Difference between revisions of "GHZState"
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− | <tt>'''GHZState'''</tt> is a [[List of functions|function]] that returns a GHZ state on a given number of qubits (or qudits). For example, the usual $3$-qubit GHZ state is $\frac{1}{\sqrt{2}}(|000\rangle + |111\rangle)$. More generally, the GHZ state on $q$ qudits with local dimension $d$ is $\frac{1}{\sqrt{d}}\sum_{j=0}^{d-1} |j\rangle^{\otimes q}$. The output of this function is a sparse vector. | + | <tt>'''GHZState'''</tt> is a [[List of functions|function]] that returns a [http://en.wikipedia.org/wiki/Greenberger%E2%80%93Horne%E2%80%93Zeilinger_state GHZ state] on a given number of qubits (or qudits). For example, the usual $3$-qubit GHZ state is $\frac{1}{\sqrt{2}}(|000\rangle + |111\rangle)$. More generally, the GHZ state on $q$ qudits with local dimension $d$ is $\frac{1}{\sqrt{d}}\sum_{j=0}^{d-1} |j\rangle^{\otimes q}$. The output of this function is a sparse vector. |
==Syntax== | ==Syntax== |
Latest revision as of 04:07, 20 December 2014
GHZState | |
Generates a (generalized) GHZ state | |
Other toolboxes required | none |
---|---|
Related functions | DickeState MaxEntangled WState |
Function category | Special states, vectors, and operators |
GHZState is a function that returns a GHZ state on a given number of qubits (or qudits). For example, the usual $3$-qubit GHZ state is $\frac{1}{\sqrt{2}}(|000\rangle + |111\rangle)$. More generally, the GHZ state on $q$ qudits with local dimension $d$ is $\frac{1}{\sqrt{d}}\sum_{j=0}^{d-1} |j\rangle^{\otimes q}$. The output of this function is a sparse vector.
Syntax
- GHZ_STATE = GHZState(DIM,Q)
- GHZ_STATE = GHZState(DIM,Q,COEFF)
Argument descriptions
- DIM: The local dimension.
- Q: The number of qubits (or qudits, if DIM > 2).
- COEFF (optional, default [1,1,...,1]/sqrt(DIM)): A vector whose $j$-th entry is the coefficient of the term $|j-1\rangle^{\otimes q}$ in the generalized GHZ state.
Examples
3-qubit GHZ state
The following code generates the usual 3-qubit GHZ state:
>> full(GHZState(2,3))
ans =
0.7071
0
0
0
0
0
0
0.7071
A 7-qudit GHZ state
The following code generates the following GHZ state living in $(\mathbb{C}^4)^{\otimes 7}$: \[\frac{1}{\sqrt{30}}\big( |0000000\rangle + 2|1111111\rangle + 3|2222222\rangle + 4|3333333\rangle \big).\]
>> GHZState(4,7,[1,2,3,4]/sqrt(30))
ans =
(1,1) 0.1826
(5462,1) 0.3651
(10923,1) 0.5477
(16384,1) 0.7303
A very large GHZ state
This script has no trouble creating GHZ states on very large numbers of qudits. The following code generates the GHZ state in $(\mathbb{C}^3)^{\otimes 30}$:
>> GHZState(3,30)
ans =
(1,1) 0.5774
(102945566047325,1) 0.5774
(205891132094649,1) 0.5774
Source code
Click here to view this function's source code on github.