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Chinese Physics Letters

Quantum Generalized Subspace Projector Measurement and Measurement Induced Entanglement

Ming Zhang, Dong Guo-Hua, Hong‐Yi Dai, HU De-wen

Published Apr 28, 2006• 2 citations
Publisher

Abstract

We propose the concept of the quantum generalized subspace projector measurement (QGSPM). The distinguished properties of QGSPM is revealed: no matter what the state of the system is prior to the measurement and what the measured result occurs, the state posterior to the measurement can be collapsed onto the specified subspace. Subsequently, the quantum generalized case-projector measurement (QGCPM), as a special case of QGSPM, is also discussed carefully. It is demonstrated that no matter what measured result occurs, the state of the system posterior to QGCPM can be collapsed into one of pure states. Consequently, QGCPM can be used to generate the maximally entangled pure states for multiple particles. As illustrative examples, several concrete methods of generating entanglement are proposed for two two-level particles. It is found that the maximally entangled pure states of two 2-level particles can be generated just by a single QGCPM and the corresponding QGCPM operators are physically realizable in principle if an ancillary four-dimensional quantum system can be introduced.

DOI
10.1088/0256-307x/23/5/003

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We propose the concept of the quantum generalized subspace projector measurement (QGSPM). The distinguished properties of QGSPM is revealed: no matter what the state of the system is prior to the measurement and what the measured result occurs, the state posterior to the measurement can be collapsed onto the specified subspace. Subsequently, the quantum generalized case-projector measurement (QGCPM), as a special case of QGSPM, is also discussed carefully. It is demonstrated that no matter what measured result occurs, the state of the system posterior to QGCPM can be collapsed into one of pure states. Consequently, QGCPM can be used to generate the maximally entangled pure states for multiple particles. As illustrative examples, several concrete methods of generating entanglement are proposed for two two-level particles. It is found that the maximally entangled pure states of two 2-level particles can be generated just by a single QGCPM and the corresponding QGCPM operators are physically realizable in principle if an ancillary four-dimensional quantum system can be introduced.
We propose the concept of the quantum generalized projector measurement (QGPM) for finite-dimensional quantum systems by studying the quantum generalized measurement. This research reveals a distinguished property of this quantum generalized measurement: no matter what the system state is prior to the measurement and what the result of the measurement occurs, the state of the system after the measurement can be collapsed into any specified pure state, i.e., the state of quantum system can be deterministically reduced to any specified pure state just by a single QGPM. Subsequently, QGPM can be used to deterministically generate the maximum entangled pure state for quantum systems. We give three concrete theoretic schemes of generating the maximum quantum entangled pure states for two 2-level particles, three 2-level particles and two 3-level particles, respectively.
For any specified pure state of quantum open system, we can construct a kind of quantum generalized measurement (QGM) that the state of the system after measurement will be deterministically collapsed into the specified pure state from any initial state. In other words, any pure state of quantum open system is reachable by QGM. Subsequently, whether the qubit is density matrix controllable is discussed in the case of pure dephasing. Our results reveal that combining QGM with coherent control will enhance the ability of controlling the quantum open system. Furthermore, it is found that the ability to perform QGM on the quantum open system, combined with the ability of coherence control and conditions of decoherence-free subspace, allows us to suppress quantum decoherence.
How to concentrate non-maximally entangled states for quantum communication is a fundamental problem in quantum information. In this paper, we will apply generalized measurements to entanglement concentration of known non-maximally entangled pure states in arbitrary dimensional system. How to design the generalized measurements for the unambiguous discrimination of linearly independent non-orthogonal states is crucial for the concentration of the known non-maximally entangled states. The result shows that, any known non-maximally entangled pure state (for arbitrary dimensional system) can be transformed to the maximally entangled state only by introducing a qubit as ancilla and a joint unitary transformation operation on one of the entangled particles and the ancilla. In addition, because the less entangled state of each fail round will be re-concentrated too, the entanglement waste during the concentration process will be greatly reduced.
Bell-state measurements are essential ingredients in many protocols for quantum information processing, ranging from quantum teleportation and dense coding to entanglement distribution in quantum networks. Their power relies on the fact that they are measurements in an entangled basis of a two-particle system and that the used Bell-state basis can be generated from a single Bell state by local unitary transformations. How can these measurements be generalized to more particles? We develop a general framework for this state-to-measurement problem: We introduce a hierarchy of classes of measurement bases, distinguished by the local transformations the parties may use for their generation from a single state. This leads to a generalization of the concept of maximally entangleable (or weighted hypergraph) states and the identification of a novel maximally entangled basis of four qubits, being a candidate for data-hiding tasks or distillation protocols. Finally, we prove that not all forms of entanglement can be encoded in an entire measurement basis.
这份报纸探索由联系量与 decoherence 作斗争的潜力有 decoherence 免费的 subspaces (DFS ) 的概括测量。联系量概括了 subspace 投影机测量(QGSPM ) ，量与操作员条件概括了盒子投影机测量(QGCPM ) 因为 DFS 将提高压制 decoherence 的能力因为 Markovian 和 non-Markovian 打开量系统，这被表明。量测量能被认为是一个工具操作量状态，这被强调。因为协调控制哈密尔顿能积极地被设计，这个方法是有益的。
We propose a measure of entanglement between two subsystems of arbitrary (but finite) number of levels. This measure is invariant under unitary transformations of the subsystems and varies between 0 (product states) and 1 (maximum entangled states). The case of two two-level systems is worked out explicitly, where the known complementarity between one- and two-particle interference results in a very natural way from a sum rule. Generalizations to more than two subsystems are discussed. Here we show that for three particles there cannot exist a pure state that is completely characterized by three-particle entanglement alone. For the example of the Greenberger-Horne-Zeilinger (GHZ) state, an experimental setup is proposed, in which its corresponding two-particle entanglement would show up.