Related papers: Upper bounds on the error probabilities and asympt…
Quantum channel discrimination is a fundamental problem in quantum information science. In this study, we consider general quantum channel discrimination problems, and derive the lower bounds of the error probability. Our lower bounds are…
Detecting the presence of multiple incoherent sources is a fundamental and challenging task for quantum imaging, especially within sub-Rayleigh region. In this paper, the discrimination of one-versus-two point-like incoherent sources in…
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…
We prove a tight and close-to-optimal lower bound on the effectiveness of local quantum measurements (without classical communication) at discriminating any two bipartite quantum states. Our result implies, for example, that any two…
Coherent states of light, and methods for distinguishing between them, are central to all applications of laser light. We obtain the ultimate quantum limit on the error probability exponent for discriminating among any M multimode…
The laws of quantum mechanics place fundamental limits on the accuracy of measurements and therefore on the estimation of unknown parameters of a quantum system. In this work, we prove lower bounds on the size of confidence regions reported…
We study quantum hypothesis testing between orthogonal states under restricted local measurements in the many-copy scenario. For testing arbitrary multipartite entangled pure state against its orthogonal complement state via the local…
A central problem in Binary Hypothesis Testing (BHT) is to determine the optimal tradeoff between the Type I error (referred to as false alarm) and Type II (referred to as miss) error. In this context, the exponential rate of convergence of…
We show that $n = \Omega(rd/\varepsilon^2)$ copies are necessary to learn a rank $r$ mixed state $\rho \in \mathbb{C}^{d \times d}$ up to error $\varepsilon$ in trace distance. This matches the upper bound of $n = O(rd/\varepsilon^2)$ from…
We study various error exponents in a binary hypothesis testing problem and extend recent results on the quantum Chernoff and Hoeffding bounds for product states to a setting when both the null-hypothesis and the counter-hypothesis can be…
The trade-off between the two types of errors in binary state discrimination may be quantified in the asymptotics by various error exponents. In the case of simple i.i.d. hypotheses, each of these exponents is equal to a divergence…
The discrimination between non-orthogonal quantum states plays a pivotal role in quantum information processing and quantum technology. Strategies that minimize the error probability are of particular importance, but they are only known for…
The problem of quickest detection of an anomalous process among M processes is considered. At each time, a subset of the processes can be observed, and the observations from each chosen process follow two different distributions, depending…
This paper is concerned with estimating the intersection point of two densities, given a sample of both of the densities. This problem arises in classification theory. The main results provide lower bounds for the probability of the…
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…
We present a theoretical study of minimum error probability discrimination, using quantum- optical probe states, of M optical phase shifts situated symmetrically on the unit circle. We assume ideal lossless conditions and full freedom for…
This paper investigates symmetric composite binary quantum hypothesis testing (QHT), where the goal is to determine which of two uncertainty sets contains an unknown quantum state. While asymptotic error exponents for this problem are…
The generalized Poor-Verdu error lower bound for multihypothesis testing is revisited. Its asymptotic expression is established in closed-form as its tilting parameter grows to infinity. It is also shown that the asymptotic generalized…
Unambiguous discrimination and exact cloning reduce the square-overlap between quantum states, exemplifying the more general type of procedure we term state separation. We obtain the maximum probability with which two equiprobable quantum…
A general scenario for an $N$-sequential conclusive state discrimination introduced recently in Loubenets and Namkung [arXiv:2102.04747] can provide a multipartite quantum communication realizable in the presence of a noise. In the present…