Scott N. Walck
We present a two-part program for state space decomposition. States are classified into entanglement classes based on local unitary transformations, and then characterized as elements of topological spaces using the language of fibre bundles.
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Schemes for topological quantum computation are usually based on the assumption that the system is initially prepared in a specific state. In practice, this state preparation is expected to be challenging as it involves non-topological operations which heavily depend on the experimental realization and are not naturally robust against noise. Here we show that this assumption can be relaxed by using composite anyons: starting from an unknown state with reasonable physical properties, it is possible to efficiently distill suitable initial states for computation purely by braiding. This is achiev…
We describe a purely algebraic method for finding the best separable approximation to a mixed state of a composite 2x2 quantum system, consisting of a decomposition of the state into a linear combination of a mixed separable part and a pure entangled one. We prove that, in a generic case, the weight of the pure part in the decomposition equals the concurrence of the state.
We present a general systematic approach to design robust and high-fidelity quantum logic gates with Raman qubits using the technique of composite pulses. We use two mathematical tools -- the Morris-Shore and Majorana decompositions -- to reduce the three-state Raman system to an equivalent two-state system. They allow us to exploit the numerous composite pulses designed for two-state systems by extending them to Raman qubits. We construct the NOT, Hadamard, and rotation gates by means of the Morris-Shore transformation with the same uniform approach: sequences of pulses with the same phases f…
We identify a general criterion for detecting entanglement of pure bipartite quantum states describing a system of two identical particles. Such a criterion is based both on the consideration of the Slater-Schmidt number of the fermionic and bosonic analog of the Schmidt decomposition and on the evaluation of the von Neumann entropy of the one-particle reduced statistical operators.
In this paper we analyze one-loop quantum effects of a scalar field induced by a composite topological defect consisting a cosmic string on a p-dimensional brane and a (m+1)-dimensional global monopole in the transverse extra dimensions. The corresponding Green function is presented as a sum of two terms. The first one corresponds to the bulk where the cosmic string is absent and the second one is induced by the presence of the string. For the points away from the cores of the topological defects the latter is finite in the coincidence limit and is used for the evaluation of the vacuum expecta…
Topological edge states in a Rydberg composite
本研究聚焦里德堡复合物的拓扑相问题，通过其电子哈密顿量与紧束缚模型的映射，证实了拓扑保护边缘态的存在，并拓展了三聚体元胞等复杂拓扑体系的模拟途径。
We propose an interpretation of quantum separability based on a physical principle: local time reversal. It immediately leads to a simple characterization of separable quantum states that reproduces results known to hold for binary composite systems and which thereby is complete for low dimensions. We then describe a constructive algorithm for finding the canonical decomposition of separable and non separable mixed states of dimensions 2x2 and 2x3.
We introduce topological gauge fields as nontrivial field configurations enforced by topological currents. These fields crucially determine the form of statistical gauge fields that couple to matter and transmute their statistics. We discuss the physical mechanism underlying the composite particle picture and argue that it is a duality of gauge forms that naturally relates to the notion of bosonisation in arbitrary dimensions. This is based on obtaining a generalised version of flux attachment, which yields a density-dependent gauge potential. We recover well-known results, resolve old controv…
For the standard Quantum Brownian Motion (QBM) model, we point out the occurrence of simultaneous (parallel), mutually irreducible and autonomous decoherence processes. Besides the standard, one Brownian particle, we show there is at least another one system undergoing the dynamics described by the QBM effect. We do this by selecting the two mutually irreducible, global structures (decompositions into subsystems) of the composite system of the QBM model. A generalization of this observation is a new, challenging task in the foundations of the decoherence theory. We do not place our findings in…
Problem of classification of parallel quantum channels for information transfer is studied by method of ladder operators. Detailed compared to http://arxiv.org/abs/quant-ph/0702076 presentation of method of ladder operators is given. Examples of paired channel and qubit-qunit pair are added. Relations between eigenvalues of density matrices of composite channel and its subchannels determining presence/absence of entanglement of arbitrary mixed state of channel are obtained.
For any bipartite quantum system the Schmidt decomposition allows us to express the state vector in terms of a single sum instead of double sums. We show the existence of the Schmidt decomposition for tripartite system under certain condition. If the partial inner product of a basis (belonging to a Hilbert space of smaller dimension) with the state of the composite system gives a disentangled basis, then the Schmidt decomposition for a tripartite system exists. In this case the reduced density matrix of each of the subsystem has equal spectrum in the Schmidt basis.
Impurity-induced topological decomposition
本文发现局域杂质可逐步分解非厄米晶格的拓扑绕数，并据此在厄米系统中实现可控拓扑边缘态，为杂质调控拓扑相提供通用框架。
We investigate the vacuum polarization effects associated with a charged massless spin-1/2 field in a higher-dimensional space-time, induced by a composite topological defect. The defect is constituted by a global monopole living on a three-brane and two-dimensional conical space transverse to the latter. In addition, we assume the presence of an extra magnetic flux along the core of the conical space. The heat kernel and the Feynman Green function are presented in the form of a sum of two terms. The first one corresponds to the contribution coming from the bulk with global monopole in the abs…
Any Hilbert space with composite dimension can be factorized into a tensor product of smaller Hilbert spaces. This allows to decompose a quantum system into subsystems. We propose a simple tractable model for a constructive study of decompositions of quantum systems.
Long-Range Order and Composite Boson Condensation in Lattice Quantum Hall States
该研究将张量网络方法应用于承载量子霍尔态的格点哈密顿量，揭示了其中复合玻色子的凝聚与长程关联，定义了可识别拓扑相变的非局域序参量，为拓扑量子物质的微观研究开辟了新途径。
Strongly correlated quantum many-body systems at low dimension exhibit a wealth of phenomena, ranging from features of geometric frustration to signatures of symmetry-protected topological order. In suitable descriptions of such systems, it can be helpful to resort to effective models which focus on the essential degrees of freedom of the given model. In this work, we analyze how to determine the validity of an effective model by demanding it to be in the same phase as the original model. We focus our study on one-dimensional spin-1/2 systems and explain how non-trivial symmetry protected topo…
The Composite Particle Duality: A New Class of Topological Quantum Matter
本文提出复合粒子对偶，将通量附着与统计嬗变推广至任意时空维度，并构造相关相互作用多体系统，揭示新型跨维度拓扑量子物质。
A topological quantum computer should allow intrinsically fault-tolerant quantum computation, but there remains uncertainty about how such a computer can be implemented. It is known that topological quantum computation can be implemented with limited quasiparticle braiding capabilities, in fact using only a single mobile quasiparticle, if the system can be properly initialized by measurements. It is also known that measurements alone suffice without any braiding, provided that the measurement devices can be dynamically created and modified. We study a model in which both measurement and braidi…
We present a complete topological characterization of a bilayer composite of two Chern insulators (specifically, Haldane models) and explicitly establish the bulk-boundary correspondences. We show that an appropriately defined Chern number accurately maps out all the possible phases of the system and remains well-defined even in the presence of degeneracies in the occupied bands. Importantly, our result paves the way for realizing adiabatic preparation of monolayer Chern insulators. This has been a major challenge till date, given the impossibility of unitarily connecting inequivalent topologi…
Composite-Dimensional Topological Codes with Boundaries and Defects
本文提出新的算法和构造方法，用于描述具有间隙边界的域墙和0D缺陷的阿贝尔复合维度扭曲量子双模型的稳定子模型。通过凝聚概念，展示了如何从bulk模型构造边界和域墙稳定子。并讨论了这些码在量子纠错中的应用，包括双Z4与双半离子相的耦合。
Rigged Hilbert Space formulation for quasi-Hermitian composite systems
本文基于装配 Hilbert 空间（RHS）探讨了准厄米量子复合系统的 Dirac 左矢-右矢形式，建立了正定度量的 RHS 以构造左矢和右矢向量并实现算子谱分解，证明了对称关系可扩展至对偶空间，并应用于共形多维多体系统组成的非厄米谐振子。
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