Theorem qubit_meas_bijection of type Forall

from the theory of proveit.physics.quantum.circuits

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.physics.quantum.circuits import qubit_meas_bijection

# check that the built expression is the same as the stored expression
assert qubit_meas_bijection.expr == stored_expr
assert qubit_meas_bijection.expr._style_id == stored_expr._style_id
print("Passed sanity check: qubit_meas_bijection matches stored_expr")

Passed sanity check: qubit_meas_bijection matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{\lvert \psi \rangle \in \mathbb{C}^{2}~|~\left \|\lvert \psi \rangle\right \| = 1}~\left(\begin{array}{c} \begin{array}{l} \left[b \mapsto \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert \psi \rangle} & \meter & \qout{\lvert b \rangle}
} \end{array}\right)\right] \in  \\ \left[\left\{0, 1\right\} \xrightarrow[\text{onto}]{\text{1-to-1}} \left\{\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert \psi \rangle} & \meter & \qout{\lvert b \rangle}
} \end{array}\right\}_{b \in \left\{0, 1\right\}}\right] \end{array} \end{array}\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameter: 55 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 36 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13
10	Lambda	parameter: 60 body: 32
11	Operation	operator: 14 operands: 15
12	Operation	operator: 36 operands: 16
13	Operation	operator: 17 operands: 18
14	Literal
15	ExprTuple	41, 19
16	ExprTuple	55, 20
17	Literal
18	ExprTuple	21, 54
19	Operation	operator: 22 operand: 28
20	Operation	operator: 24 operands: 25
21	Operation	operator: 26 operand: 55
22	Literal
23	ExprTuple	28
24	Literal
25	ExprTuple	29, 30
26	Literal
27	ExprTuple	55
28	Lambda	parameter: 60 body: 31
29	Literal
30	Literal
31	Conditional	value: 32 condition: 33
32	Operation	operator: 34 operands: 35
33	Operation	operator: 36 operands: 37
34	Literal
35	ExprTuple	38, 39, 40
36	Literal
37	ExprTuple	60, 41
38	ExprTuple	42
39	ExprTuple	43
40	ExprTuple	44
41	Operation	operator: 45 operands: 46
42	Operation	operator: 47 operands: 48
43	Operation	operator: 49 operands: 50
44	Operation	operator: 51 operands: 52
45	Literal
46	ExprTuple	53, 54
47	Literal
48	NamedExprs	state: 55
49	Literal
50	NamedExprs	basis: 56
51	Literal
52	NamedExprs	state: 57
53	Literal
54	Literal
55	Variable
56	Literal
57	Operation	operator: 58 operand: 60
58	Literal
59	ExprTuple	60
60	Variable