C/CS/Phy191
Problem Set 5
Out: October 21, 2007
1. The uncertainty principle bounds how well a quantum state can be localized simultaneously in the standard basis and the Fourier basis. In this question, we will derive an uncertainty principle for a discr
C/CS/Phy191
Problem Set 4 Solutions
Out: October 14, 2007
1. Show that the trace of an operator is independent of the basis in which it is evaluated. Answer: Let cfw_|i and cfw_| j be two orthonormal bases. Then the trace of an operator A in the first b
C/CS/Phy191
Problem Set 3 Solutions
Out: September 30, 2007
1. Show that if U and V are unitary operators acting on separate Hilbert spaces H1 and H2 respectively, then U V acting on the product space H1 H2 is also a unitary operator. If U and V are both
C/CS/Phy191
Problem Set 2 Solutions
Out: September 21, 2007
1. Alice is given as input a random bit ain and Bob a random bit bin . Without communicating with each other, Alice and Bob wish to output bits aout and bout respectively such that ain bin = aout
C/CS/Phy191
Problem Set 1 Solutions
Out: September 06, 2007
1. Consider the normalized states cos 1 sin 1 and cos 2 . sin 2 Find the condition on 1 and 2 such that the superposition cos 1 cos 2 + sin 1 sin 2 is normalized to unity ("properly normalized").