# Quantum t-design

@inproceedings{Derakhshani2008QuantumT, title={Quantum t-design}, author={Mohammad Derakhshani}, year={2008} }

The Classical notions of Computation are rapidly entering Quantum Computation. People try to find Quantum counterparts for Classical concepts. In this essay, we will discuss about classical t-design, the quantum counterpart, Mutual Unbiased bases and a new technique for evaluating the expectation of a polynomial over Haar measure.

## One Citation

### Minimax quantum state estimation under Bregman divergence

- MathematicsQuantum
- 2019

We investigate minimax estimators for quantum state tomography under general Bregman divergences. First, generalizing the work of Koyama et al. [Entropy 19, 618 (2017)] for relative entropy, we find…

## References

SHOWING 1-10 OF 16 REFERENCES

### Quantum t-designs: t-wise Independence in the Quantum World

- Mathematics, PhysicsTwenty-Second Annual IEEE Conference on Computational Complexity (CCC'07)
- 2007

It is shown that an approximate 4-design provides a derandomization of the statedistinction problem considered by Sen (quant-ph/0512085), which is relevant to solving certain instances of the hidden subgroup problem.

### Efficient Simulation of Random Quantum States and Operators

- Mathematics
- 2005

We investigate the generation of quantum states and unitary operations that are ``random'' in certain respects. We show how to use such states to estimate the average fidelity, an important measure…

### Quantum computation and quantum information

- Physics, Computer Science
- 2000

This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.

### Reexamination of optimal quantum state estimation of pure states (5 pages)

- Mathematics
- 2005

A direct derivation is given for the optimal mean fidelity of quantum state estimation of a d-dimensional unknown pure state with its N copies given as input, which was first obtained by Hayashi in…

### Mutually unbiased bases are complex projective 2-designs

- MathematicsProceedings. International Symposium on Information Theory, 2005. ISIT 2005.
- 2005

It is demonstrated that maximal sets of MUBs come with a rich combinatorial structure by showing that they actually are the same objects as the complex projective 2-designs with angle set {0, 1/d}.

### Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

- Computer ScienceLecture Notes in Computer Science
- 2003

Efficient realizations of Reed-Muller codes are presented andGraphical models for codes arise from state realizations, and algebraic tools may improve such graph-based codes.

### NUMERICAL CUBATURE FROM ARCHIMEDES' HAT-BOX

- Mathematics
- 2006

Dedicated to Krystyna Kuperberg on the occasion of her 60th birthday Abstract. Archimedes' hat-box theorem states that uniform measure on a sphere projects to uniform measure on an interval. This…

### Basic Abstract Algebra

- Mathematics
- 1986

This book is intended as a text on abstract algebra for undergraduate students and is divided into five parts. The first part contains an informal introduction to sets, number systems, matrices, and…