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Can someone explain the EPR argument with a simple description using Pauli matrices?

Two non-commuting physical quantity are being discussed philosophically whether there is an element of reality corresponds to the theory and the possibility of getting a value with certainty when measurement was made. Two argument are stated which are

- Either the Quantum Mechanic description of reality given by the wave function is not complete;
- Or the physical quantities associated with non-commuting operators cannot have simultaneous reality.

To clarify the ideas involved, let us consider a fundamental concept of state which is characterized by state vector, $|a\rangle$ which describe the particle’s behavior. Corresponding to every physical observable, there is an operator which operates on the state vector. $\hat{A}|a\rangle = a|a\rangle$ For an eigenstate $|a\rangle$ of Hermitian operator $\hat{A}$, only the eigenvalue a will be obtained after measurement, with a probability equal to unity. The state too will not suffer any change after the measurement process. We can thus predict the outcome of the measurement with a probability equal to one and without disturbing the system in any way. Therefore, by the EPR argument, for an eigenstate, the value of the corresponding observable is an element of physical reality.

How to explain the momentum and coordinate in the EPR paper using pauli matrices?

can you clarify what you mean with "explain the momentum and position coordinates using Pauli matrices"? Also note that you can write math in a post using mathjax, see https://quantumcomputing.meta.stackexchange.com/q/49/55

– glS – 2020-12-15T09:10:29.460A variant using pauli matrices is written on the wikipedia page EPR paradox

– Rammus – 2020-12-15T09:29:24.870