When measuring a quantum state, the two possible outcomes are typically referred to as the eigenvalues of the observable being measured. The specific outcomes depend on the particular observable being measured and the corresponding eigenstates.
In quantum mechanics, observables are represented by Hermitian operators, and their eigenstates represent the possible outcomes of a measurement. Upon measurement, the system collapses into one of the eigenstates associated with the observable being measured, and the corresponding eigenvalue is obtained as the measurement result.
For example, consider a spin-1/2 particle, such as an electron, with spin measured along the z-axis. The observable in this case is the spin component along the z-axis, and its eigenstates are commonly denoted as "spin-up" and "spin-down." The two possible outcomes when measuring the spin of the particle along the z-axis are "spin-up" with an associated eigenvalue of +1/2 and "spin-down" with an associated eigenvalue of -1/2.
It's important to note that quantum mechanics allows for the existence of superposition, where a quantum system can be in a state that is a linear combination of multiple eigenstates. In such cases, upon measurement, the system collapses into one of the eigenstates with probabilities determined by the coefficients of the superposition state.
The two possible outcomes described here are specific to the measurement of spin along a particular axis and may differ for other observables or quantum systems. The exact outcomes of a measurement depend on the specific context and observable under consideration.