qtools

Library to implement various quantum tools like state discrimination, non local games etc

• Only NPA Hierarchy is implemented for now

• This is in development mode

  Overview

• This implementation is general for any Bell Scenario and any array of constraints.

• You just need to input the Bell Scenario, NPA level and add the non-trivial constraints and the code will take care of the rest.

• If you want to just loop through a list of constraints say in case like you want a plot, you just need to call the add constraints with new constraints.

Methods of Installation

• Start by placing NPAsolver.py into your project directory along side your driver codes.
• MOSEK NUMPY and CVXPY are prerequisites.
• Refer the file structure in NPA Folder where check.py is the driver code.

Instantaiting NpaHierarchy Class

• Import NpaHierarchy class from NPAsolver.py from NPAsolver import NpaHierarchy
• Instantiate a NpaHierarchy object by passing in Bell Scenario and NPA level to class constructor. For eg. b=NpaHierarchy(2,level=2)
• The constructor method takes in oprArray, inputs, outputs and level as input
• You can pass in the bell scenario as array like [<Alice>,<Bob>,<Charlie>,...]
  • In <Alice> or <Bob> or ..., you need to enter [<Measurement 1>,<Measurement 2>,...]
  • In <Measurement i> for i in (1,2,...),.. you need to enter number of outcomes: this should be non-negative integer
• You can also input in oprArray just the number of measurements in , ,... and input the number of outcomes for all measurements of Alice bob and charlie using the outputs parameter
• In oprArray you can also just specifiy the number of parties, and specify the number of inputs and outputs for all parties using inputs and outputs parameter.
• If inputs and outputs parameter are left blank and it is required to calculate Bell Scenario, it will default to 2.
• If level is left blank it will do intermediate NPA. ## Examples of NpaHierarchy object.
• Bipartite Scenario with two input and two outcomes per input and 2nd NPA hierarchy b=NpaHierarchy(2,level=2)
• Bipartite Scenario where Alice has 2 inputs with one input with two comes and other input with three outcomes and Bob having three inputs with two outcomes each. The level being intermediate NPA. b=NpaHierarchy(oprArray=[[2,3],[2,2,2]])
• Bipartite Bell scenario where each Alice and Bob has three inputs with two outcomes per input(dichotomic) and 3rd NPA hierarchy. b=NpaHierarchy(2,inputs=3,outputs=2,level=3) ## Adding Constraints and Objective function:
• You can then specify the non-trivial constraints by calling addConstraints and passing in array of constraints as strings of format:
  • 0.8pab(o1o2|i1i2)+pabc(o1o2o3|i1i2i3)<=2.5, where i1,i2 are first and second inputs and o1,o2 are first and second outputs. For eg. b.addConstraints([f"pbc(00|10)<=0.25",f"pab(00|10)<=0.25",f"pac(00|01)<=0.25"])
• You can similarly pass in objective function as above just without using as equality or inequality. b.addObjective("pa(0|0)-pab(00|00)-pab(00|01)-pab(00|02)+pab(00|10)+pab(10|11)+pb(0|2)-pab(00|12)-pab(10|12)") ## Note:
• Now the code suppots a particular form of probability vectors inside addconstraints and addObjective functions.
  • The Probabilties cannot have the last outcome for any input, instead it needs to be written in particular format.
  • The banned probabilties can be expanded by thinking prob. as moments of projectors $\langle \Pia^x \Pib^y \rangle $
  • The prob. with last projector for a given input can then be written as $I(\textrm{identity})-\sum(\textrm{other outcomes of the inputs})$
  • For eg, in CHSH case, pab(10|11)= $\langle (I-\Pi0^1)A (\Pi0^1)B \rangle =$ pb(0|1)-pab(00|11)
• For now only <= and = is supported. You can frame in this format if possible. We will be adding more types.
• You can use python fstring to update values in your constraints