Figure 3
Proposed experimental setup for playing the game. Referee gives the number of row a (column b) to Alice (Bob) to fill with binary entries. The initial four-qubit state given in Eq. (1) is a composition of two EPR pairs (one illustrated with red and the other with green circles) shared by Alice and Bob. Each quantum dot (red or green circles) coupled to an optical cavity (blue toroids) constitutes one logical qubit. Following the extension strategy in Fig. 1, each two-qubit operation (given in Eqs. 2 and 3 ) on the logical qubits (distant quantum dots) is realized via an ancillary photon traveling between the optical cavities as: Following a SWAP operation between the photon and the spin coupled to the first cavity, the photon is sent to the second cavity to realize the desired operation. “Operations” represent the overall operations as decomposed in Eqs. (2) red and (3), each containing single qubit operations, and one or two CZ operations. Each CZ is realized through the interaction between ancillary photon and second spin qubit, \(q^A_2\) (or \(q^B_2\)). Each “Op” represents either an identity operator, or a set of single qubit operations on photonic or spin qubit. After the “Operations”, the photon is sent back to the first cavity for swapping back the quantum state with the spin qubit. Two-spin qubits of each party are now ready to be measured for obtaining the binary entries.
