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5 votes
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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 ...
Rammus's user avatar
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0 votes

How to verify that a certain gate was applied to a quantum code

Let's define $|\tilde\psi\rangle=S^\dagger|\psi\rangle$. Then you're asking the simply question of whether we can distinguish between $|\tilde\psi\rangle$ and $S^2|\tilde\psi\rangle=Z|\tilde\psi\...
DaftWullie's user avatar
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3 votes
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Why do Surface codes generate so much measurement data?

In a surface code, half the qubits are measurement qubits used to measure the stabilizers. In a superconducting chip you can run a surface code cycle, measuring all the stabilizers, in less than a ...
Craig Gidney's user avatar
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3 votes

Definition of a quantum gate

I wouldn't say it's coupled with the measurement gate. I think they are inherently different: A quantum gate is equivalent to a Unitary matrix. Quantum gates create together a quantum circuit (which, ...
Nati Erez's user avatar
2 votes
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Conditioned measurement on bell basis states

Since you don't give your calculations, it's a bit hard to say where you're going wrong! If I do the calculations, I get \begin{align*} \langle pp|M_0|pp\rangle&=2p(1-p) \\ \langle pp|M_3|pp\...
DaftWullie's user avatar
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4 votes

Definition of a quantum gate

Sometimes people mean unitary-only. Sometimes they mean generically anything you might do to the qubits (like a measurement gate or a reset gate or a dynamical decoupling gate or a leakage removal ...
Craig Gidney's user avatar
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2 votes

How does measuring a density matrix give Kraus operators?

TLDR If you measure a qubit in the computational basis without getting the result of the measurement the corresponding channel can be described by the Kraus operators $K_0 = |0\rangle \langle 0|$ and $...
qubitzer's user avatar
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2 votes
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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 ...
Craig Gidney's user avatar
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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 $\{...
Frederik vom Ende's user avatar
3 votes
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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 ...
glS's user avatar
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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^+\...
forky40's user avatar
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1 vote
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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\...
DaftWullie's user avatar
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3 votes
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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 ...
user173611's user avatar
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: $...
Craig Gidney's user avatar
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