Related papers: Computing Local Invariants of Qubit Systems
We show that the presented real-number quantum theories, compatible with the independent source assumption, require the inclusion of a nonlocal map. This means that if the independent source assumption holds, in these models, complex-number…
We provide several applications of a previously introduced isomorphism between physical operations acting on two systems and entangled states [1]. We show: (i) how to implement (weakly) non-local two qubit unitary operations with a small…
According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits (random binary variables). This raises the possibility of a…
We introduce new entanglement monotones which generalize, to the case of many parties, those which give rise to the majorization-based partial ordering of bipartite states' entanglement. We give some examples of restrictions they impose on…
A polynomial depth quantum circuit effects, by definition a poly-local unitary transformation of tensor product state space. It is a physically reasonable belief [Fy][L][FKW] that these are precisely the transformations which will be…
In this paper, we focus on computing local minimizers of a multivariate polynomial optimization problem under certain genericity conditions. By using a technique in computer algebra and the second-order optimality condition, we provide a…
We provide a method to write down the density operator for any pure state of multi-qubit systems in the multiparticle spacetime algebra (MSTA) introduced by Doran, Gull, and Lasenby. Using the MSTA formulation, we analyze several aspects of…
We consider local unitary invariants and entanglement monotones for the mixed two qutrit system. Character methods for the local SU(3)xSU(3) transformation group are used to establish the count of algebraically independent polynomial…
Non-invertible symmetries of quantum field theories and many-body systems generalize the concept of symmetries by allowing non-invertible operations in addition to more ordinary invertible ones described by groups. The aim of this paper is…
We introduce two methods for estimating the density matrix for a quantum system: Quantum Maximum Likelihood and Quantum Variational Inference. In these methods, we construct a variational family to model the density matrix of a mixed…
There is an ongoing search for a physical or operational definition for quantum mechanics. Several informational principles have been proposed which are satisfied by a theory less restrictive than quantum mechanics. Here, we introduce the…
The fact that quantum mechanics predicts stronger correlations than classical physics is an essential cornerstone of quantum information processing. Indeed, these quantum correlations are a valuable resource for various tasks, such as…
We study the local indistinguishability problem of quantum states. By introducing an easily calculated quantity, non-commutativity, we present an criterion which is both necessary and sufficient for the local indistinguishability of a…
We refine recent local unitary entanglement classification for symmetric pure states of $n$ qubits (that is, states invariant under permutations of qubits) using local unitary stabilizer subgroups and Majorana configurations. Stabilizer…
Quantum algorithms provide a potential strategy for solving computational problems that are intractable by classical means. Computing the topological invariants of topological matter is one central problem in research on quantum materials,…
We investigate the relation between local unitary symmetries and entanglement invariants of multi-qubit systems. The Hilbert space of such systems can be stratified in terms of states with different types of symmetry. We review the…
The degree of the generators of invariant polynomial rings of is a long standing open problem since the very initial study of the invariant theory in the 19th century. Motivated by its significant role in characterizing multipartite…
This paper presents a hybrid classical-quantum program for density estimation and supervised classification. The program is implemented as a quantum circuit in a high-dimensional quantum computer simulator. We show that the proposed quantum…
We investigate the equivalence of quantum mixed states under local unitary transformations. For a class of rank-two mixed states, a sufficient and necessary condition of local equivalence is obtained by giving a complete set of invariants…
We investigate the local quantum uncertainty (LQU) between a block of L qubits and one single qubit in a composite system of n qubits driven through a quantum phase transition (QPT). A first-order QPT is analytically considered through a…