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Update katas/content/multi_qubit_measurements/index.md
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Co-authored-by: César Zaragoza Cortés <[email protected]>
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tcNickolas and cesarzc authored Aug 20, 2024
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Expand Up @@ -247,7 +247,7 @@ Full measurements can also be used to identify the state of the system, if it's

For a system with $n>1$ qubits, it's possible to measure $m<n$ qubits one after another. The number of measurement outcomes is then $2^m$ instead of $2^n$. The probabilities of each of the outcomes and the post-measurement states of the qubits can be found using the projection formalism for measurements.

First, you recall the concept of projection operators introduced in the Measurements in Single-Qubit Systems kata. Measurements are modeled by orthogonal projection operators - matrices that satisfy
First, recall the concept of projection operators introduced in the Measurements in Single-Qubit Systems kata. Measurements are modeled by orthogonal projection operators - matrices that satisfy
$$P^2 = P^\dagger = P$$
Consider an $n$-qubit system in a state $\ket{\psi}$, for which the first $m<n$ qubits are measured in an orthogonal basis $\{ \ket{b_0} , \ket{b_1}, \dotsc, \ket{b_{2^m-1}}\}$ corresponding to the $m$ qubits being measured. Then, you define $2^m$ projectors corresponding to each of the $\ket{b_i}$ states as

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