I. INTRODUCTION Quantum algorithms offer a potential speedup over classical algorithms in solving a num- ber of problems. The origin of this speedup is not yet fully understood, but quantum entanglement is believed to play a crucial role [1–3]. Therefore, it is of interest to analyze the entanglement of the quantum register during the operation of quantum algorithms such as Grover’s search algorithm and Shor’s factoring algorithm [4–8]. Currently, all known quantum algorithms presumed to provide an exponential speedup over their classical coun- terparts rely on the quantum Fourier transform (QFT) [9]. The most notable among them is Shor’s factoring algorithm [10, 11]. During the operation of these algorithms, the quantum states of the register are characterized by multipartite entanglement. Unlike the case of bipartite entanglement [12, 13], the multipartite entanglement in a register of q > 2 qubits, is not as well understood, partly because no analog of the Schmidt decomposition was found for multipartite systems. In order to evaluate the entanglement of the state of a quantum register, an entangle- ment measure is needed [14–17]. Axiomatic considerations have provided a set of properties that entanglement measures should satisfy [14–17]. These properties include the require- ment that any entanglement measure should vanish for product (or separable) states. It should be invariant under local unitary operations and should not increase as a result of any sequence of local operations complemented by only classical communication between the parties. Quantities that satisfy these properties are called entanglement monotones. These properties provide useful guidelines in the search for entanglement measures for multipartite quantum states. Entanglement measures based on metric properties of the Hilbert space [14, 15, 18] and on polynomial invariants [19, 20] were proposed and shown to satisfy these requirements. Specific measures of multipartite entanglement include the average bipartite measure [21] the Groverian measure [22], and the geometric measure [23]. A major difficulty in the evaluation of multipartite measures is that they involve a minimization of a compli- cated function in a high-dimensional space. As a result, there are no general closed-form expressions for these measures. The Groverian entanglement generated in Shor’s algorithm was analyzed in Ref. [7]. It was shown that the entanglement builds up during the preprocessing stage and that the QFT has little effect on the Groverian measure. This is somewhat surprising since, in general, the 2