How to understand Tensor observables and Combined measurements from the perspective of quantum mechanics?

This doubt comes from

pennylane mentioned two measurements, I can’t tell the difference between the two. Such as H=0.5Z+1Yand H=0.5Z⊗1Y.

Hi @RX1,

I’m not sure what measurements you’re referring to since we don’t have any additions or scalar multiplications in the measurements there. Is your question about tensor products?

To learn more about tensor products you can go to our I.11 node in the Xanadu Quantum Codebook. You can also learn more about measurements in nodeI.9.

I also encourage you to read this blog made by one of our residents, Joana Fraxanet, which talks about measurements.

I hope some of this helps! If not please feel free to expand on your question.

May I ask what is the meaning or mathematical difference between the tensor operation of the observation operator and the addition and subtraction of the observation operator?

Hi @RX1, a tensor product is very different from addition and substraction. You can learn more about tensor products in node I.11 of the Xanadu Quantum Codebook. The tensor product can be thought of as a special kind of multiplication between vectors, matrices, and vectors and matrices. The example in the codebook should bring much clarity to this concept.

Please let me know if this helps!