Related papers: On the central limit theorem for unsharp quantum r…
We study random compositions of transformations having certain uniform fiberwise properties and prove bounds which in combination with other results yield a quenched central limit theorem equipped with a convergence rate, also in the…
Quantum nonlocality offers a secure way to produce random numbers: their unpredictability is intrinsic and can be certified just by observing the statistic of the measurement outcomes, without assumptions on how they are produced. To do…
The de Finetti representation theorem for continuous variable quantum system is first developed to approximate an N-partite continuous variable quantum state with a convex combination of independent and identical subsystems, which requires…
Unsharp measurements are increasingly important for foundational insights in quantum theory and quantum information applications. Here, we report an experimental implementation of unsharp qubit measurements in a sequential communication…
Estimation of quantum relative entropy and its R\'{e}nyi generalizations is a fundamental statistical task in quantum information theory, physics, and beyond. While several estimators of these divergences have been proposed in the…
Quantum versions of de Finetti's theorem are powerful tools, yielding conceptually important insights into the security of key distribution protocols or tomography schemes and allowing to bound the error made by mean-field approaches. Such…
In this dissertation, we show that the Central Limit Theorem and the Invariance Principle for Discrete Fourier Transforms discovered by Peligrad and Wu can be extended to the quenched setting. We show that the random normalization…
In quantum physics, measurement results are random but their statistics can be predicted assuming some knowledge about the system in the past. Additional knowledge from a future measurement deeply changes the statistics in the present and…
Searching for a weak signal at an unknown frequency is a canonical task in experiments probing fundamental physics such as gravitational-wave observatories and ultra-light dark matter haloscopes. These state-of-the-art sensors are limited…
It is shown that Quantum Mechanics is ambiguous when predicting relative frequencies for an entangled system if the measurements of both subsystems are performed in spatially separated events. This ambiguity gives way to unphysical…
Sharp, nonasymptotic bounds are obtained for the relative entropy between the distributions of sampling with and without replacement from an urn with balls of $c\geq 2$ colors. Our bounds are asymptotically tight in certain regimes and,…
The Heisenberg time-energy relation prevents determination of an atomic transition to better than the inverse of the measurement time. The relation generally applies to frequency estimation of a near-resonant field [1-3], since information…
A new finite form of de Finetti's representation theorem is established using elementary information-theoretic tools. The distribution of the first $k$ random variables in an exchangeable vector of $n\geq k$ random variables is close to a…
We introduce the notion of Benjamini-Schramm convergence for quantum graphs. This notion of convergence, intended to play the role of the already existing notion for discrete graphs, means that the restriction of the quantum graph to a…
A finite form of de Finetti's representation theorem is established using elementary information-theoretic tools: The distribution of the first $k$ random variables in an exchangeable binary vector of length $n\geq k$ is close to a mixture…
We present a procedure for averaging one-parameter random unitary groups and random self-adjoint groups. Central to this is a generalization of the notion of weak convergence of a sequence of measures and the corresponding generalization of…
We prove a version of the quantum de Finetti theorem: permutation-invariant quantum states are well approximated as a probabilistic mixture of multi-fold product states. The approximation is measured by distinguishability under fully…
Intrinsic randomness is generated when a quantum state is measured in any basis in which it is not diagonal. In an adversarial scenario, we quantify this randomness by the probability that a correlated eavesdropper could correctly guess the…
Quantum metrology uses small changes in the output probabilities of a quantum measurement to estimate the magnitude of a weak interaction with the system. The sensitivity of this procedure depends on the relation between the input state,…
The quantum probabilistic convergence in measurement, distinct from mathematical convergence, is derived for indeterminate probabilities from the weak quantum law of large numbers. This is presented in three theorems. The first establishes…