Related papers: Locally inequivalent four qubit hypergraph states

Stabilizer states and graph states find application in quantum error correction, measurement-based quantum computation and various other concepts in quantum information theory. In this work, we study party-local Clifford (PLC)…

Entanglement of any pure state of an N times N bi-partite quantum system may be characterized by the vector of coefficients arising by its Schmidt decomposition. We analyze various measures of entanglement derived from the generalized…

In quantum state discrimination, the observers are given a quantum system and aim to verify its state from the two or more possible target states. In the local quantum state marking as an extension of quantum state discrimination, there are…

We present an algorithm for verifying the local unitary (LU) equivalence of graph and stabilizer states. Our approach reduces the problem to solving a system of linear equations in modular arithmetic. Furthermore, we demonstrate that any LU…

Determining whether the original global state is uniquely determined by its local marginals is a prerequisite for some efficient tools for characterizing quantum states. This paper shows that almost all generic pure states of even…

We introduce algebriac sets in the products of complex projective spaces for multipartite mixed states, which are independent of their eigenvalues and only measure the "position" of their eigenvectors, as their non-local invariants (ie.…

Continuous-variable quantum states are of particular importance in various quantum information processing tasks including quantum communication and quantum sensing. However, a bottleneck has emerged with the fast increasing in size of the…

We show that the manifold of quantum states is endowed with a rich and nontrivial geometric structure. We derive the Fubini-Study metric of the projective Hilbert space of a multi-qubit quantum system, endowing it with a Riemannian metric…

Entangled many-body states are an essential resource for quantum computing and interferometry. Determining the type of entanglement present in a system usually requires access to an exponential number of parameters. We show that in the case…

We classify, up to local unitary equivalence, local unitary stabilizer Lie algebras for symmetric mixed states into six classes. These include the stabilizer types of the Werner states, the GHZ state and its generalizations, and Dicke…

We classify, up to local unitary equivalence, the set of $n$-qubit states that is stabilized by the diagonal subgroup of the local unitary group. We exhibit a basis for this set, parameterized by diagrams of nonintersecting chords…

A set of necessary and sufficient conditions are derived for the equivalence of an arbitrary pure state and a graph state on n qubits under stochastic local operations and classical communication (SLOCC), using the stabilizer formalism.…

Circle graph states are a structurally important family of graph states. The family's entanglement is a priori high enough to allow for universal measurement-based quantum computation (MBQC); however, MBQC on circle graph states is actually…

Using an inductive approach to classify multipartite entangled states under stochastic local operations and classical communication introduced recently by the authors [Phys. Rev. A 74, 052336 (2006)], we give the complete classification of…

We study dynamics of genuine entanglement for quantum states of three and four qubits under non-Markovian dephasing. Using a computable entanglement monotone for multipartite systems, we find that GHZ state is quite resilient state whereas…

Bell inequalities constitute a key tool in quantum information theory: they not only allow one to reveal nonlocality in composite quantum systems, but, more importantly, they can be used to certify relevant properties thereof. We provide a…

We study non-local properties of generic three-qubit pure states. First, we obtain the distributions of both the coefficients and the only phase in the five-term decomposition of Ac\'in et al. for an ensemble of random pure states generated…

We study the set of two-qubit pure states with real amplitudes and their geometrical representation in the three-dimensional sphere. In this representation, we show that the maximally entangled states --those locally equivalent to the Bell…

Quantum hypergraph states form a generalisation of the graph state formalism that goes beyond the pairwise (dyadic) interactions imposed by remaining inside the Gaussian approximation. Networks of such states are able to achieve…

Complex numbers are central to the formulation of quantum mechanics, yet their role as a genuine resource is only beginning to be understood. In this work, we demonstrate that quantum states with intrinsically complex amplitudes provide a…