From 8e4996a1013b6763a75c7571eba6fa48dc4f859f Mon Sep 17 00:00:00 2001 From: Daniel Tsvetkov Date: Mon, 3 Feb 2020 14:57:45 +0100 Subject: [PATCH] clarifications about measurements --- lib_q_computer_math.py | 8 +++++++- 1 file changed, 7 insertions(+), 1 deletion(-) diff --git a/lib_q_computer_math.py b/lib_q_computer_math.py index 034bf30..7e0ca96 100644 --- a/lib_q_computer_math.py +++ b/lib_q_computer_math.py @@ -753,6 +753,12 @@ def test(): # III: Measurement | A quantum measurement is described by an orthonormal basis |e_j> # for state space. If the initial state of the system is |ψ> # then we get outcome j with probability pr(j) = ||^2 + # Note: The postulates are applicable on closed, isolated systems. + # Systems that are closed and are described by unitary time evolution by a Hamiltonian + # can be measured by projective measurements. Systems are not closed in reality and hence + # are immeasurable using projective measurements. + # POVM (Positive Operator-Valued Measure) is a restriction on the projective measurements, + # such that it encompasses everything except the environment. assert _0.get_prob(0) == 1 # Probability for |0> in 0 is 1 assert _0.get_prob(1) == 0 # Probability for |0> in 1 is 0 @@ -805,7 +811,7 @@ def test(): assert np.isclose(bell.get_prob(0b11), 0.5) # Probability for bell in 11 is 0.5 ################################ - # TODO: Don't know where outer product fits... + # TODO: Don't know where outer product fits - something about density operator? assert _0.x(_0) == Matrix([[1, 0], [0, 0]]) assert _0.x(_1) == Matrix([[0, 1],