I'm currently working with several No-Go-Theorems in Quantum Mechanics for my master thesis and there are two, wich are confusing me: The No-Deletion-Theorem and the No-Partial Erasure-Theorem.(adsbygoogle = window.adsbygoogle || []).push({});

This is what I found out:

- The No-Deletion-Theorem shows that "there is no quantum deleting machine that can delete one onknown state against a copy in either a reversible or an irreversible manner."

It argues with the linearity of quantum operations.- In the paper about the No-Partial-Erasure-Theorem it is said that "it is ompossible to erase quantum information, even partially and even by using irreversible means [...]"
- But some lines later: "Out theorem adds new insight into the integrity of quantum information, namely that we can erase complete information but not partial information."

So... I think it's important to look at the models used in these theorems. The No-Del-Theorem seems to focus on (unitary) transformations. Even though they talk about irreversible operations, measuring the qubits doesn't seem to be allowed there. That makes sense to me, because a unitary transformation is reversible, so the quantum information is retrieveable by applying the inverse operation.

The No-Part-Era-Theorem also is about reversible and irreversible operations, too, but measuring isn't discussed there either, as far as I can see.

My first question: What are these irreversible quantum operations, that can't be used to delete quantum information? As far as I know, there are two kinds of operations: unitary transformations (reversible) and measurements (changing the quantum state irreversibly).

My second question: Let |q>= a |0> + b |1> be an arbitrary qubit. I perform a measurement, wich brings |q> into the state either |0> or |1> and if it's |1> I flip it to |0> by rotating it by 90°.

Haven't I deleted the qubit? Each qubit will be mapped to |0>. It is irreversible, because I perform a measurement, but I don't see where the information could move to.

Looking forward to your answers! :-)

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# Quantum No-Deletion/No-Partial Erasure vs. Measurement

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