相关论文: Symmetries and entanglement of stabilizer states

The determination of many special types of quantum states has been studied thoroughly, such as the generalized |GHZ> states, |W> states equivalent under stochastic local operations and classical communication and Dicke states. In this…

The central focus of this work is to make progress towards understanding entanglement as a resource for computation by examining the quantum correlations that can be extracted from stabilizer states. As such, we focus on the stabilizer…

We investigate the entanglement properties of pure quantum states describing $n$ qubits. We characterize all multipartite states which can be maximally entangled to local auxiliary systems using controlled operations. A state has this…

Entanglement types of pure states of 3 qubits are classified by means of their stabilisers in the group of local unitary operations. It is shown that the stabiliser is generically discrete, and that a larger stabiliser indicates a…

Stabiliser states play a central role in the theory of quantum computation. For example, they are used to encode computational basis states in the most common quantum error correction schemes. Arbitrary quantum states admit many stabiliser…

Consider a stabilizer state on $n$ qudits, each of dimension $D$ with $D$ being a prime or a squarefree integer, divided into three mutually disjoint sets or parts. Generalizing a result of Bravyi et al. [J. Math. Phys. \textbf{47}, 062106…

Symmetric quantum states are fascinating objects. They correspond to multipartite systems that remain invariant under particle permutations. This symmetry is reflected in their compact mathematical characterisation but also in their unique…

Stabilizer states, which are also known as the Clifford states, have been commonly utilized in quantum information, quantum error correction, and quantum circuit simulation due to their simple mathematical structure. In this work, we apply…

Symmetries are of fundamental interest in many areas of science. In quantum information theory, if a quantum state is invariant under permutations of its subsystems, it is a well-known and widely used result that its marginal can be…

Local unitary stabilizer subgroups constitute powerful invariants for distinguishing various types of multipartite entanglement. In this paper, we show how stabilizers can be used as a basis for entanglement verification protocols on…

We investigate the extremality of stabilizer states to reveal their exceptional role in the space of all $n$-qubit/qudit states. We establish uncertainty principles for the characteristic function and the Wigner function of states,…

A central challenge in quantum metrology is identifying optimal measurements that saturate the quantum Cramer-Rao bound under realistic constraints, e.g., local measurements. We show that symmetries of the probe state provide a general…

This thesis explores the use of entangled states in quantum computation and quantum information science. Entanglement, a quantum phenomenon with no classical counterpart, has been identified as an important and quantifiable resource in many…

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…

Quantum hypergraph states are the natural generalization of graph states. Here we investigate and analytically quantify entanglement and nonlocality for large classes of quantum hypergraph states. More specifically, we connect the geometric…

The stabiliser formalism allows the efficient description of a sizeable class of pure as well as mixed quantum states of N-qubit systems. That same formalism has important applications in the field of quantum error correcting codes, where…

We propose to characterize multipartite entanglement of pure states as local unitary transformations acting on some parts of a system that can be undone by local unitary transformations acting on other parts. This leads to a definition of…

Controlling operational errors and decoherence is one of the major challenges facing the field of quantum computation and other attempts to create specified many-particle entangled states. The field of quantum error correction has developed…

The theory of stabilizer quantum error correction allows us to actively stabilize quantum states and simulate ideal quantum operations in a noisy environment. It is critical is to correctly diagnose noise from its syndrome and nullify it…

Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits are described via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that…