result of the measurement is not affected by relative phases; thus, they can be ignored. The measurement result is an integer close to jQ/r for some j , and dividing by Q we are left with a number close to j/r . A continued fraction expansion can then reveal j and r . If we had measured the state before applying the QFT, the result would have been an integer of the form l + jr , which does not allow finding the period without knowledge of the shift. It is clear that periodic states are central to the success of Shor’s algorithm, and their importance is further demonstrated by their use in several other algorithms that make use of the QFT, all of which belong to a class of problems derived from the hidden subgroup problem [28]. The lack of a general analytical formula for the Groverian entanglement makes it hard to construct a model that explains the fact that the QFT does not seem to affect the entan- glement of periodic states. Nevertheless, an approximated formula may suffice, provided it remains close to the exact value when the number of qubits increases. Such an approximation may be attainable, since the set of periodic states is only a restricted set. Let us first consider a somewhat less restricted set of states, namely, states that are superpositions of any number of computational basis states, with amplitudes that have equal magnitudes and zero phases. Given some nonempty subset of basis states S , we refer to their superposition as an equal superposition state of q qubits (ES state) , 7 | + 〉 = 1 √$_{2}$ ( | 0 〉 + | 1 〉 ) . (10) | ψ q S 〉 = 1 √ | S | ∑ k ∈ S | k 〉 ;  ⊂ S ⊆ { 0 , 1 , . . . , Q − 1 } , (9) where | S | is the size of the set S . Clearly all periodic states are ES states. Some ES states are nonentangled, like the computational basis states themselves. Another example is the complete ES state | η 〉 , which is the superposition of all basis states and can be written as | + 〉 ⊗ $^{q}$, where 1. Definition of the equal superposition states A. Equal superposition states IV. THE ENTANGLEMENT OF PERIODIC STATES