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Represent Hadamard gate in terms of rotations and reflections in Bloch sphere

but how about γ? Gamma doesn't show up on the Bloch sphere. It's a global phase. It's unobservable without conditioning the operation on a second qubit, in which case it turns into phase kickback ...
• 37.9k

What's the Schmidt decomposition of $|\psi\rangle = 1/ \sqrt{3}( |0\rangle| 0\rangle + |0\rangle |1\rangle + |1\rangle |1\rangle)$?

One way of computing the decomposition is through density matrices, but then you will have to diagonalize those density matrices. This requires the eigenvalue decomposition of each density matrix. ...
• 2,666

Represent Hadamard gate in terms of rotations and reflections in Bloch sphere

The Hadamard gate is a $\pi$ rotation about the diagonal axis in the XZ-plane. It is not a $\pi/2$ rotation about the $y$ axis. This can be easily seen from the fact that the Hadamard squares to the ...
• 6,749

Finding the effect of conjugate transpose on a state $|b\rangle$

For a unitary $U$, the conjugate transpose $U^\dagger$ is the inverse of $U$, i.e. the linear operator such that$^1$ $U^\dagger U=UU^\dagger=I$. Guess and check The inverse is unique$^2$, so a general ...
• 22.9k
Accepted

In the QECC condition $\langle\psi|E_a^\dagger E_b|\phi\rangle=C_{ab}\langle\psi|\phi\rangle$, what is $C_{ab}$?

The concept of $C_{ab}$ in the context of the Quantum Error-Correcting Code (QECC) conditions as described in Theorem 2.7 can indeed be confusing due to the mathematical notation and the terminology ...
• 654

• 25.4k
1 vote

• 25.4k
1 vote

How to compute the post-measurement state when measuring only the first of a three-qubit system?

tl;dr: The approach is correct but OP's calculation features multiple errors. Just to be precise about what I'll be doing: In the POVM formulation a quantum measurement is described by a collection \$\{...
• 1,779

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