Unextendible mutually unbiased bases from Pauli C\classes
نویسندگان
چکیده
We provide a construction of sets of d/2 + 1 mutually unbiased bases (MUBs) in dimensions d = 4, 8 using maximal commuting classes of Pauli operators. We show that these incomplete sets cannot be extended further using the operators of the Pauli group. What is more, specific examples of sets of MUBs obtained using our construction are shown to be strongly unextendible; that is, there does not exist another vector that is unbiased with respect to the elements in the set. We conjecture the existence of such unextendible sets in higher dimensions d = 2(n > 3) as well. Furthermore, we prove an interesting connection between these unextendible sets and state-independent proofs of the Kochen-Specker (KS) theorem for two-qubit systems. Our construction also leads to a proof of the tightness of an H2 entropic uncertainty relation for any set of three MUBs constructed from Pauli classes in d = 4.
منابع مشابه
Unextendible Mutually Unbiased Bases (after Mandayam, Bandyopadhyay, Grassl and Wootters)
We consider questions posed in a recent paper of Mandayam et al. (2014) on the nature of “unextendible mutually unbiased bases.” We describe a conceptual framework to study these questions, using a connection proved by the author in Thas (2009) between the set of nonidentity generalized Pauli operators on the Hilbert space of N d-level quantum systems, d a prime, and the geometry of non-degener...
متن کامل16 2 v 2 3 0 M ar 2 00 1 A new proof for the existence of mutually unbiased bases ∗
We develop a strong connection between maximally commuting bases of orthogonal unitary matrices and mutually unbiased bases. A necessary condition of the existence of mutually unbiased bases for any finite dimension is obtained. Then a constructive proof of the existence of mutually unbiased bases for dimensions which are power of a prime is presented. It is also proved that in any dimension d ...
متن کاملnt - p h / 01 03 16 2 v 1 2 9 M ar 2 00 1 A new proof for the existence of mutually unbiased bases ∗
We develop a strong connection between maximally commuting bases of orthogonal unitary matrices and mutually unbiased bases. A necessary condition of the existence of mutually unbiased bases for any finite dimension is obtained. Then a constructive proof of the existence of mutually unbiased bases for dimensions which are power of a prime is presented. It is also proved that in any dimension d ...
متن کاملAn angular momentum approach to quadratic Fourier transform , Hadamard matrices , Gauss sums , mutually unbiased bases , unitary group and Pauli group
The construction of unitary operator bases in a finite-dimensional Hilbert space is reviewed through a nonstandard approach combinining angular momentum theory and representation theory of SU(2). A single formula for the bases is obtained from a polar decomposition of SU(2) and analysed in terms of cyclic groups, quadratic Fourier transforms, Hadamard matrices and generalized Gauss sums. Weyl p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Quantum Information & Computation
دوره 14 شماره
صفحات -
تاریخ انتشار 2014