Constructions of Mutually Unbiased Bases
نویسندگان
چکیده
Two orthonormal bases B andB′ of a d-dimensional complex inner-product space are called mutually unbiased if and only if |〈b|b〉| = 1/d holds for all b ∈ B and b′ ∈ B′. The size of any set containing pairwise mutually unbiased bases of C cannot exceed d + 1. If d is a power of a prime, then extremal sets containing d+1 mutually unbiased bases are known to exist. We give a simplified proof of this fact based on the estimation of exponential sums. We discuss conjectures and open problems concerning the maximal number of mutually unbiased bases for arbitrary dimensions.
منابع مشابه
Constructions of Approximately Mutually Unbiased Bases
We construct systems of bases of C which are mutually almost orthogonal and which might turn out to be useful for quantum computation. Our constructions are based on bounds of classical exponential sums and exponential sums over elliptic curves.
متن کاملec 2 00 3 There is no generalization of known formulas for mutually unbiased bases
In a quantum system having a finite number N of orthogonal states, two orthonormal bases {a i } and {b j } are called mutually un-biased if all inner products a i |b j have the same modulus 1/ √ N. This concept appears in several quantum information problems. The number of pairwise mutually unbiased bases is at most N + 1 and various constructions of N + 1 such bases have been found when N is a...
متن کاملSymplectic spreads, planar functions and mutually unbiased bases
In this paper we give explicit descriptions of complete sets of mutually unbiased bases (MUBs) and orthogonal decompositions of special Lie algebras sln(C) obtained from commutative and symplectic semifields, and from some other non-semifield symplectic spreads. Relations between various constructions are studied as well. We showed that automorphism groups of complete sets of MUBs and correspon...
متن کاملEquiangular Vectors Approach to Mutually Unbiased Bases
Two orthonormal bases in the d-dimensional Hilbert space are said to be unbiased if the square modulus of the inner product of any vector of one basis with any vector of the other equals 1 d . The presence of a modulus in the problem of finding a set of mutually unbiased bases constitutes a source of complications from the numerical point of view. Therefore, we may ask the question: Is it possi...
متن کاملEntanglement in mutually unbiased bases
One of the essential features of quantum mechanics is that most pairs of observables cannot be measured simultaneously. This phenomenon manifests itself most strongly when observables are related to mutually unbiased bases. In this paper, we shed some light on the connection between mutually unbiased bases and another essential feature of quantum mechanics, quantum entanglement. It is shown tha...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003