Related papers: A Non-Commuting Stabilizer Formalism
The nonstabilizerness of quantum states is a necessary resource for universal quantum computation, yet its characterization is notoriously demanding. Quantifying nonstabilizerness typically requires an exponential number of measurements and…
This work is concerned with multi-party stabilizer states in the sense of quantum information theory. We investigate the homological invariants for states of which each party holds a large equal number N of quantum bits. We show that in…
Non-Gaussian entangled states play a crucial role in harnessing quantum advantage in continuous-variable quantum information. However, how to fully characterize N-partite (N > 3) non-Gaussian entanglement without quantum state tomography…
A non-associative quantum mechanics is proposed in which the product of three and more operators can be non-associative one. The multiplication rules of the octonions define the multiplication rules of the corresponding operators with…
Searches for possible new quantum phases and classifications of quantum phases have been central problems in physics. Yet, they are indeed challenging problems due to the computational difficulties in analyzing quantum many-body systems and…
This paper considers the problem of robust stability for a class of uncertain quantum systems subject to unknown perturbations in the system coupling operator. A general stability result is given for a class of perturbations to the system…
Operator quantum error correction is a recently developed theory that provides a generalized framework for active error correction and passive error avoiding schemes. In this paper, we describe these codes in the stabilizer formalism of…
We develop a method for visualizing the internal structure of multipartite entanglement in pure stabilizer states. Our algorithm graphically organizes the many-body correlations in a hierarchical structure. This provides a rich taxonomy…
We study the stabiliser formalism for qudits of arbitrary dimension $d$. In the free case, we show that the basic theorem of the stabiliser formalism remains valid: if the stabiliser subgroup $H$ is free as a $Z/dZ$-module and contains no…
In this work, we present a novel method to express the stabilizer of a k-uniform complete hypergraph state as a linear combination of local operators. Quantum hypergraph states generalize graph states and exhibit properties that are not…
Typical stabilizer codes aim to solve the general problem of fault-tolerance without regard for the structure of a specific system. By incorporating a broader representation-theoretic perspective, we provide a generalized framework that…
Our aim in this paper is to show an example of the formalism we have developed to avoid the label-tensor-product-vector-space-formalism of quantum mechanics when dealing with indistinguishable quanta. States in this new vector space, that…
Quantum entanglement plays an important role in quantum computation and communication. It is necessary for many protocols and computations, but causes unexpected disturbance of computational states. Hence, static analysis of quantum…
Any account of the emergence of classicality from quantum theory must address the fact that the quantum operators representing positions and momenta do not commute, whereas their classical counterparts suffer no such restrictions. To…
Of crucial importance to the development of quantum computing and information has been the construction of a quantum operations formalism that admits a description of quantum noise while simultaneously revealing the behavior of an open…
The Lindblad master equation describes the evolution of a large variety of open quantum systems. An important property of some open quantum systems is the existence of decoherence-free subspaces. A quantum state from a decoherence-free…
We develop a non-extensive thermodynamic formalism for the one-sided shift on a finite alphabet, inspired by Tsallis' generalization of Boltzmann entropy in statistical physics. We introduce notions of $q$-entropy, $q$-pressure, and…
A non-associative algebra of observables cannot be represented as operators on a Hilbert space, but it may appear in certain physical situations. This article employs algebraic methods in order to derive uncertainty relations and…
Classical and quantum states can be distinguished by entanglement entropy, which can be viewed as a measure of quantum resources. Entanglement entropy also plays a pivotal role in understanding computational complexity in simulating quantum…
Nonseparability - multipartite states that cannot be factorized - is one of the most striking features of quantum mechanics, as it gives rise to entanglement and non-causal correlations. In quantum computing, it also contributes directly to…