Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Many partially-successful attempts have been made to find the most natural discrete-variable version of Shannon's entropy por inequality (EPI).  develop an axiomatic framework from which  deduce the natural form of a discrete-variable EPI and an associated entropic monotonicity in a discrete-variable central limit theorem. In this discrete EPI, the geometric distribution, which has the maximum entropy among all discrete distributions with a given mean, assumes a role analogous to the Gaussian distribution in Shannon's EPI. The entropy por of X is defined as the mean of a geometric random variable with entropy H(X). The crux of our construction is a discrete-variable version of Lieb's scaled addition X ⊞ η  Y of two random variables X and Y with η ∈ (0, 1).  discuss the relationship of our discrete EPI with recent work of Yu and Johnson who developed an EPI for a restricted class of random variables that have ultra-log-concave (ULC) distributions. Even though  leave open the proof of the aforesaid natural form of the discrete EPI,  show that this discrete EPI holds true for variables with arbitrary discrete distributions when the entropy por is redefined as e H(X)  in analogy with the continuous version. Finally,  show that our conjectured discrete EPI is a special case of the yet-unproven Entropy Photon-number Inequality (EPnI), which assumes a role analogous to Shannon's EPI in capacity proofs for Gaussian bosonic (quantum) channels.
['Saikat Guha', 'Jeffrey H. Shapiro', 'Raul Garcia-Patron Sanchez']
I am writing a research paper on a idea Thinning, photonic beamsplitting, and a general discrete Entropy power Inequality
[{"from": "human", "value": "I am writing a research paper on a idea Thinning, photonic beamsplitting, and a general discrete Entropy power Inequality"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Many partially-successful attempts have been made to find the most natural discrete-variable version of Shannon's entropy por inequality (EPI).  develop an axiomatic framework from which  deduce the natural form of a discrete-variable EPI and an associated entropic monotonicity in a discrete-variable central limit theorem. In this discrete EPI, the geometric distribution, which has the maximum entropy among all discrete distributions with a given mean, assumes a role analogous to the Gaussian distribution in Shannon's EPI. The entropy por of X is defined as the mean of a geometric random variable with entropy H(X). The crux of our construction is a discrete-variable version of Lieb's scaled addition X \u229e \u03b7  Y of two random variables X and Y with \u03b7 \u2208 (0, 1).  discuss the relationship of our discrete EPI with recent work of Yu and Johnson who developed an EPI for a restricted class of random variables that have ultra-log-concave (ULC) distributions. Even though  leave open the proof of the aforesaid natural form of the discrete EPI,  show that this discrete EPI holds true for variables with arbitrary discrete distributions when the entropy por is redefined as e H(X)  in analogy with the continuous version. Finally,  show that our conjectured discrete EPI is a special case of the yet-unproven Entropy Photon-number Inequality (EPnI), which assumes a role analogous to Shannon's EPI in capacity proofs for Gaussian bosonic (quantum) channels."}]