Related papers: Biunitary constructions in quantum information
We define generalised notions of biunitary elements in planar algebras and show that objects arising in quantum information theory such as Hadamard matrices, quantum latin squares and unitary error bases are all given by biunitary elements…
Unitary error bases have a great number of applications across quantum information and quantum computation, and are fundamentally linked to quantum teleportation, dense coding and quantum error correction. Werner's combinatorial…
In this paper we introduce quantum Latin squares, combinatorial quantum objects which generalize classical Latin squares, and investigate their applications in quantum computer science. Our main results are on applications to unitary error…
We introduce a construction that, given a pair (u,v) of complex Hadamard matrices of the same order, generates infinitely many biunitary matrices of varying (and distinct) orders. As a key application, this framework yields nested sequences…
Some combinatorial designs, such as Hadamard matrices, have been extensively researched and are familiar to readers across the spectrum of Science and Engineering. They arise in diverse fields such as cryptography, communication theory, and…
Error operator bases for systems of any dimension are defined and natural generalizations of the bit/sign flip error basis for qubits are given. These bases allow generalizing the construction of quantum codes based on eigenspaces of…
For the complete estimation of arbitrary unknown quantum states by measurements, the use of mutually unbiased bases has been well-established in theory and experiment for the past 20 years. However, most constructions of these bases make…
Unitary error bases generalize the Pauli matrices to higher dimensional systems. Two basic constructions of unitary error bases are known: An algebraic construction by Knill, which yields nice error bases, and a combinatorial construction…
We study the problem of constructing mutually unbiased bases in dimension six. This approach is based on an efficient numerical method designed to find solutions to the quantum state reconstruction problem in finite dimensions. Our…
Some problems of the quantum error-correcting codes theory can be reduced to the investigation of the higher-rank numerical ranges of the operators related to the error operators. We constructively verify a conjecture on the structure of…
Motivated by the classical comatrix coalgebra, we introduce the concept of a Newtonian comatrix coalgebra. We construct an infinitesimal unitary bialgebra on a matrix algebra and a weighted infinitesimal unitary bialgebra on a…
Recent works have investigated the emergence of a new kind of random matrix behaviour in unitary dynamics following a quantum quench. Starting from a time-evolved state, an ensemble of pure states supported on a small subsystem can be…
Unit derived schemes applied to Hadamard matrices are used to construct and analyse linear block and convolutional codes. Codes are constructed to prescribed types, lengths and rates and multiple series of self-dual, dual-containing, linear…
Bargmann invariants, multivariate traces of states, completely characterize any unitary-invariant property of a set of states. Unitary invariants enable the description of quantum resources such as basis-independent coherence and…
It is always possible to decide, with one-sided error, whether two quantum states are the same under a specific unitary transformation. However we show here that it is {\em impossible} to do so if the transformation is anti-linear and…
Complex Hadamard matrices, consisting of unimodular entries with arbitrary phases, play an important role in the theory of quantum information. We review basic properties of complex Hadamard matrices and present a catalogue of inequivalent…
We deepen the theory of quasiorthogonal and approximately quasiorthogonal operator algebras through an analysis of the commutative algebra case. We give a new approach to calculate the measure of orthogonality between two such subalgebras…
Based on the group structure of a unitary Lie algebra, a scheme is provided to systematically and exhaustively generate quantum error correction codes, including the additive and nonadditive codes. The syndromes in the process of…
The present survey results from the will to reconcile two approaches to quantum probabilities: one rather physical and coming directly from quantum mechanics, the other more algebraic. The second leading idea is to provide a unified picture…
Quantum access to arbitrary classical data encoded in unitary black-box oracles underlies interesting data-intensive quantum algorithms, such as machine learning or electronic structure simulation. The feasibility of these applications…