Yes, it is possible to observe two entangled photons in a way that provides information about the correlation between their states without directly measuring the state of each individual photon. This phenomenon is known as quantum entanglement.
When two photons are entangled, their quantum states become intertwined, and the measurement of one photon's state can instantaneously affect the state of the other, regardless of the distance between them. This effect is often referred to as "spooky action at a distance."
To determine if the states of two entangled photons are equal or opposite without measuring the individual state of each photon, one can perform a specific type of measurement called a Bell measurement. A Bell measurement is designed to extract correlations between the entangled photons' states rather than revealing the exact state of each photon individually.
By performing a series of Bell measurements on a large number of entangled photon pairs, statistical analysis can be carried out to determine the overall correlation between the two photons. This statistical analysis can reveal whether the entangled photons have the same state (correlated) or opposite states (anti-correlated) without explicitly measuring the state of each photon.
It's important to note that while this method can provide information about the correlation between the entangled photons' states, it does not reveal the precise state of each photon individually. The entanglement between the photons remains intact throughout the process.
This type of measurement allows for studying the non-local correlations of entangled particles without breaking their entanglement. It demonstrates the unique and counterintuitive nature of quantum mechanics, where measurements on entangled particles can reveal information about their correlation while still preserving their entangled state.