Consider the state of two qubits | = 1 2 |00 + i 3 4 |01 + 3 4 |10. a) Find out the expected values of both qubits separately. b) The product of the values of the qubits corresponds to the operator b1 b2 = (b I)(I b) = (b b), where bn is n the operator corresponding to the value of the qubit. Find the expected value of the product of the values of the qubits. c) It is true for statistically independent variables that the expected value of their product is the expected value income. Are the values of the qubits statistically independent in the state |?

Tarkastellaan kahden kubitin tilaa [I) = =100) + i- 3 4 101) + 110) . a) Selvita molempien kubittien odotusarvot erikseen. b) Kubittien arvojen tuloa vastaa operaattori b1b2 = (b 8 I) (1 2 b) = (bg b), missa bn on nin kubitin arvoa vastaava operaattori. Selvita kubittien arvojen tulon odotusarvo. c) Tilastollisesti riippumattomille suureille patee, etta niiden tulon odotusarvo on odotusarvojen tulo. Ovatko kubittien arvot tilastollisesti riippumattomat tilassa [I)