Fig. 2: NLWE in the case of \({\theta }_{1}={\theta }_{0}\,\ne \,\frac{\pi }{4}\). | npj Quantum Information

Fig. 2: NLWE in the case of \({\theta }_{1}={\theta }_{0}\,\ne \,\frac{\pi }{4}\).

From: Quantum nonlocality without entanglement: explicit dependence on prior probabilities of nonorthogonal mirror-symmetric states

Fig. 2

In two-qubit system, a party R prepares N0 number of quantum state \(\left|{{{\Psi }}}_{0}\right\rangle\) (red), N1 number of quantum state \(\left|{{{\Psi }}}_{1}\right\rangle\) (green), and N1 number of quantum state \(\left|{{{\Psi }}}_{2}\right\rangle\) (yellow). R combines N0 + 2N1 quantum systems and randomly chooses one out of them. Then, the prior probability q1 of quantum state \(\left|{{{\Psi }}}_{1}\right\rangle\) is equal to the prior probability q2 of quantum state \(\left|{{{\Psi }}}_{2}\right\rangle\). The ratio r between the prior probability q0 of quantum state \(\left|{{{\Psi }}}_{0}\right\rangle\) and the prior probability q1 is N0/N1. After the preparation, R sends each qubit to A and B, respectively. When 0 < r < γ+ is satisfied, NLWE occurs in the view of MD, but if r = γ+, NLWE does not occur. More explicitly, because γ+ becomes 343/600 when θ0 satisfies \(\sin\,{\theta }_{0}=3/5\), if N1 = 600, NLWE does not occur when N0 is 343. However, NLWE occurs in the case of N0 = 1, 2, … , 342.

Back to article page