Yes, it is possible to create entangled photon pairs in the state |HH⟩ + |VV⟩, where H and V represent horizontal and vertical polarization states, respectively. This specific state is known as a maximally entangled state of two qubits. Numerous experiments have been conducted to generate such entangled photon pairs.
One common method for creating entangled photon pairs is through a process called spontaneous parametric down-conversion (SPDC). In SPDC, a nonlinear crystal is used to convert a higher energy photon into two lower energy photons, known as signal and idler photons. The polarization states of these two photons can be entangled.
By carefully engineering the setup and properties of the crystal, it is possible to generate entangled photon pairs in various polarization states, including the |HH⟩ + |VV⟩ state. This can be achieved by ensuring that the crystal's properties preserve the phase relationship between the two polarization states.
Experimental setups utilizing SPDC have been used to generate entangled photon pairs with various polarization states, including the |HH⟩ + |VV⟩ state. These experiments have played a crucial role in testing quantum entanglement and exploring its applications in quantum information processing, quantum cryptography, and other areas of quantum physics research.