Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

Questions tagged [mub]

For questions about Mutually Unbiased Bases (MUBs).

8 questions
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votes
1 answer

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 a variety of reasons, e.g. because they provide…
glS
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6
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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 to 1. $$\left\langle V_i\middle|V_i\right\rangle…
user2669
6
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1 answer

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 Unbiased Bases (MUBs) if $\lvert\langle u_i\lvert…
glS
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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 X} \mathbb{P}_x = \frac{\Pi_{\rm…
glS
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High-dimensional QKD with abstract mutually unbiased bases

In trying to understand the mathematical details of high-dimensional QKD with few mutually unbiased bases. First, prepare a state $|\psi\rangle \in H^d$ as a linear combination of a first orthonormal basis $A$. Then use a second mutually unbiased…
JMark
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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 are implementations in Qiskit available which do…
Juri V
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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 strings. The procedure is implemented here. I want to…
Juri V
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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 [XX, ZZ] can be transferred to [ZI, IZ] by…
劉承瀚
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