Related papers: Guesswork with Quantum Side Information
Heisenberg's uncertainty principle provides a fundamental limitation on an observer's ability to simultaneously predict the outcome when one of two measurements is performed on a quantum system. However, if the observer has access to a…
The states of the qubit, the basic unit of quantum information, are $2 \times 2$ positive semi-definite Hermitian matrices with trace 1. We contribute to the program to axiomatize quantum mechanics by characterizing these states in terms of…
Ultrafast physical random bit generation at hundreds of Gb/s rates, with verified randomness, is a crucial ingredient in secure communication and have recently emerged using optics based physical systems. Here we examine the inverse problem…
We give an operational meaning to the min-entropy of a quantum state as a resource measure for various interconnected tasks. In particular, we show that the min-entropy without smoothing measures the amount of quantum information that can…
We devise a simple modification that essentially doubles the efficiency of a well-known quantum key distribution scheme proposed by Bennett and Brassard (BB84). Our scheme assigns significantly different probabilities for the different…
Motivated by earlier results on universal randomized guessing, we consider an individual-sequence approach to the guessing problem: in this setting, the goal is to guess a secret, individual (deterministic) vector $x^n=(x_1,\ldots,x_n)$, by…
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…
Geometric quantum mechanics, through its differential-geometric underpinning, provides additional tools of analysis and interpretation that bring quantum mechanics closer to classical mechanics: state spaces in both are equipped with…
We address the problem of uncertainty quantification and propose measures of total, aleatoric, and epistemic uncertainty based on a known decomposition of (strictly) proper scoring rules, a specific type of loss function, into a divergence…
Verifying entanglement between parties is essential for creating secure quantum communication. However, finite statistics can lead to false positive outcomes in any tests for entanglement. Here, we introduce a one-sided device-independent…
We consider the problem of determining the mixed quantum state of a large but finite number of identically prepared quantum systems from data obtained in a sequence of ideal (von Neumann) measurements, each performed on an individual copy…
The paper describes an approach to measuring convergence of an algorithm to its result in terms of an entropy-like function of partitions of its inputs of a given length. The goal is to look at the algorithmic data processing from the…
We introduce a semidefinite programming algorithm to find the minimal quantum Fisher information compatible with an arbitrary dataset of mean values. This certification task allows one to quantify the resource content of a quantum system…
We characterize new universal features of the dynamics of chaotic quantum many-body systems, by considering a hypothetical task of "time estimation." Most macroscopic observables in a chaotic system equilibrate to nearly constant late-time…
The uncertainty principle brings out intrinsic quantum bounds on the precision of measuring non-commuting observables. Statistical outcomes in the measurement of incompatible observables reveal a trade-off on the sum of corresponding…
We use entropy numbers in combination with the polynomial method to derive a new general lower bound for the n-th minimal error in the quantum setting of information-based complexity. As an application, we improve some lower bounds on…
In this work, we aim at augmenting the decisions output by quantum models with "error bars" that provide finite-sample coverage guarantees. Quantum models implement implicit probabilistic predictors that produce multiple random decisions…
The uncertainty principle can be understood as constraining the probability of winning a game in which Alice measures one of two conjugate observables, such as position or momentum, on a system provided by Bob, and he is to guess the…
Certified randomness guaranteed to be unpredictable by adversaries is central to information security. The fundamental randomness inherent in quantum physics makes certification possible from devices that are only weakly characterised, i.e.…
The states needed in a quantum computation are extremely affected by decoherence. Several methods have been proposed to control error spreading. They use two main tools: fault-tolerant constructions and concatenated quantum error correcting…