Michaelmas

Question 1

Give the properties of the inner product

Answer 1

Question 2

What does a self adjoint operator represet?

Answer 2

Observables

Question 3

What do unitary operators represent?

Answer 3

Time evolution

Question 4

What do the eigenvalues of Hermitian operators represent

Answer 4

The outcomes of measurements

Question 5

Give the formula for matrix elements

Answer 5

Aij = <i|A|j>

Question 6

Give the exponential of a matrix

Answer 6

Question 7

Give the density operator formula

Answer 7

Question 8

What is the trace of p^2

Answer 8

Question 9

What is the trace of a pure state

Answer 9

Question 10

What is the expectation value of A using the density operator

Answer 10

Question 11

Give the bloch sphere definition of qubit

Answer 11

Question 12

Give the bloch vector form of the density matrix

Answer 12

Question 13

Give a qubit in terms of theta and phi

Answer 13

Question 14

Give the formula for the distance between two qubits

Answer 14

Question 15

Give basis for tensor product space

Answer 15

Question 16

Give inner product on tensor product space

Answer 16

Question 17

What is the density matrix of a tensor product

Answer 17

Question 18

What is the density operator after measurement

Answer 18

Question 19

Define the partial traces

Answer 19

Question 20

Define the reduced density matrices

Answer 20

Question 21

When is the reduced density matrix pure?

Answer 21

Question 22

Define a Bell state

Answer 22

Question 23

What is the no cloning theorem

Answer 23

You cannot clone an arbitrary quantum state

Question 24

What is super dense coding?

Answer 24

Question 25

Outline Teleportation

Answer 25

Question 26

Outline QKD

Answer 26

Question 27

Give the CHSH inequality

Answer 27

Question 28

Define the types of entropy

Answer 28

Question 29

Define mutal info

Answer 29

Question 30

Define the types of quantum entropy

Answer 30

Question 31

Give schimdt number

Answer 31