Related papers: The stabilizer for $n$-qubit symmetric states
Let $S$ be a complete intersection of a smooth quadric 3-fold $Q$ and a hypersurface of degree $d$ in ${\mathbb P}^4$. In this paper we analyze GIT stability of $S$ with respect to the natural $G=SO(5, {\mathbb C})$-action. We prove that if…
In this paper we treat faithful actions of simple algebraic groups on irreducible modules and on the associated Grassmannian varieties. By explicit calculation, we show that in each case, with essentially one exception (only in…
The group of local unitary transformations partitions the space of n-qubit quantum states into orbits, each of which is a differentiable manifold of some dimension. We prove that all orbits of the n-qubit quantum state space have dimension…
Groverian and Geometric entanglement measures of the n-party pure state are expressed by the (n-1)-party reduced state density operator directly. This main theorem derives several important consequences. First, if two pure n-qudit states…
We investigate stabilizer codes with carrier qudits of equal dimension $D$, an arbitrary integer greater than 1. We prove that there is a direct relation between the dimension of a qudit stabilizer code and the size of its corresponding…
Given a 6-dimensional complex vector space $W$, we consider linear systems of skew-symmetric forms on W. The $n$-dimensional linear systems this kind, that can also be interpreted as $n$-dimensional linear subspaces of…
We study the entanglement structure of tripartite stabilizer states on $N$ qudits of dimension $D$, distributed across parties $A$, $B$, and $C$, under arbitrary local unitaries. Prior work by Bravyi et al. and Looi et al. showed that qubit…
The state hidden subgroup problem (StateHSP) is a recent generalization of the hidden subgroup problem. We present an algorithm that solves the non-abelian StateHSP over $N$ copies of the dihedral group of order $8$ (the symmetries of a…
In a recent paper (Phys. Rev. A 90, 022316 (2014) ), Goyeneche et al. established a link between the combinatorial notion of orthogonal arrays and k-uniform states and present open issue. (B) Find for what N there are 3-uniform states of…
In this paper, we mainly discuss the separability of $n$-partite quantum states from elements of density matrices. Practical separability criteria for different classes of $n$-qubit and $n$-qudit quantum states are obtained. Some of them…
We prove that the stabiliser group G of the Segre variety product in PG(V) of three projective lines over a field F has four orbits on singular points of PG(V), and that G has five orbits on points of PG(V) if F is finite.
The embedding of the $n$-qubit space into the $n$-fermion space with $2n$ modes is a widely used method in studying various aspects of these systems. This simple mapping raises a crucial question: does the embedding preserve the…
We study the dissipative stabilization of entangled states in arrays of quantum systems. Specifically, we are interested in the states of qubits (spin-1/2) which may or may not interact with one or more cavities (bosonic modes). In all…
The stabilizer ground state is defined is the lowest energy stabilizer state with respect to a given Hamiltonian. In many cases it is highly degenerate and does not give a unique stabilizer state. We define the optimal stabilizer ground…
We propose a reservoir design, composed of fixed dissipation operators acting each on few local subsystems, to stabilize an approximate GHZ state on n qubits. The main idea is to work out how a previously proposed sequence of two…
The unavoidable interaction of quantum systems with their environment usually results in the loss of desired quantum resources. Suitably chosen system Hamiltonians, however, can, to some extent, counteract such detrimental decay, giving…
The class of entangled $N$-qubit states known as graph states, and the corresponding stabilizer groups of $N$-qubit Pauli observables, have found a wide range of applications in quantum information processing and the foundations of quantum…
We investigate stabilizers of finite sets of rational points in Cantor space for the Higman-Thompson groups $V_{n,r}$. We prove that the pointwise stabilizer is an iterated ascending HNN extension of $V_{n,q}$ for any $q\geq 1$. We also…
The symmetric collective states of an atomic spin ensemble (i.e., many-body states that are invariant under particle exchange) are not preserved by decoherence that acts identically but individually on members of the ensemble. We develop a…
Non-stabilizer eigenstates of Clifford operators are natural candidates for endpoints of magic state distillation routines. We provide an explicit bestiary of all inequivalent non-stabilizer Clifford eigenstates for qutrits and ququints.…