# Off-diagonal elements in a density matrix

• A
• CarvalhoGD
In summary, the speaker is seeking help with a math/physics question regarding the minimum value a sum of off-diagonal elements in a density matrix can have. They mention that the complex conjugates of the elements should also be included in the sum. They request more clarification or a reference to better understand the question.
CarvalhoGD
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.

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.

## 1. What are off-diagonal elements in a density matrix?

Off-diagonal elements in a density matrix represent the quantum coherence between different states of a quantum system. They describe the probability amplitude for a system to transition from one state to another.

## 2. How are off-diagonal elements calculated in a density matrix?

Off-diagonal elements are calculated by taking the inner product of the wavefunctions corresponding to the two states in question. This can be written as the integral of the product of the complex conjugate of one wavefunction and the other wavefunction.

## 3. What is the significance of off-diagonal elements in a density matrix?

Off-diagonal elements play a crucial role in quantum mechanics as they represent the interference between different states of a system. They are responsible for phenomena such as quantum superposition and entanglement.

## 4. How do off-diagonal elements affect the behavior of a quantum system?

The magnitude and phase of off-diagonal elements determine the probability of a system transitioning between states. They also affect the time evolution of a system, as they can cause interference between different pathways of a system.

## 5. Can off-diagonal elements be measured in an experiment?

Yes, off-diagonal elements can be measured indirectly through various techniques such as quantum state tomography and quantum process tomography. These methods involve performing measurements on the system multiple times and using statistical analysis to extract the off-diagonal elements.

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