Mermin Polynomials for Entanglement Evaluation in Grover's algorithm and Quantum Fourier Transform
arXiv:2001.05192 · doi:10.1007/s11128-020-02976-z
Abstract
The entanglement of a quantum system can be valuated using Mermin polynomials. This gives us a means to study entanglement evolution during the execution of quantum algorithms. We first consider Grover's quantum search algorithm, noticing that states during the algorithm are maximally entangled in the direction of a single constant state, which allows us to search for a single optimal Mermin operator and use it to evaluate entanglement 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 at each execution step, since in this case there is no single direction of evolution. 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 replayed thanks to a structured and documented open-source code that we provide.
arXiv comment24 pages
References in corpus (17)
- Entanglement detection
- Geometric measure of entanglement and applications to bipartite and multipartite quantum states
- On the role of entanglement in quantum computational speed-up
- Four qubits can be entangled in nine different ways
- Global entanglement in multiparticle systems
- Bell-type inequalities to detect true n-body non-separability
- Entanglement Detection in the Stabilizer Formalism
- Quantum Algorithms: Entanglement Enhanced Information Processing
- How entangled can two couples get?
- The polynomial invariants of four qubits
- Entanglement and non-locality are different resources
- Experimental test of Mermin inequalities on a 5-qubit quantum computer
- Entanglement monotones and maximally entangled states in multipartite qubit systems
- An entanglement monotone derived from Grover's algorithm
- Entangled Quantum States Generated by Shor's Factoring Algorithm
- Operational approach to Bell inequalities: applications to qutrits
- Quantum Entanglement involved in Grover's and Shor's algorithms: the four-qubit case