# Quantum Computing and Entanglement for Mathematicians

@inproceedings{Wallach2008QuantumCA, title={Quantum Computing and Entanglement for Mathematicians}, author={N. Wallach}, year={2008} }

These notes are an expanded form of lectures to presented at the C.I.M.E. summer school in representation theory in Venice, June 2004. The sections of this article roughly follow the five lectures given. The first three lectures (sections) are meant to give an introduction to an audience of mathematicians (or mathematics graduate students) to quantum computing. No attempt is given to describe an implementation of a quantum computer (it is still not absolutely clear that any exist). There are… Expand

#### 13 Citations

Locally Maximally Entangled States of Multipart Quantum Systems

- Mathematics, Physics
- 2018

For a multipart quantum system, a locally maximally entangled (LME) state is one where each elementary subsystem is maximally entangled with its complement. This paper is a sequel to… Expand

Permutation symmetry and entanglement in quantum states of heterogeneous systems

- Mathematics, Physics
- 2017

Permutation symmetries of multipartite quantum states are defined only when the constituent subsystems are of equal dimensions. In this work we extend this notion of permutation symmetry to… Expand

Asymptotic properties of entanglement polytopes for large number of qubits

- Mathematics, Physics
- 2017

Entanglement polytopes have been recently proposed as the way of witnessing the SLOCC multipartite entanglement classes using single particle information. We present first asymptotic results… Expand

Invariants, Kronecker products, and combinatorics of some remarkable Diophantine systems

- Mathematics, Computer Science
- Adv. Appl. Math.
- 2009

This work lies across three areas of investigation that are by themselves of independent interest that led to a link that tied these areas together, which consists of a single formal power series with a multifaced interpretation. Expand

The black-hole/qubit correspondence: an up-to-date review

- Physics
- 2012

We give a review of the black-hole/qubit correspondence that incorporates not only the earlier results on black-hole entropy and entanglement measures, seven qubits and the Fano plane, wrapped branes… Expand

Existence of Locally Maximally Entangled Quantum States via Geometric Invariant Theory

- Mathematics, Physics
- 2017

We study a question which has natural interpretations both in quantum mechanics and in geometry. Let $$V_{1},\cdots , V_{n}$$V1,⋯,Vn be complex vector spaces of dimension $$d_{1},\ldots… Expand

via Symmetric Functions and Constant Term identities

- Mathematics
- 2010

This work lies across three areas of investigation that are by themselves of independent interest. A problem that arose in quantum computing led us to a link that tied these areas together. This link… Expand

On the black-hole/qubit correspondence

- Physics
- 2011

Abstract.The entanglement classification of four qubits is related to the extremal black holes of the 4-dimensional STU model via a time-like reduction to three dimensions. This correspondence is… Expand

Products of characters of the symmetric group

- Mathematics
- 2017

In a recent paper, the authors introduced a new basis of the ring of symmetric functions which evaluate to the irreducible characters of the symmetric group at roots of unity. The structure… Expand

Products of symmetric group characters

- Mathematics, Computer Science
- J. Comb. Theory, Ser. A
- 2019

Abstract In [33] , the authors introduced a new basis of the ring of symmetric functions which evaluate to the irreducible characters of the symmetric group at roots of unity. The structure… Expand

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