Reduced density matrix and partial trace

The reduced matrix is defined as the partial trace of the density matrix. In linear algebra and functional analysis, the partial trace is a generalization of the trace. Whereas the trace is a scalar valued function on operators, the partial trace is an operator-valued function. The partial trace has applications in quantum information and decoherence which is relevant for quantum measurement and thereby to the decoherent approaches to interpretations of quantum mechanics, including consistent histories and the relative state interpretation.

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One way quantum computer

The one-way or measurement based quantum computer (MBQC) is a method of quantum computing that first prepares an entangled resource state, usually a cluster state or graph state, then performs single qubit measurements on it. It is "one-way" because the resource state is destroyed by the measurements.

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Cluster States

In quantum information and quantum computing, a cluster state is a type of highly entangled state of multiple qubits. Cluster states are generated in lattices of qubits with Ising type interactions. A cluster C is a connected subset of a d-dimensional lattice, and a cluster state is a pure state of the qubits located on C. Another way of thinking of cluster states is as a particular instance of graph states, where the underlying graph is a connected subset of a d-dimensional lattice. Cluster states are especially useful in the context of the one-way quantum computer.

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Renyi entropy of the wormholes

In information theory, the Rényi entropy generalizes the Hartley entropy, the Shannon entropy, the collision entropy and the min entropy. Entropies quantify the diversity, uncertainty, or randomness of a system. The Rényi entropy is named after Alfréd Rényi.

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Geometrical Optics in Continuum

Fermat’s Principle

Fermat’s Principle is

$$\delta s=\delta\int n\dd \ell=0$$

If we choose the path …

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Invariance of Euler-Lagrange Equations

E-L is deduced from the Hamilton’s principle

$$\delta S=\delta\int L(\bm q, \dot{\bm q}, t)dt …
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Jacobi Identity for Classical Possion Bracket

Definition of Classical Possion Bracket:

$$[f, g]=\sum_{i=1, 2,\ldots, n}\frac{\pp(f, g)}{\pp …
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From d’Alembert to Lagrange

Nowtonian

Assume \(\bm F\) is active force and \(\bm R\) is constraint force. Then for …

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Tn格点上逾渗的几何结构

《$T_n$格点上逾渗的几何结构》是我的本科毕业论文。

具体算法原理等请参考论文。以及章彦博写的算法原理

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