Related papers: Entropy of Quantum Measurements
It is observed that the entropy reduction (the information gain in the initial terminology) of an efficient (ideal or pure) quantum measurement coincides with the generalized quantum mutual information of a q-c channel mapping an a priori…
Quantum coherence is the most distinguished signature of quantum mechanics, also recognized to be an essential resource for many promising quantum technologies, playing a central role in phenomena related to quantum information science,…
Due to the Unruh effect, accelerated and inertial observers differ in their description of a given quantum state. The implications of this effect are explored for the entropy assigned by such observers to localized objects that may cross…
The use of coarse graining to connect physical and information theoretic entropies has recently been given a precise formulation in terms of ``observational entropy'', describing entropy for observers with respect to a measurement. Here we…
Whenever a physical quantity becomes essential to the realization of useful tasks, it is desirable to define proper measures or monotones to quantify it. In quantum mechanics, coherence, entanglement, and Bell nonlocality are examples of…
By using relative entropy of coherence, we characterize the coherence gain induced by some quantum evolutions, including the cohering power of unitary operations and the decohering power of quantum operations. We find that the cohering…
Entropy is a famous and well established concept in physics and engineering that can be used for explanation of basic fundamentals as well it finds applications in several areas, from quantum physics to astronomy, from network communication…
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…
The quantum entropy power inequality, proven by K\"onig and Smith (2012), states that $\exp(S(\rho \boxplus \sigma)/m)\geq \frac 12 (\exp(S(\rho)/m) + \exp(S(\sigma)/m))$ for two $m$-mode bosonic quantum states $\rho$ and $\sigma$. One…
Entropy is a measure of self-information which is used to quantify losses. Entropy was developed in thermodynamics, but is also used to compare probabilities based on their deviating information content. Corresponding model uncertainty is…
Quantum informatic quantities such as entanglement entropy are useful in detecting quantum phase transitions. Recently, a new entanglement measure called pseudo-entropy was proposed which is a generalization of the more well-known…
Uncertainty relations and quantum entanglement are pivotal concepts in quantum theory. Beyond their fundamental significance in shaping our understanding of the quantum world, they also underpin crucial applications in quantum information…
Various lower bounds are established for the entropy of sums, products and their combinations. First, we derive a prime-field analogue of a version of the entropy power inequality established by Tao over torsion-free groups. Next, we prove…
Quantum physics, despite its observables being intrinsically of a probabilistic nature, does not have a quantum entropy assigned to them. We propose a quantum entropy that quantify the randomness of a pure quantum state via a conjugate pair…
This paper presents the measurement problem from the point of view of the thermal interpretation of quantum physics introduced in Part II. The measurement of a Hermitian quantity $A$ is regarded as giving an uncertain value approximating…
Entropies are fundamental measures of uncertainty with central importance in information theory and statistics and applications across all the quantitative sciences. Under a natural set of operational axioms, the most general form of…
The strong subadditivity of entropy plays a key role in several areas of physics and mathematics. It states that the entropy S[\rho]= - Tr (\rho \ln \rho) of a density matrix \rho_{123} on the product of three Hilbert spaces satisfies…
The observables associated with a quantum system $S$ form a non-commutative algebra ${\mathcal A}_S$. It is assumed that a density matrix $\rho$ can be determined from the expectation values of observables. But $\mathcal A_S$ admits inner…
Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…
Quantum measurement is a class of quantum channels that sends quantum states to classical states. We set up resource theories of quantum coherence and quantum entanglement for quantum measurements and find relations between them. For this,…