Entangled measurements are an indispensable tool for quantum information processing, such as Bell-state measurements in quantum teleportation and entanglement swapping. However, to date, the realization of entangled measurements has mainly focused on bipartite systems or Greenberger-Horne-Zeilinger (GHZ) states. Here, we demonstrate a practical scheme to realize entangled measurements for [Formula: see text] states. Thanks to the cyclic shift symmetry in the discrete Fourier transformation (DFT) of bosonic modes, the DFT measurement outcomes can be used to deterministically project multiqubit states onto [Formula: see text] states. Experimentally, we show that three-qubit [Formula: see text] state discrimination can be achieved by detecting the cyclic shift symmetry with a three-mode DFT optical circuit, yielding a measurement discrimination fidelity of 0.871 ± 0.039. Our experimental demonstration opens the door for the development of new quantum network protocols between multipartite systems.
Entangled measurements are an indispensable tool for quantum information processing, such as Bell-state measurements in quantum teleportation and entanglement swapping. However, to date, the realization of entangled measurements has mainly focused on bipartite systems or Greenberger-Horne-Zeilinger (GHZ) states. Here, we demonstrate a practical scheme to realize entangled measurements for [Formula: see text] states. Thanks to the cyclic shift symmetry in the discrete Fourier transformation (DFT) of bosonic modes, the DFT measurement outcomes can be used to deterministically project multiqubit states onto [Formula: see text] states. Experimentally, we show that three-qubit [Formula: see text] state discrimination can be achieved by detecting the cyclic shift symmetry with a three-mode DFT optical circuit, yielding a measurement discrimination fidelity of 0.871 ± 0.039. Our experimental demonstration opens the door for the development of new quantum network protocols between multipartite systems.
Optical multi-mode systems provide large scale Hilbert spaces that can be accessed and controlled using single photon sources, linear optics and photon detection. Here, we consider the bipartite entanglement generated by coherently distributing M photons in M modes to two separate locations, where linear optics and photon detection is used to verify the non-classical correlations between the two M -mode systems. We show that the entangled state is symmetric under mode shift operations performed in the two systems and use this symmetry to derive correlations between photon number distributions detected after a discrete Fourier transform (DFT) of the modes. The experimentally observable correlations can be explained by a simple and intuitive rule that relates the sum of the output mode indices to the eigenvalue of the input state under the mode shift operation. Since the photon number operators after the DFT do not commute with the initial photon number operators, entanglement is necessary to achieve strong correlations in both the initial mode photon numbers and the photon numbers observed after the DFT. We can therefore derive entanglement witnesses based on the experimentally observable correlations in both photon number distributions, providing a practical criterion for the evaluation of large scale entanglement in optical multi-mode systems. Our method thus demonstrates how non-classical signatures in large scale optical quantum circuits can be accessed experimentally by choosing an appropriate combination of modes in which to detect the photon number distributions that characterize the quantum coherences of the state.
Abstract Bell state measurements, which project bipartite states onto the maximally entangled Bell basis, are central to a wide range of quantum information processing tasks, including quantum teleportation, entanglement swapping, and fusion-gate quantum computation. In photonic platforms, where information is encoded in optical degrees of freedom, the realization of efficient Bell state measurements is particularly challenging, especially when constrained to linear optical elements. In this review, we provide a comprehensive examination of existing proposals for the implementation of Bell state measurements, highlighting their fundamental limitations and the strategies developed to overcome them. Moreover, we survey recent advances and discuss open challenges, with a particular focus on Bell state measurements for high-dimensional systems, an area of growing interest due to its relevance for quantum repeaters and scalable quantum networks.
Quantum entanglement swapping is one of the most promising ways to realize the quantum connection among local quantum nodes. In this Letter, we present an experimental demonstration of the entanglement swapping between two independent multipartite entangled states, each of which involves a tripartite Greenberger-Horne-Zeilinger (GHZ) entangled state of an optical field. The entanglement swapping is implemented deterministically by means of a joint measurement on two optical modes coming from the two multipartite entangled states respectively and the classical feedforward of the measurement results. After entanglement swapping the two independent multipartite entangled states are merged into a large entangled state in which all unmeasured quantum modes are entangled. The entanglement swapping between a tripartite GHZ state and an Einstein-Podolsky-Rosen entangled state is also demonstrated and the dependence of the resultant entanglement on transmission loss is investigated. The presented experiment provides a feasible technical reference for constructing more complicated quantum networks.
Quantum entanglement is the fundamental hallmark of quantum mechanics and a core resource for realizing long-distance quantum communication and scalable linear quantum computing. Accordingly, the precise detection and quantitative quantification of entanglement constitute a foundational and critical problem in quantum information theory. To date, researchers have proposed numerous sufficient conditions for entanglement detection as well as a variety of entanglement measures to characterize the entanglement strength of quantum states; nevertheless, efficient and direct measurement schemes for core entanglement parameters remain underdeveloped. Based on unitary transformations and auxiliary measurements, this paper proposes a set of quantum circuit schemes capable of directly measuring the bipartite concurrence and the tripartite 3-tangle entanglement measure. By introducing auxiliary qubits and constructing specific controlled unitary operations, the proposed scheme maps the analytical expressions of the two entanglement measures onto the measurement probabilities of output states from quantum circuits. It enables efficient and direct quantitative measurement of bipartite and tripartite entanglement without performing full quantum state tomography. This work provides a feasible technical route for the experimental characterization of entanglement properties and lays a groundwork for the practical deployment of multipartite entanglement resources in quantum information processing.
The focal point of this thesis is strongly based on quantum entanglement within Quantum Information Science. We provide an indepth analysis of entanglement quantification in both bipartite and multipartite quantum systems, with an emphasis on many-body entanglement. We examine the definitions of entanglement, introduce several entanglement measures, and examine the challenges in expanding these measures to multipartite scenarios. For bipartite systems, we detail entropy-based measures such as von Neumann and Rényi entropies, the entanglement spectrum and important algebraic metrics such as negativity and concurrence. We then elaborate on multipartite entanglement, introducing modern measures and detection techniques including geometric and global entanglement measurements, generalised multipartite concurrence, multipartite negativity, fidelity-based entanglement benchmarks, and entanglement witnesses. Some examples include Greenberger-Horne-Zeilinger (GHZ), and the W states to illustrate the distinction between biseparable and truly multi-partite-entangled states, as well as the SLOCC classification of families of entangled states. We also briefly introduce practical ways of measuring entanglement, such as the SWAP test, quantum state tomography for experimental estimation of entanglement and consequently randomised measurements. We apply these measures to specific quantum states (GHZ, W , graph states, and random states), analysing how entanglement evolves under operations and how different metrics capture distinct features of multi-qubit entanglement. Finally, we conclude with a summary of findings, a discussion of current limitations such as scalability of measures. The thesis is organised into five chapters: Introduction, Entanglement, Multipartite Entanglement Measures, Negativity vs. Three-Tangle, and Conclusion.
The states of three-qubit systems split into two inequivalent types of genuine tripartite entanglement, namely, the Greenberger-Horne-Zeilinger (GHZ) type and the W type. A state belonging to one of these classes can be stochastically transformed only into a state within the same class by local operations and classical communications. We provide local quantum operations, consisting of the most general two-outcome measurement operators, for the deterministic transformations of three-qubit pure states in which the initial and the target states are in the same class. We explore these transformations, originally having standard GHZ and standard W states, under the local measurement operations carried out by a single party and p (p=2,3) parties (successively). We find a notable result that the standard GHZ state cannot be deterministically transformed to a GHZ-type state in which all its bipartite entanglements are nonzero, i.e., a transformation can be achieved with unit probability when the target state has at least one vanishing bipartite concurrence.