5 votes
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Swap test vs measurement in a specific basis

Probably the most important difference between the swap test and the projective measurement technique is that performing the swap test does not require knowledge of its inputs. When applying the swap ...
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2 votes

Given a state $\rho$ and operator $0\le \Lambda\le I$, what does $\sqrt\Lambda \rho \sqrt\Lambda$ represent?

TL;DR: Yes, we can give meaning to $\sqrt{\Lambda}\rho\sqrt{\Lambda}$: it is the post-measurement state up to an unknown change of basis (the correct basis being exactly the piece of information that ...
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2 votes
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How does interference help to bias the measurement of a qubit towards a desired state?

Maybe a simple example (modified from https://quantumcomputing.stackexchange.com/a/16701/14597) can help answer your question. Let us take a single qubit and see how interference can lead to a bias of ...
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2 votes

How does interference help to bias the measurement of a qubit towards a desired state?

Generally speaking: Each entry of a quantum statevector is a probability amplitude of a basis state. The probability to measure each basis state equals to the squared magnitude of the probability ...
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  • 600
2 votes
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In a state $\alpha \vert HL \rangle + \beta \vert VR \rangle$ can a particle be measured in the $\{|L\rangle,|R\rangle\}$ basis?

The overall state must have unit norm, i.e. for $|\psi\rangle=\alpha |HL\rangle+\beta|VR\rangle$ we should have $\langle\psi|\psi\rangle=1$. If I understood the question, by your assumption $\langle ...
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1 vote

Exact Probabilities of Outcomes for Clifford Circuits with Mid-Circuit Measurements Using Stim

In a stabilizer circuit that doesn't allow classically-controlled Cliffords feedback, every outcome that is possible is equally likely. Also, when a measurement is random, it's always 50/50 random. So ...
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1 vote

What projective measurement discriminates between a set of pairwise orthogonal states?

If the states $|\psi_j\rangle$ are orthogonal, then the set of projections $\{|\psi_j\rangle\!\langle \psi_j|\}_j$ form a projective measurement. Performing this measurement, if the input state is $|\...
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