Computer Science
Physics
Quantum Computation

Calculate Entanglement Monotones

Determine if [sub]systems are entangled and quantify the entanglement

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In the Wolfram Quantum Framework, one can test if parts of a quantum system are entangled and quantify the amount of entanglement using different measures.

Install and load the QuantumFramework paclet:

In[1]:=

PacletInstall["Wolfram/QuantumFramework"]Needs["Wolfram`QuantumFramework`"]

Show the formula of the W-state for 4-qubits:

In[2]:=

QuantumState[{"W",4}]["Formula"]

Out[2]=

|0001〉+

|0010〉+

|0100〉+

|1000〉

One can calculate different quantum entanglement monotones using the function QuantumEntanglementMonotone. Many different monotones are supported, such as concurrence, negativity, log-negativity, entanglement entropy, Renyi entropy, and realignment.

Calculate the concurrence:

In[3]:=

QuantumEntanglementMonotone[ψ,"Concurrence"]

Out[3]=

Given a Werner state of 1-qubits, with the probability p, calculate the negativity:

In[4]:=

$Assumptions=p∈Reals;FullSimplify@QuantumEntanglementMonotone[QuantumState[{"Werner",p,2}],"Negativity"]

Out[4]=

(-2+Abs[1-2p]+Abs[3-2p])

Create a random graph:

In[5]:=

g=RandomGraph[{4,5},VertexLabels"Name"]

Out[5]=

Create the corresponding graph-state:

In[6]:=

ϕ=QuantumState[{"Graph",g}];

One can also test if two systems are entangled or not, using the function QuantumEntangledQ.

Show that qubits that are connected by an edge, are entangled:

In[7]:=

QuantumEntangledQ[ϕ,List@@#]&/@EdgeList[g]

Out[7]=

{True,True,True,True,True}

Plot different types of entanglement monotone for state

β|00〉+

|11〉

In[8]:=

PlotQuantumEntanglementMonotone[QuantumState[{β,0,0,Sqrt[1-

]}],{{1},{2}},"Concurrence"], QuantumEntanglementMonotoneQuantumState[{β,0,0,Sqrt[1-

]}],{{1},{2}},"LogNegativity", QuantumEntanglementMonotoneQuantumState[{β,0,0,Sqrt[1-

]}],{{1},{2}},"EntanglementEntropy",{β,0,1},



Out[8]=

	Concurrence
	LogNegativity
	Entanglement Entropy

External Links

QuantumEntangledQ
QuantumEntanglementMonotone

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Contributed by: Wolfram Research, Quantum Computation Framework Team

Wolfram Language Example Repository

Calculate Entanglement Monotones

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