DeepAI AI Chat
Log In Sign Up

Quantifying coherence with quantum addition

by   Chiranjib Mukhopadhyay, et al.

Quantum addition channels have been recently introduced in the context of deriving entropic power inequalities for finite dimensional quantum systems. We prove a reverse entropy power equality which can be used to analytically prove an inequality conjectured recently for arbitrary dimension and arbitrary addition weight. We show that the relative entropic difference between the output of such a quantum additon channel and the corresponding classical mixture quantitatively captures the amount of coherence present in a quantum system. This new coherence measure admits an upper bound in terms of the relative entropy of coherence and is utilized to formulate a state-dependent uncertainty relation for two observables. Our results may provide deep insights to the origin of quantum coherence for mixed states that truly come from the discrepancy between quantum addition and the classical mixture.


page 1

page 2

page 3

page 4


The conditional Entropy Power Inequality for quantum additive noise channels

We prove the quantum conditional Entropy Power Inequality for quantum ad...

Sufficiency of Rényi divergences

A set of classical or quantum states is equivalent to another one if the...

Quantifying coherence in terms of Fisher information

In quantum metrology, the parameter estimation accuracy is bounded by qu...

Coherence Optimization in Neutron Interferometry through Defocussing

A zero-area four-blade perfect crystal neutron interferometer (NI) posse...

Entropy of a quantum channel

The von Neumann entropy of a quantum state is a central concept in physi...

Coherence for braided distributivity

In category-theoretic models for the anyon systems proposed for topologi...

Complexity of quantum circuits via sensitivity, magic, and coherence

Quantum circuit complexity-a measure of the minimum number of gates need...