Method for securely computing a logical and between two bits using quantum communication

Abstract

Method for computing a logical AND between two chosen bits, xi, xj, held by first and second participants, including a first phase comprising a step in which said first and second participants determine a first correlation variable and a second correlation variable, each determine a random bit, p and q, and transmit, to said server, a value dependent on said random bit p, q, a step in which the server prepares a photon in a first state; a step in which said first participant applies a first transformation V Up to said photon; a step in which the second participant applies a second transformation V Uq to said photon, and a step in which the server performs a third transformation (U*)p+q, measures the state of the photon and determines a third correlation variable; and a second phase comprising a step in which said first and second participants exchange a value u1, u2 dependent on the sum of the random bit, p, q and the chosen bit, xi, xj; and a step in which said first participant computes and delivers a first value a=+xiΛu2, said second participant computes and delivers a second value b=+xjΛu1+u1Λu2 and said server delivers the third correlation value, so that the result of the computation of the logical 'and' between said chosen bits may be obtained by summing said first and second values and said third correlation variable.