Does measurement at the end of all transformations in quantum computing have a specified time?

Question

The concept of measurement in quantum mechanics is usually discussed without specifying how much time such measurement might take. In principle, one can imagine that the time needed to perform measurement of some properties of a physical system can be longer when a particular system is more complex in a certain sense. For example, measurement time may depend on the "extent" of entanglement. This might mean that measurement time may increase exponentially with the number of qubits as their state becomes more entangled. Is there anything in quantum mechanics theory that would prevent that from happening? If not, how can a quantum algorithm designer be sure that measurement will not be the primary limiting factor influencing the time-complexity of an algorithm? Thank you.

Answer 1

Initially I think the idea that:

measurement time may depend on the "extent" of entanglement...

is ruled out by the no-signaling theorem. For example, let's have Alice on Earth and Bob on Mars share an entangled Bell pair. If measurement "knows about" the entanglement present in the Bell pair, and takes longer if the qubits are entangled than if they are not, then Alice on Earth could send a signal to Bob on Mars by deciding whether or not to measure her qubit (and, destroy the entanglement therebetween). If she decides not to pre-measure her qubit then when Bob measures his qubit, by hypothesis it would take longer for Bob to measure his qubit than it would have if Alice had decided to pre-measure hers, and Bob could get a signal from Alice based on her pre-measurement decision, in contradiction of the no-signaling theorem.

Alternatively perhaps the OP is asking about wall-clock time. Indeed, measurement time is critical for any real-world quantum processor, and does vary based on processor-type and modality, but it should scale linearly with the number of qubits (and not with the amount of entangled).

Lastly perhaps as @Martin suggests the question is about quantum state tomography - that is, learning all about the state $|\psi\rangle$ and all of its coefficients. I do not know much about tomography, but the OP might want to review various topics around shadow tomography for example.