# Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

This resource function is obsolete. Use the paclet Wolfram/QuantumFramework instead.

Function Repository Resource:

Represent the outcomes of a quantum measurement

Contributed by:
Jonathan Gorard and Taufiq Murtadho

ResourceFunction["QuantumMeasurement"][<| represents the result of a quantum measurement with possible outcomes |

ResourceFunction["QuantumMeasurement"] shares many properties in common with CategoricalDistribution.

The Association <|*o*_{1}→*p*_{1},*o*_{2}→*p*_{2},…|> has keys given by named measurement outcomes *o*_{i} and values given by probabilities *p*_{i}.

ResourceFunction["QuantumMeasurement"][…]["*prop*"] gives the property "*prop*" of the specified quantum measurement. Possible properties include:

"Distribution" | CategoricalDistribution object representing the measurement outcome(s) |

"Outcomes" | list of possible measurement outcomes |

"Probabilities" | association of measurement outcomes and their respective probabilities |

"ProbabilitiesList" | list of measurement probabilities |

"ProbabilityTable" | measurement outcomes and their probabilities in a Dataset |

"ProbabilityArray" | measurement probabilities in a SparseArray |

"ProbabilityPlot" | visualization of the measurement probability function |

"TopProbabilities" | list of measurement outcomes with the highest probabilities |

"TopProbabilities"→n | list of top n measurement outcomes with the highest probabilities |

"Entropy" | exact entropy of the measurement distribution |

"NEntropy" | numerical approximation of entropy of the measurement distribution |

"SimulatedMeasurement" | outcome of one simulated measurement |

{"SimulatedMeasurement",n} | list of outcomes from n simulated measurements |

"Mean" | (symbolic) mean of all measurement outcomes |

"States" | list of possible QuantumDiscreteState objects following measurement |

"StateAssociation" | association of measurement outcomes and their respective QuantumDiscreteState objects |

"StateProbabilities" | association of QuantumDiscreteState objects and their respective probabilities |

"StateProbabilityTable" | QuantumDiscreteState objects and their probabilities in a Dataset |

"TopStateProbabilities" | list of QuantumDiscreteState objects with the highest probabilities |

"TopStateProbabilities"→n | list of top n QuantumDiscreteState objects with the highest probabilities |

"SimulatedStateMeasurement" | QuantumDiscreteState object yielded by one simulated measurement |

{"SimulatedStateMeasurement",n} | list of QuantumDiscreteState objects yielded by n simulated measurements |

"MeanState" | (symbolic) mean of all QuantumDiscreteState objects |

"Properties" | list of all property names |

Define a QuantumMeasurement object for a two-level quantum system with two possible measurement outcomes:

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Return the associated CategoricalDistribution object:

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Return the list possible QuantumDiscreteState objects following measurement:

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Conduct a simulated measurement:

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Conduct 100 simulated measurements:

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QuantumMeasurement automatically normalizes the input probabilities:

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Return the association of measurement outcomes and their respective probabilities:

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Return the association of measurement outcomes and their respective QuantumDiscreteState objects:

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Compute the QuantumDiscreteState object yielded by a simulated measurement:

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Compute the list of QuantumDiscreteState objects yielded by 10 simulated measurements:

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Compute the exact entropy of the measurement distribution:

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Compute the approximate (numerical) entropy of the measurement distribution:

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Define a QuantumMeasurement object for a three-level quantum system with four possible measurement outcomes:

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Return the association of measurement outcomes and their respective probabilities:

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Return the association of QuantumDiscreteState objects and their respective probabilities:

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View a list of properties that can be extracted from a QuantumMeasurement object:

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Return the CategoricalDistribution object representing the measurement outcomes:

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Return the list of possible measurement outcomes:

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Return the association of measurement outcomes and their respective probabilities:

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Return the list of measurement probabilities:

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Return the measurement outcomes and their probabilities in a Dataset:

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Return the measurement probabilities in a SparseArray:

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Visualize the measurement probability function:

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Return the list of measurement outcomes with the highest probabilities:

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Return the list of 1 top measurement outcomes with the highest probabilities:

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Return the exact entropy of the measurement distribution:

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Return the approximate (numerical) entropy of the measurement distribution:

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Return the outcome of one simulated measurement:

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Return the list of outcomes from 100 simulated measurements:

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Return the symbolic mean of all measurement outcomes:

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Return the list of possible QuantumDiscreteState objects following measurement:

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Return the association of measurement outcomes and their respective QuantumDiscreteState objects:

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Return the association of QuantumDiscreteState objects and their respective probabilities:

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Return the QuantumDiscreteState objects and their probabilities in a Dataset:

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Return the list of QuantumDiscreteState objects with the highest probabilities:

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Return the list of 1 top QuantumDiscreteState objects with the highest probabilities:

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Return the QuantumDiscreteState object yielded by one simulated measurement:

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Return the list of QuantumDiscreteState objects yielded by 10 simulated measurements:

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Return the symbolic mean of all QuantumDiscreteState objects:

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- 1.0.0 – 12 April 2021

This work is licensed under a Creative Commons Attribution 4.0 International License