Question

Q5 a) Compute the en B where 6 В -4 - 1 3 b) compute the square root of A= 31 2 3 2 3 c) compute the A 6 exp(A) where (G d) using the Peres partial transpose condition whether or not the state 14>= { (C1007 + 1017+1107-117) is entangled

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Answer 1

so PE 4 3. { p-T 1 - 1 IN -3 4 then B = PD pe < 41 30711-17 -3 4 31 0 2 digonal mations then In B E [in3 G 4 1 31 I-1 the - 3 4 4 17 th3 Th3 -3 In 2 4 In 2 4 ln 3-3 In2 - 4Th 3 + 4 In 2 3 103-31n2 -31n3 4 4 1n2 4 11134 In12 123 34 33 3. In [ 4.2) In 2 ( 414 (23) [sta (32) in (1 l In

(b) Square root of A = 2 3 1 3 1 2 3 1 2 Eigen value ho 3 1-1 2 3-) 1 2 (2-1)3+12-413-3 (9- 313-4) +1(6-1) (2-1) (x2 - 4 1 + 3) - 3 (5-34) + 5-1=0 - 13 +672 +31 0-18=0 so da da = 1:73, 1.73 edgen nector 126. by using matrix calentatore fas dz=1.22 to.7827 01266 132 -3.73

So. A = PD ha 2 So. JA= 1 -0.732 2.73 6 - 0.268 -3.73 8 1.730 h 1 0 0 -1.73 - 0.333 0.333 0.333 -0.455 -0.167 0,622 0.0447 0.122 -0.167 Amp

exp (A) when os --- (os) eigen neelue d! کی عمو eigen vector (5) ( so P= 1) tog pl 25-025 2 Dz -0.25 125 601 'exp (1) o 1/0.25 -0.28) So exp(A) -0.25 1257 expisy & And