Can POVM measurements be explained by projective measurements?

In summary, premises 1 + 2 + 3 give us a quantum mechanically describable ancilla that must exist and premises 4 + 3 + 4 say the measurement scenario involving this ancilla must also be describable with a projective decomposition.
  • #36
Demystifier said:
I make fewer explicit assumptions, but the assumptions are implicitly there. That's because I think like physicist, not mathematician, so I try to explain how nature works, not to present a mathematical proof. I don't make explicit assumptions which seem obvious to me from a physical point of view, because I see such details as distraction from really important ideas. But I perfectly understand that you, as a mathematician, don't like this type of reasoning.
I am not requiring mathematical rigor. But physics has a long and successful tradition in giving proofs at a high level, a level missing in your paper. You make suggestions, which might motivate why the results could possibly be true, but fail to give arguments that would satisfy anyone who really wants to understand what is behind. Your references to the literature only cover conditions where much stronger assumptions are needed to actually make a convincing justification.

In any case, nothing in your paper except for a few passing words relate to POVMs, thus making a further discussion of it off-topic in this thread.
 
<h2> What is a POVM measurement?</h2><p>A POVM (positive operator-valued measure) measurement is a type of quantum measurement that allows for a more general description of the outcomes compared to projective measurements. It involves a set of positive operators that sum to the identity operator, and each operator corresponds to a possible measurement outcome.</p><h2> How is a POVM measurement different from a projective measurement?</h2><p>A projective measurement is a type of quantum measurement that involves projecting a quantum state onto one of the eigenstates of the measured observable. In contrast, a POVM measurement allows for a wider range of possible outcomes and does not require the measured observable to have discrete eigenvalues.</p><h2> Can POVM measurements be explained by projective measurements?</h2><p>Yes, POVM measurements can be explained by projective measurements in the sense that any POVM measurement can be decomposed into a set of projective measurements. However, this decomposition may not be unique and may involve multiple projective measurements for each POVM element.</p><h2> What are the advantages of using POVM measurements?</h2><p>POVM measurements have several advantages over projective measurements. They allow for a more general description of measurement outcomes, can be used to measure non-commuting observables, and can be implemented more easily in experiments. Additionally, POVM measurements can provide more information about the quantum state being measured.</p><h2> Are POVM measurements commonly used in quantum experiments?</h2><p>Yes, POVM measurements are commonly used in quantum experiments, particularly in areas such as quantum information and quantum computing. They have also been used in various applications such as quantum cryptography and quantum metrology. However, projective measurements are still more widely used in many experimental setups due to their simplicity and ease of implementation.</p>

FAQ: Can POVM measurements be explained by projective measurements?

What is a POVM measurement?

A POVM (positive operator-valued measure) measurement is a type of quantum measurement that allows for a more general description of the outcomes compared to projective measurements. It involves a set of positive operators that sum to the identity operator, and each operator corresponds to a possible measurement outcome.

How is a POVM measurement different from a projective measurement?

A projective measurement is a type of quantum measurement that involves projecting a quantum state onto one of the eigenstates of the measured observable. In contrast, a POVM measurement allows for a wider range of possible outcomes and does not require the measured observable to have discrete eigenvalues.

Can POVM measurements be explained by projective measurements?

Yes, POVM measurements can be explained by projective measurements in the sense that any POVM measurement can be decomposed into a set of projective measurements. However, this decomposition may not be unique and may involve multiple projective measurements for each POVM element.

What are the advantages of using POVM measurements?

POVM measurements have several advantages over projective measurements. They allow for a more general description of measurement outcomes, can be used to measure non-commuting observables, and can be implemented more easily in experiments. Additionally, POVM measurements can provide more information about the quantum state being measured.

Are POVM measurements commonly used in quantum experiments?

Yes, POVM measurements are commonly used in quantum experiments, particularly in areas such as quantum information and quantum computing. They have also been used in various applications such as quantum cryptography and quantum metrology. However, projective measurements are still more widely used in many experimental setups due to their simplicity and ease of implementation.

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