A method for calculating a logical AND between two chosen bits x i, x j held by a first and a second participant, C i, Cj respectively, connected to each other and to a server (C 1), by at least one quantum communication channel (Lq) and one conventional communication channel (Lc), comprising a first phase using said quantum communication channel and comprising a first step in which said first and second participants randomly determine, respectively, a first α and second β correlation variable; they each determine a random bit, respectively p and q, and transmit to said server (C 1) a value dependent on the corresponding random bit p, q respectively; a second step in which said server (C 1) prepares a photon in a first state in an orthonormal basis, and transmits it to said first participant (Ci); a third step in which said first participant (C i) applies a first transformation V α U p to said photon, and transmits it to said second participant (C j), the logic gate V transforming a state into an orthogonal state and the logic gate U being a square root of the logic gate V; a fourth step in which said second participant (C j) applies a second transformation V β U q to said photon, and transmits it to said server; a fifth step in which the server C 1 performs a third transformation (U*) p+q, measures the state of said photon and determines a third correlation variable γ based on said state, so as to form a correlation between said correlation variables; and a second phase comprising a sixth step in which said first and second participants exchange a value u1, u2 depending on the sum between the random bit, p, q, and the chosen bit, x i, x j, they hold, respectively; a seventh step in which said first participant calculates and provides a first value a = α + x i Λu2, said second participant calculates and provides a second value b = β + x j Λu1 + u1Λu2 and said server provides the third correlation variable γ, so that the result of the calculation of the logical "and" between said chosen bits can be obtained by summing said first and second values and said third correlation variable. a first phase using said quantum communication channel and comprising a first step in which said first and second participants randomly determine, respectively, a first α and second β correlation variable; they each determine a random bit, respectively p and q, and transmit to said server (C 1) a value dependent on the corresponding random bit p, q respectively; a second step in which said server (C 1) prepares a photon in a first state in an orthonormal basis, and transmits it to said first participant (Ci); a third step in which said first participant (C i) applies a first transformation V α U p to said photon, and transmits it to said second participant (C j), the logic gate V transforming a state into an orthogonal state and the logic gate U being a square root of the logic gate V; a fourth step in which said second participant (C j) applies a second transformation V β U q to said photon, and transmits it to said server; a fifth step in which the server C 1 performs a third transformation (U*) p+q, measures the state of said photon and determines a third correlation variable γ based on said state, so as to form a correlation between said correlation variables; and a second phase comprising a sixth step in which said first and second participants exchange a value u1, u2 depending on the sum between the random bit, p, q, and the chosen bit, x i, x j, they hold, respectively; a seventh step in which said first participant calculates and provides a first value a = α + x i Λu2, said second participant calculates and provides a second value b = β + x j Λu1 + u1Λu2 and said server provides the third correlation variable γ, so that the result of the calculation of the logical "and" between said chosen bits can be obtained by summing said first and second values and said third correlation variable.