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Questions tagged [mub]

For questions about Mutually Unbiased Bases (MUBs).

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Simultaneous measurement using mutually unbiased bases (MUB)

I have some questions about the paper “O(N^3) Measurement Cost for Variational Quantum Eigensolver on Molecular Hamiltonians”. About the section 8 of this paper, they mentioned that the measurement of ...
劉承瀚's user avatar
1 vote
2 answers
95 views

Algorithm for Mutually Unbiased Basis Sets Available?

I'm looking for an implementation or a slightly more efficient algorithm for finding optimal Mutually Unbiased Bases (MUB). What I mean here are MUBs in terms of Pauli Strings as described here. There ...
Juri V's user avatar
  • 105
1 vote
1 answer
71 views

Stabilizer Matrices for Mutually Unbiased Bases - what goes wrong here?

In section VIII D of this paper, the authors describe a circuit synthesis procedure to find the unitary transformation (as a quantum circuit) which diagonalizes a set of mutually commuting pauli ...
Juri V's user avatar
  • 105
4 votes
2 answers
138 views

Are MUBs complex projective 3-designs?

Consider a finite subset $X\subset\mathbb{CP}^{d-1}$ of $d$-dimensional pure states. Following e.g. (Roy and Scott 2007), we say that $X$ is a complex projective $t$-design if $$\frac1{|X|}\sum_{x\in ...
glS's user avatar
  • 25.4k
7 votes
1 answer
504 views

Are SIC-POVMs optimal for quantum state reconstruction?

Mutually unbiased bases (MUBs) are pairs of orthonormal bases $\{u_j\}_j,\{v_j\}_j\in\mathbb C^N$ such that $$|\langle u_j,v_k\rangle|= \frac{1}{\sqrt N},$$ for all $j,k=1,...,N$. These are useful for ...
glS's user avatar
  • 25.4k
6 votes
1 answer
150 views

Why does full state reconstruction require at least $N+1$ MUBs?

Consider an $N$-dimensional space $\mathcal H$. Two orthonormal bases $\newcommand{\ket}[1]{\lvert #1\rangle}\{\ket{u_j}\}_{j=1}^N,\{\ket{v_j}\}_{j=1}^N\subset\mathcal H$ are said to be Mutually ...
glS's user avatar
  • 25.4k
6 votes
3 answers
650 views

Maximum number of "almost orthogonal" vectors one can embed in Hilbert space

In a Hilbert space of dimension $d$, how do I calculate the largest number $N(\epsilon, d)$ of vectors $\{V_i\}$ which satisfies the following properties. Here $\epsilon$ is small but finite compared ...
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