Related papers: The stabilizer for $n$-qubit symmetric states

The standard stabilizer formalism provides a setting to show that quantum computation restricted to operations within the Clifford group are classically efficiently simulable: this is the content of the well-known Gottesman-Knill theorem.…

We show an improved inverse theorem for the Gowers-$3$ norm of $n$-qubit quantum states $|\psi\rangle$ which states that: for every $\gamma\geq 0$, if the $\textsf{Gowers}(|\psi \rangle,3)^8 \geq \gamma$ then the stabilizer fidelity of…

Verifying prepared quantum states is crucial for hybrid systems whose subsystems may have different local dimensions. We present a generalized stabilizer framework and associated test that apply to general multi-qudit states, including…

Let $G$ be a permutation group on the finite set $\Omega$. We prove various results about partitions of $\Omega$ whose stabilizers have good properties. In particular, in every solvable permutation group there is a set-stabilizer whose…

The $n$-qubit stabilizer states are those left invariant by a $2^n$-element subset of the Pauli group. The Clifford group is the group of unitaries which take stabilizer states to stabilizer states; a physically--motivated generating set,…

Hypergraph states of many quantum bits share the rich interplay between simple combinatorial description and nontrivial entanglement properties enjoyed by the graph states that they generalize. In this paper, we consider hypergraph states…

We show that quantum states with "low stabilizer complexity" can be efficiently distinguished from Haar-random. Specifically, given an $n$-qubit pure state $|\psi\rangle$, we give an efficient algorithm that distinguishes whether…

We propose a measurement scheme that validates the preparation of an $n$-qubit stabilizer state. The scheme involves a measurement of $n$ Pauli observables, a priori determined from the stabilizer state and which can be realized using…

We derive necessary and sufficient conditions for the LU-equivalence of two general (pure or mixed) $n$-qubit states as well as we determine the local unitary operators connecting them. Almost all relevant information is contained in the…

Let $|\Psi>$ be an arbitrary stabilizer state distributed between three remote parties, such that each party holds several qubits. Let $S$ be a stabilizer group of $|\Psi>$. We show that $|\Psi>$ can be converted by local unitaries into a…

Despite growing interest in beyond-group symmetries in quantum condensed matter systems, there are relatively few microscopic lattice models explicitly realizing these symmetries, and many phenomena have yet to be studied at the microscopic…

Let G be a finite solvable permutation group. Then modulo a possibly trivial normal elementary abelian 3-subgroup, some set-stabilizer in G is a 2-group.

Non-symmetric GHZ states ($n$-GHZ$_\alpha$), defined by unequal superpositions of $|00...0>$ and $|11...1>$, naturally emerge in experiments due to decoherence, control errors, and state preparation imperfections. Despite their relevance in…

We find an interesting relationship between multipartite bound entangled states and the stabilizer formalism. We prove that if a set of commuting operators from the generalized Pauli group on $n$ qudits satisfy certain constraints, then the…

Recently, Ji et al disproved the LU-LC conjecture and showed that the local unitary and local Clifford equivalence classes of the stabilizer states are not always the same. Despite the fact this settles the LU-LC conjecture, a sufficient…

We show that measuring pairs of qubits in the Bell basis can be used to obtain a simple quantum algorithm for efficiently identifying an unknown stabilizer state of n qubits. The algorithm uses O(n) copies of the input state and fails with…

The group of local unitary transformations acts on the space of n-qubit pure states, decomposing it into orbits. In a previous paper we proved that a product of singlet states (together with an unentangled qubit for a system with an odd…

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…

Statistical verification of a quantum state aims to certify whether a given unknown state is close to the target state with confidence. So far, sample-optimal verification protocols based on local measurements have been found only for…

We describe the symmetry group of the stabilizer polytope for any number $n$ of systems and any prime local dimension $d$. In the qubit case, the symmetry group coincides with the linear and anti-linear Clifford operations. In the case of…