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|name=MaxEntangled | |name=MaxEntangled | ||
|desc=Produces a [[maximally entangled]] [[bipartite]] [[pure state]] | |desc=Produces a [[maximally entangled]] [[bipartite]] [[pure state]] | ||
| | |rel=[[Bell]]<br />[[BrauerStates]] | ||
| | |cat=[[List of functions#Special_states,_vectors,_and_operators|Special states, vectors, and operators]] | ||
|upd=November | |upd=November 28, 2012 | ||
|v= | |v=0.50}} | ||
<tt>'''MaxEntangled'''</tt> is a [[List of functions|function]] that returns the canonical [[maximally entangled]] [[bipartite]] [[pure state]]. The state can be chosen to be either full or sparse. | <tt>'''MaxEntangled'''</tt> is a [[List of functions|function]] that returns the canonical [[maximally entangled]] [[bipartite]] [[pure state]]. The state can be chosen to be either full or sparse. | ||
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===A maximally entangled qubit state=== | ===A maximally entangled qubit state=== | ||
To generate a maximally entangled pair of qubits you can use the following line of code: | To generate a maximally entangled pair of qubits you can use the following line of code: | ||
< | <syntaxhighlight> | ||
>> MaxEntangled(2) | >> MaxEntangled(2) | ||
| Line 30: | Line 30: | ||
0 | 0 | ||
0.7071 | 0.7071 | ||
</ | </syntaxhighlight> | ||
If you want an unnormalized version of this state in which each entry of the vector is 0 or 1, specify <tt>NRML=0</tt>: | If you want an unnormalized version of this state in which each entry of the vector is 0 or 1, specify <tt>NRML=0</tt>: | ||
< | <syntaxhighlight> | ||
>> MaxEntangled(2,0,0) | >> MaxEntangled(2,0,0) | ||
| Line 42: | Line 42: | ||
0 | 0 | ||
1 | 1 | ||
</ | </syntaxhighlight> | ||
===In larger systems=== | ===In larger systems=== | ||
When <tt>DIM</tt> is large, it is usually best to specify <tt>SP=1</tt> in order to save memory. For example, this produces a maximally entangled pure state in $\mathbb{C}^{10} \otimes \mathbb{C}^{10}$: | When <tt>DIM</tt> is large, it is usually best to specify <tt>SP=1</tt> in order to save memory. For example, this code produces a maximally entangled pure state in $\mathbb{C}^{10} \otimes \mathbb{C}^{10}$: | ||
< | <syntaxhighlight> | ||
>> MaxEntangled(10,1) | >> MaxEntangled(10,1) | ||
| Line 61: | Line 61: | ||
(89,1) 0.3162 | (89,1) 0.3162 | ||
(100,1) 0.3162 | (100,1) 0.3162 | ||
</ | </syntaxhighlight> | ||
{{SourceCode|name=MaxEntangled}} | |||
Latest revision as of 20:01, 6 November 2014
| MaxEntangled | |
| Produces a maximally entangled bipartite pure state | |
| Other toolboxes required | none |
|---|---|
| Related functions | Bell BrauerStates |
| Function category | Special states, vectors, and operators |
MaxEntangled is a function that returns the canonical maximally entangled bipartite pure state. The state can be chosen to be either full or sparse.
Syntax
- PSI = MaxEntangled(DIM)
- PSI = MaxEntangled(DIM,SP)
- PSI = MaxEntangled(DIM,SP,NRML)
Argument descriptions
- DIM: The dimension of the local subsystems on which PSI lives.
- SP (optional, default 0): A flag (either 1 or 0) indicating that PSI should or should not be sparse.
- NRML (optional, default 1): A flag (either 1 or 0) indicating that PSI should or should not be scaled to have Euclidean norm 1. If NRML=0 then PSI has Euclidean norm sqrt(DIM) and every element of PSI is 0 or 1.
Examples
A maximally entangled qubit state
To generate a maximally entangled pair of qubits you can use the following line of code:
>> MaxEntangled(2)
ans =
0.7071
0
0
0.7071If you want an unnormalized version of this state in which each entry of the vector is 0 or 1, specify NRML=0:
>> MaxEntangled(2,0,0)
ans =
1
0
0
1In larger systems
When DIM is large, it is usually best to specify SP=1 in order to save memory. For example, this code produces a maximally entangled pure state in $\mathbb{C}^{10} \otimes \mathbb{C}^{10}$:
>> MaxEntangled(10,1)
ans =
(1,1) 0.3162
(12,1) 0.3162
(23,1) 0.3162
(34,1) 0.3162
(45,1) 0.3162
(56,1) 0.3162
(67,1) 0.3162
(78,1) 0.3162
(89,1) 0.3162
(100,1) 0.3162Source code
Click here to view this function's source code on github.