Graduate Off-diagonal elements in a density matrix

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The discussion centers on determining the minimum value of the sum of specific off-diagonal elements in a density matrix. The inquiry highlights that when including an off-diagonal element, its complex conjugate must also be included in the sum. Participants express confusion about the question's clarity and suggest providing more context or references for better understanding. The need for a more concrete formulation of the question is emphasized to facilitate accurate responses. Overall, the thread seeks to clarify the mathematical properties of density matrices in quantum mechanics.
CarvalhoGD
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Hello everyone,

I have a math / physics question that has been with me for a while. I would be grateful if someone could help me.

Given a density matrix, what is the minimum value a sum of some of its off-diagonal elements can assume (or the most negative value)?
Remark: if one collect an off-diagonal element to compose the sum, its complex conjugate will also compose the sum.

Thank you.
 
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Sorry,but I don't understand your question not good enough to give you an answer.Try to make your question a little bit more concrete.Maybe you should post the reference where question is related to.
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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