# Use of PauliZ gate

**URL:** <https://discuss.pennylane.ai/t/use-of-pauliz-gate/522>\
**Category:** PennyLane Help\
**Created:** [August 19, 2020, 4:36pm UTC](https://discuss.pennylane.ai/t/use-of-pauliz-gate/522 "2020-08-19T16:36:02Z")\
**Posts on this page:** 1\
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**Author:** ![Jay\_Timbadia](https://yyz2.discourse-cdn.com/flex012/user_avatar/discuss.pennylane.ai/jay_timbadia/32/261_2.png) [@Jay\_Timbadia](https://discuss.pennylane.ai/u/Jay_Timbadia)\
**Post date:** [August 21, 2020, 6:03am UTC](https://discuss.pennylane.ai/t/use-of-pauliz-gate/522/3 "2020-08-21T06:03:48Z")

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Thank you for the reply.

By reading the diagonal elements of the Pauli-Z matrix, we can see that  
Z has two eigenvectors, |0⟩ and |1⟩ ,with corresponding eigenvalues  
±1. Thus, if we measure the qubit and obtain Zero (corresponding to the state |0⟩), we know that the state of our qubit is a +1 eigenstate of the Z  
operator and vice versa.

But PauliX also has the same eigen vectors. What makes Z different?

Also I found these table ? Can you explain these?

| Pauli Measurement | Unitary transformation |
| --- | --- |
| Z | 1 |
| X | H |
| Y | HS† |

That is, using this language, “measure Y” is equivalent to applying  
HS†.

What does these mean? Also how many values expval takes for average for single wire?

Waiting for reply. Too curious.

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