived an asymptotic bound the accuracy of the estimation when we use the quantum correlation in the measuring apparatus. It is also proved that this bound can be achieved in any model in the quantum two-level system. Moreover, we show…
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…
The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…
Many results related to quantitative problems in the metric theory of Diophantine approximation are asymptotic, such as the number of rational solutions to certain inequalities grows with the same rate almost everywhere modulo an asymptotic…
In quantum purity amplification, one is given $n$ copies of a noisy quantum state $\rho \in \mathbb{C}^{d \times d}$ and asked to prepare $k$ copies of its principal eigenstate $|v_d\rangle$. Several prior works have derived…
We investigate the spectral statistics of the difference of two density matrices, each of which is independently obtained by partially tracing a random bipartite pure quantum state. We first show how a closed-form expression for the exact…
We consider the problem of detecting the true quantum state among r possible ones, based on measurements performed on n of copies of a finite dimensional quantum system. It is known that the exponent for the rate of decrease of the averaged…
We study quantum soft covering and privacy amplification against quantum side information. The former task aims to approximate a quantum state by sampling from a prior distribution and querying a quantum channel. The latter task aims to…
Information theory has become an increasingly important research field to better understand quantum mechanics. Noteworthy, it covers both foundational and applied perspectives, also offering a common technical language to study a variety of…
Various quantum analogues of the central limit theorem, which is one of the cornerstones of probability theory, are known in the literature. One such analogue, due to Cushen and Hudson, is of particular relevance for quantum optics. It…
We show that measuring any two quantum states by a random POVM, under a suitable definition of randomness, gives probability distributions having total variation distance at least a universal constant times the Frobenius distance between…
We analyze the behavior of estimation errors evaluated by two loss functions, the Hilbert-Schmidt distance and infidelity, in one-qubit state tomography with finite data. We show numerically that there can be a large gap between the…
We formulate a passive quantum detector based on a quantum hypothesis testing framework under the setting of finite sample size. In particular, we exploit the fundamental limits of performance of the passive quantum detector asymptotically.…
New non-asymptotic random coding theorems (with error probability $\epsilon$ and finite block length $n$) based on Gallager parity check ensemble and Shannon random code ensemble with a fixed codeword type are established for discrete input…
Properties of random mixed states of order $N$ distributed uniformly with respect to the Hilbert-Schmidt measure are investigated. We show that for large $N$, due to the concentration of measure, the trace distance between two random states…
The concept of asymptotic correctability of Bell-diagonal quantum states is generalised to elementary quantum systems of higher dimensions. Based on these results basic properties of quantum state purification protocols are investigated…
The decoy-state scheme is the most widely implemented quantum key distribution protocol in practice. In order to account for the finite-size key effects on the achievable secret key generation rate, a rigorous statistical fluctuation…
Quantum metrology is a general term for methods to precisely estimate the value of an unknown parameter by actively using quantum resources. In particular, some classes of entangled states can be used to significantly suppress the…
We characterize the asymptotic performance of nonparametric goodness of fit testing. The exponential decay rate of the type-II error probability is used as the asymptotic performance metric, and a test is optimal if it achieves the maximum…
We consider estimation of a single unknown parameter embedded in a quantum state. Quantum Cram\'er-Rao bound (QCRB) is the ultimate limit of the mean squared error for any unbiased estimator. While it can be achieved asymptotically for a…