# Tag Info

Accepted

### Why are only projective measurements considered in nonlocal games to get optimal strategy?

As you correctly state, POVMs can be dilated into a projective measurement on a larger Hilbert space. Because we do not restrict the possible dimension of the Hilbert spaces in the game, we can ...
• 5,958

• 439
Accepted

### How to find the $+1$ eigenvectors of the stabilizers for the Shor code

For CSS stabilizers it's easy. Every X stabilizer will project the computational basis state $|k\rangle$ into $|k\rangle + |k \oplus x\rangle$ where $x$ is the bits flipped by the X gates of the ...
• 38.5k
1 vote

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 $\{... • 1,991 3 votes Accepted ### Can Bell states be reexpressed with respect to arbitrary local bases? A maximally entangled state like$|00\rangle+|11\rangle$can be generally written as $$\frac{|00\rangle+|11\rangle}{\sqrt2} = |u_0, \bar u_0\rangle+|u_1,\bar u_1\rangle$$ for any pair of orthonormal ... • 25.5k 2 votes ### Can Bell states be reexpressed with respect to arbitrary local bases? For your first question: If you pick a change of basis$U$such that$|b_0\rangle = U|0\rangle$and$|b_1\rangle = U|1\rangle$, then you are asking for conditions such that $$(U\otimes U)|\Phi^+\... • 7,183 1 vote Accepted ### Moving pauli product rotations past measurements Let \sigma and \tau be two tensor products of Paulis. Imagine you have a gate sequence$$ e^{i\theta\tau}\sqrt{\sigma}, $$then you can always rewrite this as$$ e^{i\theta\tau}=\sqrt{\sigma}e^{i\... • 59.3k 3 votes Accepted ### Measuring stabilizers for qutrit stabilizer code$\def\braket#1#2{\langle#1|#2\rangle}\def\bra#1{\langle#1|}\def\ket#1{|#1\rangle}$I think your confusion lies with measuring qudit Pauli operators. It is true that operators like$X$and$Z$are not ... • 118 1 vote ### How to mathematically describe the action of CNOT on the control qubit alone? In the ZX calculus, the CNOT gate factors into a Z type node for the control linked to an X type node for the target. The Z type node (the "control part of the operation") has three ports:$...
• 38.5k

Top 50 recent answers are included