Code to accompany Quantum steering: a review with focus on semi-definite programming

Daniel Cavalcanti and Paul Skrzypczyk

This repository provides a small collection of code which implements many of the semidefinite programs presented in the review article
Quantum steering: a review with focus on semi-definite programming
Daniel Cavalcanti and Paul Skrzypczyk
Rep. Prog. Phys. 80 024001 (2017) .

All code is written in MATLAB and requires:

• CVX - a Matlab-based convex modeling framework
• QETLAB - A MATLAB Toolbox for Quantum Entanglement

It has been tested on Matlab R2014a, and CVX 2.1

The code comprises the following:

• Membership, helper, and misc:

  • NSAssemblage: determine whether a bipartite assemblage is a valid non-signalling assemblage or not^§.
  • LHSAssemblage: determine whether a biparitte assemblage has an LHS model or not^§.
  • genAssemblage: generate an assemblage starting from a quantum state and a set of measurements.
  • validPOVMs: determine whether a set of POVMs is valid or not^§.
  • JMPOVMs: determine whether a set of measurements is jointly measurable or not^§.
  • genRandProjMeas: generate a random set of projective measurements.
  • genSinglePartyArray: generate the single-party determinstic probability distributions
  • bestSteeringMeasurements: find the optimal measurements given a state and a steering functional.
  • bestSteeringState: find the optimal state given a set of measurements and a steering functional.
  • findRadiusPolytopeInBlochSphere: determine the radius of the largest ball which can fit inside a polytope contained in the Bloch ball determined by a set of measurements^¶.

• Steering quantifiers:

  • steeringRobustness: calculate the (standard/consistent) Steering Robustness of an assemblage.
  • steeringWeight: calculate the (standard/consistent) Steering Weight of an assemblage.
  • steeringLHSRobustness: calculate the (standard/consistent) Steering LHS-Robustness of an assemblage.
  • steeringRobustnessState: estimate the Steering Robustness of a state.
  • steeringWeightState: estimate the Steering Weight of a state.

• Local-Hidden-State models:

  • targetStatePVMLHS: determine if a qubit-qudit state has an LHS model for all projective measurements on Alice.
  • targetStatePOVMLHS: determine if a qubit-qudit state has an LHS model for all POVMs on Alice.
  • findPVMLHSStateGivenWitness: find a qubit-qudit state that has an LHS model for all projective measurements on Alice and violates a given entanglement witness.
  • findPOVMLHSStateGivenWitness: find a qubit-qudit state that has an LHS model for all POVMs on Alice and violates a given entanglement witness.

• Multipartite steering:

  • fLHSTripartite1Unt: determine if a tripartite assemblage with one untrusted device could have arisen from a fully-local state.
  • fLHSTripartite2Unt: determine if a tripartite assemblage with two untrusted devices could have arisen from a fully-local state.
  • bLHSTripartite1Unt: determine if a tripartite assemblage with one untrusted device could have arisen from a bi-separable state.
  • bLHSTripartite2Unt: determine if a tripartite assemblage with two untrusted devices could have arisen from a bi-separable state. still to come

• Applications:

  • localSteeringGuessProb: calculate the one-sided device-independent local guessing prob. of an assemblage.
  • globalSteeringGuessProb: calculate the one-sided device-independent global guessing prob. of an assemblage.
  • localSteeringGuessProbState: estimate the one-sided device-independent local guessing prob. of a state.
  • globalSteeringGuessProbState: estimate the one-sided device-independent global guessing prob. of a state.

^§: These files can be used inside CVX as a means to enforce the corresponding constraint.

^¶: This file additionally needs vert2lcon.