from an experimental perspective because they are easy to use and have a high measurement cross-section. For entanglement in a single qubit variable, only three distinct classes out of four Bell states are distinguishable using such linear optical techniques. This means two Bell states cannot be distinguished from each other, limiting the efficiency of quantum communication protocols such as teleportation. If a Bell state is measured from this ambiguous class, the teleportation event fails. Entangling particles in multiple qubit variables, such as (for photonic systems) polarization and a two-element subset of orbital angular momentum states, allows the experimenter to trace over one variable and achieve a complete Bell state measurement in the other. Leveraging so-called hyper-entangled systems thus has an advantage for teleportation. It also has advantages for other protocols such as superdense coding, in which hyper-entanglement increases the channel capacity. In general, for hyper-entanglement in variables, one can distinguish between at most classes out of Bell states using linear optical techniques. Bell state correlations Independent measurements made on two qubits that are entangled in Bell states positively correlate perfectly if each qubit is measured in the relevant basis. For the state, this means selecting the same basis for both qubits. If an experimenter chose to measure both qubits in a Bell state using the same basis, the qubits would appear positively correlated when measuring in the basis, anti-correlated in the basis, and partially (probabilistically) correlated in other bases. The correlations can be understood by measuring both qubits in the same basis and observing perfectly anti-correlated results. More generally, can be understood by measuring the first qubit in basis , the second qubit in basis , and observing perfectly positively correlated results. Applications Superdense coding Superdense coding allows two individuals to communicate two bits of classical information by only sending a single qubit. The basis of this phenomenon is the entangled states or Bell states of a two qubit system. In this example, Alice and Bob are very far from each other, and have each been given one qubit of the entangled state. . In this example, Alice is trying to communicate two bits of classical information, one of four two bit strings: or . If Alice chooses to send the two bit message , she would perform the phase flip to her qubit. Similarly, if Alice wants to send , she would apply a NOT gate; if she wanted