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Article Dans Une Revue Quantum Information Processing Année : 2021

Mermin polynomials for non-locality and entanglement detection in Grover’s algorithm and Quantum Fourier Transform

Résumé

The non-locality and thus the presence of entanglement of a quantum system can be detected using Mermin polynomials. This gives us a means to study non-locality evolution during the execution of quantum algorithms. We first consider Grover’s quantum search algorithm, noticing that states during the execution of the algorithm reach a maximum for an entanglement measure when close to a predetermined state, which allows us to search for a single optimal Mermin operator and use it to evaluate non-locality through the whole execution of Grover’s algorithm. Then the Quantum Fourier Transform is also studied with Mermin polynomials. A different optimal Mermin operator is searched for at each execution step, since in this case nothing hints us at finding a predetermined state maximally violating the Mermin inequality. The results for the Quantum Fourier Transform are compared to results from a previous study of entanglement with Cayley hyperdeterminant. All our computations can be repeated thanks to a structured and documented open-source code that we provide.
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Dates et versions

hal-03221875 , version 1 (10-05-2021)

Identifiants

  • HAL Id : hal-03221875 , version 1

Citer

Henri de Boutray, Hamza Jaffali, Frédéric Holweck, Alain Giorgetti, Pierre-Alain Masson. Mermin polynomials for non-locality and entanglement detection in Grover’s algorithm and Quantum Fourier Transform. Quantum Information Processing, 2021, 20 (3), pp.91 (29). ⟨hal-03221875⟩
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