Related papers: On the Algorithmic Information Between Probabiliti…
We conclusively show that the entanglement- and the mutual information-based measures of quantum non-Markovianity are inequivalent. To this aim, we first analytically solve the optimization problem in the definition of the…
Due to lack of scientific understanding, some mechanisms may be missing in mathematical modeling of complex phenomena in science and engineering. These mathematical models thus contain some uncertainties such as uncertain parameters. One…
Randomness is intrinsic to quantum mechanics; the outcome of a measurement on a quantum state is a random variable. This feature has been applied to randomness certification, where one party must decide whether the data they receive is…
We consider quantum enhanced measurements with initially mixed states. We show very generally that for any linear propagation of the initial state that depends smoothly on the parameter to be estimated, the sensitivity is bound by the…
Quantum measurement has conventionally been regarded as the final step in quantum information processing, which is essential for reading out the processed information but collapses the quantum state into a classical state. However, recent…
In this paper, we consider the generalized measurement where one particular quantum signal is unambiguously extracted from a set of non-commutative quantum signals and the other signals are filtered out. Simple expressions for the maximum…
A Holevo measure is used to discuss how much information about a given POVM on system $a$ is present in another system $b$, and how this influences the presence or absence of information about a different POVM on $a$ in a third system $c$.…
Random probabilities are a key component to many nonparametric methods in Statistics and Machine Learning. To quantify comparisons between different laws of random probabilities several works are starting to use the elegant Wasserstein over…
A large literature has grown up around the proposed use of 'weak measurements' (i.e., unsharp measurements followed by post-selection) to allegedly provide information about hidden ontological features of quantum systems. This paper…
We investigate the connection between measure, capacity and algorithmic randomness for the space of closed sets. For any computable measure m, a computable capacity T may be defined by letting T(Q) be the measure of the family of closed…
New algorithm for quantum state estimation based on the maximum likelihood estimation is proposed. Existing techniques for state reconstruction based on the inversion of measured data are shown to be overestimated since they do not…
This study confirms a local trade-off between information and disturbance in quantum measurements. It is represented by the correlation between the changes in these two quantities when the measurement is slightly modified. The correlation…
The advantages of quantum information processing are in many cases obtained as consequences of quantum interactions, especially for computational tasks where two-qubit interactions are essential. In this work, we establish the framework of…
How much information about an unknown quantum state can be obtained by a measurement? We propose a model independent answer: the information obtained is equal to the minimum entropy of the outputs of the measurement, where the minimum is…
Any measurement is intended to provide information on a system, namely knowledge about its state. However, we learn from quantum theory that it is generally impossible to extract information without disturbing the state of the system or its…
The peculiar uncertainty or randomness of quantum measurements stems from coherence, whose information-theoretic characterization is currently under investigation. Under the resource theory of coherence, it is interesting to investigate…
Observations or measurements taken of a quantum system (a small number of fundamental particles) are inherently random. If the state of the system depends on unknown parameters, then the distribution of the outcome depends on these…
Consider a photon that has just emerged from a linear polarizing filter. If the photon is then subjected to an orthogonal polarization measurement-e.g., horizontal vs vertical-the photon's preparation cannot be fully expressed in the…
The equivalence of the characteristic function approach and the probabilistic approach to monotone and boolean convolutions is proven for non-compactly supported probability measures. A probabilistically motivated definition of the…
We analyze mean fidelity between random density matrices of size N, generated with respect to various probability measures in the space of mixed quantum states: Hilbert-Schmidt measure, Bures (statistical) measure, the measures induced by…