Abstract
In this study, we provide a positive answer to the problem of whether N-qubit pure quantum states exist in which all k-body reduced density are maximally mixed for in []. In addition, for k ⩾ 4 and any d, there exists an integer N 0(k, d) such that whenever N ⩾ N 0(k, d), we can construct a series of infinite classes of k-uniform states of N qudits with any level d, including infinitely many absolutely maximally entangled states.
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