# given an EPR pair, how do I calculate expectation values?

given A and B share EPR pairs (|00⟩+|11⟩)/√2

Here A is the 1st-qubit while B is the 2nd-qubit. And, both A and B are free to measure their own qubit with the following measurement settings

A measures with [|0⟩,|1⟩] or [|+⟩,|−⟩]

B measures with [sin(3π/8)|0⟩+cos(3π/8)|1⟩,−sin(π/8)|0⟩+cos(π/8)|1⟩] or [sin(π/8)|0⟩+cos(π/8)|1⟩,−sin(3π/8)|0⟩+cos(3π/8)|1⟩]

$[sin(\pi /8)|0\u27e9+cos(\pi /8)|1\u27e9,-sin(3\pi /8)|0\u27e9+cos(3\pi /8)|1\u27e9]$So, let Ψ=(|00⟩+|11⟩)/√2

How do I calculate the expectation value, if A measures in

$[|0\u27e9,|1\u27e9]$basis and b measures in [sin(3π/8)|0⟩+cos(3π/8)|1⟩,−sin(π/8)|0⟩+cos(π/8)|1⟩] basis?

I know that expectation value is in this format E=<Ψ|x|Ψ> , I would like to know what should be in place of x and how to find it ?