Entanglement in quantum search database: periodicity variations and countingEntanglement in quantum search database: periodicity variations and counting Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2024-04-182022enEmploying the single item search algorithm of N dimensional database it is shown that: First, the entanglement developed between two any-size parts of database space varies periodically during the course of searching. The periodic entanglement of the associated reduced density matrix quantified by several entanglement measures (linear entropy, von Neumann, Renyi), is found to vanish with period 𝒪(𝑠𝑞𝑟𝑡(𝑁)) . Second, functions of equal entanglement are shown to vary also with equal period. Both those phenomena, based on size-independent database bi-partition, manifest a general scale invariant property of entanglement in quantum search. Third, measuring the entanglement periodicity via the number of searching steps between successive canceling out, determines N, the database set cardinality, quadratically faster than ordinary counting. An operational setting that includes an Entropy observable and its quantum circuits realization is also provided for implementing fast counting. Rigging the marked item initial probability, either by initial advice or by guessing, improves hyper-quadratically the performance of those phenomena.http://creativecommons.org/licenses/by/4.0/Quantum Reports43221-237Ellinas_et_al_Quantum Rep._4(3)_2022.pdfChania [Greece]Library of TUC2024-04-18application/pdf1.2 MBfree Ellinas Dimosthenis Ελληνας Δημοσθενης Konstantakis Christos Κωνσταντακης Χρηστος MDPI Quantum search Quantum entanglement Grover Counting