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| In [[quantum information]] theory, '''mutually unbiased bases''' in [[Hilbert space]] '''C'''<sup>''d''</sup> are two [[orthonormal basis|orthonormal bases]] <math>\{|e_1\rangle, \dots, |e_d\rangle\}</math> and <math>\{|f_1\rangle, \dots, |f_d\rangle\}</math> such that the [[square (algebra)|square]] of the [[magnitude (mathematics)|magnitude]] of the [[inner product]] between any basis states <math>|e_j\rangle</math> and <math>|f_k\rangle</math> equals the [[multiplicative inverse|inverse]] of the [[dimension]] ''d'':<ref name="bengtsson1">I. Bengtsson, Three ways to look at mutually unbiased bases, http://arxiv.org/abs/quant-ph/0610216.</ref>
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| :<math> |\langle e_j|f_k \rangle|^2 = \frac{1}{d}, \quad \forall j,k \in \{1, \dots, d\}. </math>
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| These bases are ''unbiased'' in the following sense: if a system is prepared in a state belonging to one of the bases, then all outcomes of the [[measurement in quantum mechanics|measurement]] with respect to the other basis will occur with equal probabilities.
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| == Overview ==
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| The notion of mutually unbiased bases was first introduced by Schwinger in 1960,<ref>J. Schwinger, Unitary Operator Bases, Harvard University, 1960, http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=222876&blobtype=pdf.</ref> and the first person to consider applications of mutually unbiased bases was Ivanovic<ref>I. D. Ivanovic, J. Phys. A. 14. 3241 (1981).</ref> in the problem of quantum state determination.
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| Another area where mutually unbiased bases can be applied is [[quantum key distribution]], more specifically in secure quantum key exchange.<ref name="planat1">M. Planat et al, A Survey of Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements, http://hal.ccsd.cnrs.fr/docs/00/07/99/18/PDF/MUB_FP.pdf.</ref> Mutually unbiased bases are used in many protocols since the outcome is random when a measurement is made in a basis unbiased to that in which the state was prepared. When two remote parties share two non-orthogonal quantum states, attempts by an eavesdropper to distinguish between these by measurements will affect the system and this can be detected. While many quantum cryptography protocols have relied on 1-[[qubit]] technologies, employing higher dimensional states, such as [[Qudit#Variations_of_the_qubit|qutrits]], allows for better security against eavesdropping.<ref name="planat1"/> This motivates the study of mutually unbiased bases in higher-dimensional spaces.
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| Other uses of mutually unbiased bases include [[Quantum tomography|quantum state reconstruction]],<ref>W. K. Wootters and B. D. Fields, Optimal State-Determination by Mutually Unbiased Measurements, Ann. Phys. 191 (1989) 363-381.</ref> [[quantum error correction|quantum error correction codes]],<ref>D. Gottesman, Class of quantum error-correcting codes saturating the quantum Hamming bound, Phys. Rev. A 54 (1996) 1862-1868.</ref><ref>A. R. Calderbank et al, Quantum Error Correction and Orthogonal Geometry, Phys. Rev. Lett. 78 (1997) 405-408.</ref> detection of [[quantum entanglement]],<ref>C. Spengler, M. Huber, S. Brierley, T. Adaktylos, B. C. Hiesmayr, [http://arxiv.org/abs/1202.5058 Entanglement detection via mutually unbiased bases], Phys. Rev. A 86, 022311 (2012).</ref> and the so called "mean king's problem".<ref>L. Vaidman et al, How to ascertain the values of <math>\sigma_x, \sigma_y,</math> and <math>\sigma_z</math> of a spin-1/2 particle, Phys. Rev. Lett. 58 (1987) 1385-1387.</ref><ref>B.-G. Englert and Y. Aharonov, The mean king’s problem: prime degrees of freedom, Phys. Lett. A 284 (2001) 1-5.</ref>
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| == Existence problem ==
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| Let <math>\mathfrak{M}(d)</math> denote the maximal number of mutually unbiased bases in the ''d''-dimensional Hilbert space '''C'''<sup>''d''</sup>. It is an open question<ref>T. Durt, B.-G. Englert, I. Bengtsson, K. Życzkowski, "On mutually unbiased bases", Int. J. Quantum Information, 8, 535-640 (2010), http://arxiv.org/abs/1004.3348.</ref> how many mutually unbiased bases, <math>\mathfrak{M}(d)</math>, one can find in '''C'''<sup>''d''</sup>, for arbitrary ''d''.
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| In general, if
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| :<math> d = p_1^{n_1} p_2^{n_2}...p_k^{n_k} </math>
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| is the [[integer factorization|prime number decomposition]] of ''d'', where
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| :<math> p_1^{n_1} < p_2^{n_2}<...<p_k^{n_k} </math>
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| then the maximal number of mutually unbiased bases which can be constructed satisfies<ref name="bengtsson1"/>
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| :<math>p_1^{n_1}+1 \le \mathfrak{M}(d) \le d+1. </math>
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| It follows that if the dimension of a Hilbert space ''d'' is an integer power of a prime number, then it is possible to find ''d'' + 1 mutually unbiased bases. This can be seen in the previous equation, as the prime number decomposition of ''d'' simply is <math> d = p_1^{n_1} </math>. Therefore,
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| :<math> \mathfrak{M}(d) = d + 1. </math>
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| Though the maximal number of mutually unbiased bases is known when ''d'' is an integer power of a prime number, it is not known for arbitrary ''d''.
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| == Examples of sets of mutually unbiased bases ==
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| === Example for ''d'' = 2 ===
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| The three bases
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| :<math> M_0 = \left\{ | 0 \rangle,| 1 \rangle \right\} </math>
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| :<math> M_1 = \left\{ \frac{| 0 \rangle+| 1 \rangle}{\sqrt{2}},\frac{| 0 \rangle-| 1 \rangle}{\sqrt{2}} \right\} </math>
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| :<math> M_2 = \left\{ \frac{| 0 \rangle+i | 1 \rangle}{\sqrt{2}},\frac{| 0 \rangle-i| 1 \rangle}{\sqrt{2}} \right\} </math>
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| provides the simplest example of mutually unbiased bases in '''C'''<sup>2</sup>. The above bases are composed of the [[eigenvectors]] of the [[Pauli spin matrices]] <math> \sigma_x, \sigma_z </math> and their product <math>\sigma_x \sigma_z</math>.
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| === Example for ''d'' = 4 ===
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| For ''d'' = 4, an example of ''d'' + 1 = 5 mutually unbiased bases where each basis is denoted as ''M''<sub>''j''</sub>, 0 ≤ ''j'' ≤ 4, is given as follows:<ref>A. Klappenecker, M. Roetteler, Constructions of Mutually Unbiased Bases, 2003, http://arxiv.org/abs/quant-ph/0309120.</ref>
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| :<math> M_0 = \left\{(1,0,0,0),(0,1,0,0),(0,0,1,0),(0,0,0,1)\right\} </math>
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| :<math> M_1 = \left\{\frac{1}{2}(1,1,1,1),\frac{1}{2}(1,1,-1,-1),\frac{1}{2}(1,-1,-1,1),\frac{1}{2}(1,-1,1,-1)\right\} </math>
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| :<math> M_2 = \left\{\frac{1}{2}(1,-1,-i,-i),\frac{1}{2}(1,-1,i,i),\frac{1}{2}(1,1,i,-i),\frac{1}{2}(1,1,-i,i)\right\} </math>
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| :<math> M_3 = \left\{\frac{1}{2}(1,-i,-i, -1),\frac{1}{2}(1,-i,i,1),\frac{1}{2}(1,i,i,-1),\frac{1}{2}(1,i,-i,1)\right\} </math>
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| :<math> M_4 = \left\{\frac{1}{2}(1,-i,-1,-i),\frac{1}{2}(1,-i,1,i),\frac{1}{2}(1,i,-1,i),\frac{1}{2}(1,i,1,-i)\right\} </math>
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| == Methods for finding mutually unbiased bases ==
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| === [[Weyl group]] method<ref name="bengtsson1"/> ===
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| Let <math> \hat{X} </math> and <math> \hat{Z} </math> be two [[unitary operators]] in the Hilbert space '''C'''<sup>''d''</sup> such that
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| :<math> \hat{X}\hat{Z} = \omega\hat{Z}\hat{X} </math>
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| for some [[phase factor]] <math> \omega </math>. If <math>\omega</math> is a [[primitive root of unity]], for example <math> \omega \equiv e^{\frac{2 \pi i}{d}} </math> then the [[eigenbasis|eigenbases]] of <math> \hat{X} </math> and <math> \hat{Z} </math> are mutually unbiased.
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| By choosing the eigenbasis of <math> \hat{Z} </math> to be the [[standard basis]], we can generate another basis unbiased to it using a Fourier matrix. The elements of the Fourier matrix are given by
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| :<math>F_{ab} = \omega^{ab}, 0 \le a,b \le N-1 </math>
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| Other bases which are unbiased to both the standard basis and the basis generated by the Fourier matrix can be generated using Weyl groups.<ref name="bengtsson1"/> The dimension of the Hilbert space is important when generating sets of mutually unbiased bases using Weyl groups. When ''d'' is a prime number, then the usual ''d'' + 1 mutually unbiased bases can be generated using Weyl groups. When ''d'' is not a prime number, then it is possible that the maximal number of mutually unbiased bases which can be generated using this method is 3.
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| === Unitary operators method using [[finite field]]s<ref name="bandy1">S. Bandyopadhyay, P. O. Boykin, V. Roychowdhury, F. Vatan, A new proof for the existence of mutually unbiased bases, 2001, http://arxiv.org/abs/quant-ph/0103162.</ref> ===
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| When ''d'' = ''p'' is [[prime]], we define the [[unitary operator]]s <math>\hat{X}</math> and <math>\hat{Z}</math> by
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| :<math> \hat{X} = \sum_{k=0}^{d-1} |k+1 \rangle \langle k| </math>
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| :<math> \hat{Z} = \sum_{k=0}^{d-1} \omega^k |k \rangle \langle k| </math>
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| where <math>\{ |k \rangle | 0 \le j \le d-1 \} </math> is the standard basis and <math>\omega = e^{\frac{2\pi i}{d}}</math> is a [[root of unity]].
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| Then the [[eigenbasis|eigenbases]] of the following ''d'' + 1 operators are mutually unbiased:<ref name="bandy1"/>
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| :<math> \hat{X}, \hat{Z}, \hat{X} \hat{Z}, \hat{X} \hat{Z}^2 ... \hat{X} \hat{Z}^{d-1} </math>
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| When <math>d=p^r</math> is a power of a prime, we make use of the [[finite field]] <math>\mathbb{F}_d</math> to construct a maximal set of ''d'' + 1 mutually unbiased bases. We label the elements of the computational basis of '''C'''<sup>''d''</sup> using the finite field:
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| <math>\{ |a \rangle | a \in \mathbb{F}_d \}</math>.
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| We define the operators <math> \hat{X_a} </math> and <math> \hat{Z_b} </math> in the following way
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| :<math>\hat{X_a} = \sum_{c \in \mathbb{F}_d} |c + a \rangle \langle c| </math>
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| :<math>\hat{Z_b} = \sum_{c \in \mathbb{F}_d} \chi (bc)|c \rangle \langle c| </math>
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| where
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| :<math>\chi(\theta) = \exp \left [ \frac{2\pi i }{p} \left ( \theta+ \theta^p + \theta^{p^2}+ \cdots + \theta^{p^{r-1}} \right ) \right ],</math>
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| is an additive character over the field and the addition and multiplication in the kets and <math>\chi(\cdot)</math> is that of <math>\mathbb{F}_d</math>.
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| Then we form ''d'' + 1 sets of [[commutativity|commuting]] unitary operators:
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| :<math>\{ \hat{Z_s} | s \in \mathbb{F}_d \} </math> and <math> \{ \hat{X_s}\hat{Z_{sr}} | s \in \mathbb{F}_d \} </math> for each <math> r \in \mathbb{F}_d </math>
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| The joint eigenbases of the operators in one set are mutually unbiased to that of any other set.<ref name="bandy1"/> We thus have ''d'' + 1 mutually unbiased bases.
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| === Hadamard matrix method<ref name="bengtsson1"/> ===
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| Given that one basis in a Hilbert space is the standard basis, then all bases which are unbiased with respect to this basis can be represented by the columns of a [[complex Hadamard matrix]] multiplied by a normalization factor. For ''d'' = 3 these matrices would have the form
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| :<math> U = \frac{1}{\sqrt{d}}
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| \begin{bmatrix}
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| 1 & 1 & 1 \\
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| e^{i \phi_{10}} & e^{i \phi_{11}} & e^{i \phi_{12}} \\
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| e^{i \phi_{20}} & e^{i \phi_{21}} & e^{i \phi_{22}}
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| \end{bmatrix}
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| </math>
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| The problem of finding a set of ''k''+1 mutually unbiased bases therefore corresponds to finding ''k'' mutually unbiased complex Hadamard matrices.
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| An example of a one parameter family of Hadamard matrices in a 4 dimensional Hilbert space is
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| :<math> H_4(\phi) = \frac{1}{2}
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| \begin{bmatrix}
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| 1 & 1 & 1 & 1 \\
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| 1 & e^{i\phi} & -1 & -e^{i \phi} \\
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| 1 & -1 & 1 & -1 \\
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| 1 & -e^{i\phi} & -1 & e^{i\phi}
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| \end{bmatrix}
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| </math>
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| == The problem of finding a maximal set of MUBs when ''d'' = 6 ==
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| The smallest dimension that is not an integer power of a prime is ''d'' = 6. This is also the smallest dimension for which the number of mutually unbiased bases is not known. The methods used to determine the number of mutually unbiased bases when ''d'' is an integer power of a prime number cannot be used in this case. Searches for a set of four mutually unbiased bases when ''d'' = 6, both by using Hadamard matrices<ref name="bengtsson1"/> and numerical methods<ref>P. Butterley, W. Hall, Numerical evidence for the maximum number of mutually unbiased bases in dimension six, 2007, http://arxiv.org/abs/quant-ph/0701122.</ref><ref>S. Brierley and S. Weigert, Maximal sets of mutually unbiased quantum states in dimension six, Phys. Rev. A 78, 042312 (2008) http://arxiv.org/abs/0808.1614.</ref> have been unsuccessful. The general belief is that the maximum number of mutually unbiased bases for ''d'' = 6 is <math>\mathfrak{M}(6) = 3 </math>.<ref name="bengtsson1"/>
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| == Entropic uncertainty relations and MUBs ==
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| There is an alternative characterization of mutually unbiased bases that considers them in terms of [[uncertainty principle|uncertainty relations]].<ref>I.I. Hirschman, Jr., A note on entropy. American Journal of Mathematics (1957) pp. 152–156.</ref>
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| [[Uncertainty_principle#Entropic_uncertainty_principle|Entropic uncertainty relations]] are analogous to the [[uncertainty principle|Heisenberg uncertainty principle]], and Maassen and Uffink<ref>H. Maassen, J.B.M. Uffink: Generalized entropic uncertainty relations: Phys. Rev. Lett. 60, 1103–1106 (1988).</ref> found that for any two bases <math>B_1 = \{ |a_{i}\rangle_{i=1}^d \} </math> and <math>B_2 = \{ | b_{j} \rangle _{j=1}^{d} \}</math>:
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| :<math> H_{B_1} + H_{B_2} \geq -2\log c.</math>
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| where <math>c = max | \langle a_j | b_k \rangle |</math> and <math> H_{B_1}</math> and <math>H_{B_2}</math> is the respective [[Entropy_(information_theory)#Definition|entropy]] of the bases <math>B_1</math> and <math>B_2</math>, when measuring a given state.
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| Entropic uncertainty relations are often preferable<ref>I. Damgard, S. Fehr, R. Renner, L. Salvail, C. Schaner(2006), http://arxiv.org/abs/quant-ph/0612014.</ref> to the [[uncertainty principle|Heisenberg uncertainty principle]], as they are not phrased in terms of the state to be measured, but in terms of ''c''.
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| In scenarios such as [[Quantum_cryptography#Quantum_key_exchange|quantum key distribution]], we aim for measurement bases such that full knowledge of a state with respect to one basis implies minimal knowledge of the state with respect to the other bases. This implies a high entropy of measurement outcomes, and thus we call these ''strong'' entropic uncertainty relations.
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| For two bases, the lower bound of the uncertainty relation is maximized when the measurement bases are mutually unbiased, since mutually unbiased bases are ''maximally incompatible'': the outcome of a measurement made in a basis unbiased to that in which the state is prepared in is completely random. In fact, for a ''d''-dimensional space, we have:<ref>D. Deutsch, Uncertainty in Quantum Measurements. Physical Review Letters, 50(9):631–633, February 1982.</ref>
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| :<math> H_{B_1} + H_{B_2} \geq \log (d) </math>
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| for any pair of mutually unbiased bases <math>B_1</math> and <math>B_2</math>. This bound is ''optimal'':<ref>A. Ambainis, Limits on entropic uncertainty relations for 3 and more MUBs, http://arxiv.org/abs/0909.3720.</ref> If we measure a state from one of the bases then the outcome has entropy 0 in that basis and an entropy of <math>\log(d)</math> in the other.
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| If the dimension of the space is a prime power, we can construct ''d'' + 1 MUBs, and then it has been found that<ref name="wehner1">S. Wehner and A. Winter, 2010 New J. Phys. 12 025009: http://iopscience.iop.org/1367-2630/12/2/025009/.</ref>
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| :<math> \sum_{k=1}^{d+1} H_{B_k} \geq \frac{d+1}{2} \log(\frac{d+1}{2} )</math>
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| which is stronger than the relation we would get from pairing up the sets and then using the Maassen and Uffink equation. Thus we have a characterization of ''d'' + 1 mutually unbiased bases as those for which the uncertainty relations are strongest.
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| Although the case for two bases, and for ''d'' + 1 bases is well studied, very little is known about uncertainty relations for mutually unbiased bases in other circumstances.<ref name="wehner1"/>
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| <ref name="yu1">S. Wu, S. Yu, K. Mølmer, Entropic uncertainty relation for mutually unbiased bases, Phys. Rev. A 79, 022104 (2009), http://arxiv.org/abs/0811.2298.</ref>
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| When considering more than two, and less than <math>d+1</math> bases it is known that large sets of mutually unbiased bases exist which exhibit very little uncertainty.<ref name="ballester">{{cite journal|last=Ballester|first=M.|coauthors=S. Wehner|title = Entropic uncertainty relations and locking: tight bounds for mutually unbiased bases |journal=Physical Review A| volume=75| pages=022319|year=2007|url=http://arxiv.org/abs/quant-ph/0606244|arxiv = 0704.1506 |bibcode = 2007PhRvA..75a2319C |doi = 10.1103/PhysRevA.75.012319 }}</ref> This means merely being mutually unbiased does not lead to high uncertainty, except when considering measurements in only two bases. Yet there do exist other measurements that are very uncertain.<ref name="wehner1"/><ref>{{cite journal|last=Wehner|first=S.|coauthors=A. Winter|title=Higher entropic uncertainty relations for anti-commuting observables|journal=Journal of Mathematical Physics|volume=49|pages=062105|year=2008|url=http://arxiv.org/abs/0710.1185}}</ref>
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| == Mutually unbiased bases in infinite dimension Hilbert spaces ==
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| While there has been investigation into mutually unbiased bases in infinite dimension Hilbert space, their existence remains an open question. It is conjectured that in a continuous Hilbert space, two [[orthonormal basis|orthonormal bases]] <math> |\psi_s^b \rangle </math> and <math> |\psi_{s'}^{b'} \rangle </math> are said to be mutually unbiased if<ref name="weigert1">S. Weigert, M. Wilkinson, Mutually Unbiased Bases for Continuous Variables, Phys. Rev. A 78, 020303(R) (2008), http://arxiv.org/abs/0802.0394.</ref>
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| :<math> |\langle \psi_s^b | \psi_{s'}^{b'} \rangle|^2 = k>0, s,s'\in \mathbb{R} </math>
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| For the generalized position and momentum eigenstates <math> | q \rangle, q\in \mathbb{R} </math> and <math> | p \rangle,p\in \mathbb{R} </math>, the value of ''k'' is
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| :<math> |\langle q | p \rangle|^2 = \frac{1}{2 \pi \hbar} </math>
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| The existence of mutually unbiased bases in a continuous Hilbert space remains open for debate, as further research in their existence is required before any conclusions can be reached.
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| Position states <math> | q \rangle </math> and momentum states <math> | p \rangle </math> are eigenvectors of Hermitian operators <math> \hat{x} </math> and <math> -i \frac{\partial}{\partial x} </math>, respectively. Weigert and Wilkinson<ref name="weigert1"/> were first to notice that also a linear combination of these operators have eigenbases, which have some features typical for the mutually unbiased bases. An operator <math> \alpha \hat{x}-i\beta\frac{\partial}{\partial x}</math> has eigenfunctions proportional to <math> \exp(i(ax^2+bx)) \,</math> with <math> \alpha+2\beta a=0 </math> and the corresponding eigenvalues <math> b\beta </math>. If we parametrize <math> \alpha </math> and <math> \beta </math> as <math> \cos \theta </math> and <math> \sin \theta </math>, the overlap between any eigenstate of the linear combination and any eigenstate of the position operator (both states normalized to the Dirac delta) is constant, but dependent on <math> \beta </math>:
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| :<math> |\langle x_\theta|x \rangle |^2=\frac{1}{2\pi|\sin\theta|}, </math>
| |
| where <math> |x\rangle </math> and <math> |x_\theta\rangle </math> stand for eigenfunctions of <math> \hat{x}</math> and <math> \cos\theta\hat{x}-i \sin \theta \frac{\partial}{\partial x}</math>.
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| | |
| == References ==
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| {{reflist|2}}
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| | |
| [[Category:Quantum information theory]]
| |
With so much of our focus uggs on sale our health and well-being, it's no wonder that companies such as ViSalus are seeing the success they have been over the past few years.
This bodes well for early investors and associates in the ViSalus company, but bodes even better for those who are looking to get in now that the company has established some solid groundwork. With the new expansion to the west coast in two locations, ViSalus is picking up steam, making now a great time to get involved with their MLM networking program.
What is ViSalus?
ViSalus Sciences is based in Troy, MI and now, in two locations on the west coast. Under the watchful eye of Dr. Michael Seidman, the Director of Product Research and Development at ViSalus, the company has patented several health and nutritional products.
These patents were based on the clinical and scientific studies performed and the results have been great so far.
ViSalus ugg boots sale products aim to optimize a person's health, but cheap ugg boots their business model is set up as a Unilevel MLM so that people can startup their own home business using the products ViSalus sells. With Dr. Seidman firmly in command of the health and well-being side of the company, CEO Ryan Blair has a firm grip on the reins in the business department.
Featured on CNBC, Time Magazine, Business Week, The Wall Street Journal and Forbes Magazine, Blair works alongside co-founders Nick Sarnicola and Blake Mallen to help their representatives meet their own personal earning goals through the unilevel MLM compensation plan.
What Products does ViSalus Sell?
ViSalus sells a number of science-based "nutraceuticals," a portmanteau of nutritional and pharmaceuticals. These products are designed to improve general health and well-being. Their signature product is the "Body by Vi," a 90-day challenge designed to improve your physical, mental and spiritual health.
Other products include ViSalus Science Vi-Pak, Neuro, Vimmunity, and their award-winning weight loss supplement, Slim Trim Shape Program.
These products help people become healthier by increasing their energy, providing mental clarity, helping with healthy ways to lose weight, lowering blood pressure and cholesterol and similar effects. Their products have been studied by the University of California Berkeley, New York University, National Institutes of Health (NIH), National Institute of Anti Aging (NIA), Stanford, MIT and the Beijing Medical University to name a few.
ViSalus is a legit company selling a unique brand of health and wellness products.
Unilevel Marketing Opportunities with ViSalus
Not only are the products successful at ViSalus, so are the associates and representatives of the marketing network. By utilizing a unilevel compressed MLM compensation plan, ViSalus has recorded some of the highest commissioned payouts in the history of multi-level marketing.
By building your first leg, you can get paid immediately, all the while earning commissions through your entire organization.
The weekly payouts come from many bonuses such as Fast Start Bonuses, while your monthly commissions are based on the sales volume in your organization. Plus, the way that the compressed unilevel plan is set up, you don't need too many people in your downstream to be successful.
All you need are the few quality frontline people any good frontline has and you're well on your way to earning sustainable residual income, even if you're a newcomer to MLM.
Eight Ways to Make Money with ViSalus
There are eight different ways to make money with ViSalus, all of which add up to a nice income when it's all said and done:
Direct Sales Commissions-- Commissions that are pulled from your direct sales of ViSalus products
First Order Bonus--A special thank you for getting started from the ViSalus team
Weekly Enroller Pool--A unique way to keep yourself and your organization motivated
Fast Start Bonus--An incentive to hit the ground with both feet running Team
Commissions--The big chunk of a successful MLM income will come from your team's ability to meet volume
BMW Bonus--ViSalus's unique program that covers the costs of a new BMW
Ambassador Star Bonus--An elite bonus that sets you apart in the industry not only in earnings, but in status as well
Residual Income on Backend--The best way to have constant money flowing in without having to do much work
The Bottom Line uggs on sale the ViSalus MLM Compensation Plan
When it's all said and done, ViSalus presents some very unique opportunities and incentives, giving anyone who is highly motivated and at least semi-knowledgeable about MLM a great shot at earning a lot of money. Of course, there are others who are seeing this opportunity, so whether you want to be recruited first or become a sponsor yourself is up to you.
If you choose the latter, you're going to have to be able to bring something to the table, not only in your own marketing knowledge, but in the high-level of recruits you bring in for your frontline.
Remember, unilevel plans are all frontline so there isn't much room for teamwork as they are all crossline competitors. Your prospects should be highly-qualified, not just friends and family. Generate the right leads online and be fully prepared with some cash ugg boots outlet on hand to pay for some leads if you can't get them organically.
It's highly suggested that you know how to build a successful downline here because there are a lot of products to be sold, but none are at the highest rates (which is why this is unilevel instead of binary).
If you enjoy a healthy lifestyle at home and are passionate about living well and helping others do the same, some of that passion will translate over into the ViSalus product line. Plus, when you become a representative, you can always get the latest information on the newest product lines, helping you to not only ugg boots live better with your new income, but healthier as well.