Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Communications in Theoretical Physics

Quantum Generalized Measurement and Deterministic Generation of Maximum Entangled Pure State

Ming Zhang, Hong‐Yi Dai, HU De-wen, Hongwei Xie

Published Nov 1, 2006• 2 citations
Publisher

Abstract

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.

DOI
10.1088/0253-6102/46/5/012

Related papers

Quantum Generalized Subspace Projector Measurement and Measurement Induced Entanglement

Ming Zhang, Dong Guo-Hua, Hong‐Yi Dai +1 more

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.

Chinese Physics Letters•Apr 28, 2006•2 citations

Quantum Generalized Measurement and Deterministic Generation of Maximum Entangled Pure State

Zhang, Ming Ming, Dai +5 more

我们建议量的概念概括了投影机测量(QGPM ) 因为由学习量的有限维的量系统概括了测量。Thisresearch 表明这量的一个著名性质概括了测量：不管系统状态在测量以前是什么并且测量的结果什么发生，在测量以后的系统的状态能被折叠进任何指定纯状态，即，量系统的状态能是就作为壁炉 QGPM 归结为任何指定纯状态的确定的联盟者。随后， QGPM 能习惯于确定的联盟者为量系统产生最大的纠缠的咕噜咕噜叫房地产。我们分别地为二个 2 水平粒子，三个 2 水平粒子和二 3-levelparticles 给产生最大的量的三个具体理论上的计划纠缠的纯状态。

理论物理通讯：英文版•Jan 1, 2006•2 citations

Control of the quantum open system via quantum generalized measurement

Ming Zhang, Hong‐Yi Dai, Xiaocai Zhu +2 more

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.

Physical Review A•Mar 3, 2006•26 citations

The Entanglement Content of Quantum Measurement Bases

Jef Pauwels, Otfried Gühne

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.

quant-pharXiv:2608.21185•Aug 24, 2026•0 citations

Scheme for realizing entanglement concentration via generalized measurements

Ch. -Q. Du, Ming Yang, Y. Lu +1 more

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.

Journal of Experimental and Theoretical Physics Letters•Dec 1, 2012•0 citations

Description of entanglement

J. Schlienz, G. Mahler

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.

Physical Review A•Dec 1, 1995•179 citations
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.
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.
我们建议量的概念概括了投影机测量(QGPM ) 因为由学习量的有限维的量系统概括了测量。Thisresearch 表明这量的一个著名性质概括了测量：不管系统状态在测量以前是什么并且测量的结果什么发生，在测量以后的系统的状态能被折叠进任何指定纯状态，即，量系统的状态能是就作为壁炉 QGPM 归结为任何指定纯状态的确定的联盟者。随后， QGPM 能习惯于确定的联盟者为量系统产生最大的纠缠的咕噜咕噜叫房地产。我们分别地为二个 2 水平粒子，三个 2 水平粒子和二 3-levelparticles 给产生最大的量的三个具体理论上的计划纠缠的纯状态。
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.
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.
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.
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.