Wolfram/QuantumFramework | Paclet Repository

Wolfram`QuantumFramework`

QuantumDistance

QuantumDistance [ qs 1 , qs 2 ,t]
	returns the distance between two quantum discrete states using measure t .

Details and Options



Examples

(7)

Basic Examples

(4)

Find the distance between two pure states in terms of fidelity:

In[1]:=

QuantumDistance



QuantumState

["0"],

QuantumState

["1"]

Out[1]=

0

Find the distance between two mixed states:

In[1]:=

QuantumDistance



QuantumState

[{{1/4,0},{0,3/4}}],

QuantumState

[{{1,0},{0,1}}]

Out[1]=

1

2

+

3

2

Find the distance between a pure state and a mixed state:

In[1]:=

QuantumDistance



QuantumState

[{{1/4,0},{0,3/4}}],

QuantumState

[{1,0}]

Out[1]=

1

2

Find the distance between two quantum states using the trace metric:

In[1]:=

QuantumDistance



QuantumState

[{{1/4,1},{1,3/4}}],

QuantumState

[{{1/2,2},{2,1/2}}],"Trace"

Out[1]=

17

4

Scope

(2)



Applications

(1)



SeeAlso

QuantumState

TechNotes

▪

The fidelity is calculated as

Tr[

1/2

ρ

1

.

ρ

2

.

1/2

ρ

1

]

with

ρ

1,2

the corresponding density matrices. The trace distance is

1

2

Tr[

2

(

ρ

1

-

ρ

2

)

]

. The Bures distance is

2(1-

fidelity

)

, and Bures angle is

ArcCos[fidelity]

. The Hilbert-Schmidt is the

Hilbert-Schmidt norm

of the difference between density matrices. The Bloch distance is the EuclideanDistance between two Bloch vectors. And the relative entropy is

Tr[

ρ

1

.Log[

ρ

1

]-

ρ

1

.Log[

ρ

2

]]

.

RelatedGuides

▪

Wolfram Quantum Computation Framework

""