Entanglement in mutually unbiased bases
نویسندگان
چکیده
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 that a complete set of mutually unbiased bases of a bipartite system contains a fixed amount of entanglement, independent of the choice of the set. This has implications for entanglement distribution among the states of a complete set. In prime-squared dimensions we present an explicit experiment-friendly construction of a complete set with a particularly simple entanglement distribution. Finally, we describe the basic properties of mutually unbiased bases composed of product states only. The constructions are illustrated with explicit examples in low dimensions. We believe that the properties of entanglement in mutually unbiased bases may be one of the ingredients to be taken into account to settle the question of the existence of complete sets. We also expect that they will be relevant to applications of bases in the experimental realization of quantum protocols in higher-dimensional Hilbert spaces. 4 Present address: Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, Poland. 5 Author to whom any correspondence should be addressed. New Journal of Physics 13 (2011) 053047 1367-2630/11/053047+24$33.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft
منابع مشابه
Constructing Mutually Unbiased Bases from Quantum Latin Squares
We introduce orthogonal quantum Latin squares, which restrict to traditional orthogonal Latin squares, and investigate their application in quantum information science. We use quantum Latin squares to build maximally entangled bases, and show how mutually unbiased maximally entangled bases can be constructed in square dimension from orthogonal quantum Latin squares. We also compare our construc...
متن کاملMutually unbiased bases and discrete Wigner functions
Mutually unbiased bases and discrete Wigner functions are closely, but not uniquely related. Such a connection becomes more interesting when the Hilbert space has a dimension that is a power of a primeN = d, which describes a composite system of n qudits. Hence, entanglement naturally enters the picture. Although our results are general, we concentrate on the simplest nontrivial example of dime...
متن کاملComments on “Best Conventional Solutions to the King’s Problem”
The (Mean) King’s problem [1 – 3] is a kind of quantum estimation problem with delayed (classical) information and has been studied in detail [2, 3], relating with an unsolved problem on the existence of a maximal set of mutually unbiased bases (MUBs) [4]. The standard approach to solve the King’s problem is to utilize entanglement, and nowadays it is shown that the success probability is in fa...
متن کاملDetecting three-qubit bound MUB diagonal entangled states via Nonlinear optimal entanglement witnesses
One of the important approaches to detect quantum entanglement is using linear entanglement witnesses (EW s). In this paper, by determining the envelope of the boundary hyper-planes defined by a family of linear EW s, a set of powerful nonlinear optimal EW s is manipulated. These EW s enable us to detect some three qubits bound MUB (mutually unbiased bases) diagonal entangled states, i.e., the ...
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 2011