Abstract Detecting genuine multipartite entanglement (GME) is a state-characterization task that benchmarks coherence and experimental control in quantum systems. Existing GME tests often require joint measurements on many qubits, posing challenges for systems like time-bin encoded qubits and microwave photons from superconducting circuits, where qubit connectivity is limited or measurement noise grows with the number of jointly measured qubits. Here we introduce versatile GME and k -inseparability criteria applicable to any state, which only require measuring O ( n 2 ) out of 2 n (at most) m -body stabilizers of n -qubit target graph states, with m upper-bounded by twice the graph’s maximum degree. For cluster or ring-graph states, only constant-weight stabilizers are needed. Using semidefinite programming (and sometimes graph-local complementations), we can reduce the number or weight of required stabilizers. Analytical and numerical results show that our criteria are noise-robust and may infer state infidelity from certified k -inseparability in microwave photonic graph states generated under realistic conditions.
Abstract Detecting genuine multipartite entanglement (GME) is a state-characterization task that benchmarks coherence and experimental control in quantum systems. Existing GME tests often require joint measurements on many qubits, posing challenges for systems like time-bin encoded qubits and microwave photons from superconducting circuits, where qubit connectivity is limited or measurement noise grows with the number of jointly measured qubits. Here we introduce versatile GME and k -inseparability criteria applicable to any state, which only require measuring O ( n 2 ) out of 2 n (at most) m -body stabilizers of n -qubit target graph states, with m upper-bounded by twice the graph’s maximum degree. For cluster or ring-graph states, only constant-weight stabilizers are needed. Using semidefinite programming (and sometimes graph-local complementations), we can reduce the number or weight of required stabilizers. Analytical and numerical results show that our criteria are noise-robust and may infer state infidelity from certified k -inseparability in microwave photonic graph states generated under realistic conditions.
Detecting genuine multipartite entanglement (GME) is a state-characterization task that benchmarks coherence and experimental control in quantum systems. Existing GME tests often require joint measurements on many qubits, posing challenges for systems like time-bin encoded qubits and microwave photons from superconducting circuits, where qubit connectivity is limited or measurement noise grows with the number of jointly measured qubits. Here we introduce versatile GME and k-inseparability criteria applicable to any state, which only require measuring O(n2) out of 2n (at most) m-body stabilizers of n-qubit target graph states, with m upper-bounded by twice the graph’s maximum degree. For cluster or ring-graph states, only constant-weight stabilizers are needed. Using semidefinite programming (and sometimes graph-local complementations), we can reduce the number or weight of required stabilizers. Analytical and numerical results show that our criteria are noise-robust and may infer state infidelity from certified k-inseparability in microwave photonic graph states generated under realistic conditions.
Genuine multipartite entanglement (GME) is a valuable resource for quantum technologies, but quantifying it in many-body systems can be demanding since measures defined through optimizations over bipartitions are often assumed to require large joint measurements and many measurement settings. We introduce the concepts of GME evaluation length and GME evaluation number, which capture, respectively, the largest subsystem that must be jointly measured and the number of distinct subsystems that need to be measured to evaluate multipartite entanglement measures defined via bipartition optimizations. Taking the genuine multipartite concurrence (GMC) as a canonical example, we show that, for N-qubit Haar-random pure states, the GMC can be evaluated using only N single-qubit purity measurements. Thus, for typical many-body states, evaluating the GMC requires considering only the N single-site bipartitions, rather than the exponentially many distinct bipartitions. We further corroborate this behavior numerically for physically accessible states generated by local random quantum circuits. Our results show that the practical cost of quantifying GME can be dramatically lower than suggested by its formal definition, establishing measurement complexity as a complementary operational lens for multipartite entanglement.
Quantum networks form the backbone of long-distance quantum information processing. Genuine multipartite entanglement (GME) serves as a key indicator of network performance and overall state quality. However, the widely used methods for certifying GME suffer from a major drawback that they either detect only a limited range of states or are applicable only to systems with a small number of parties. To overcome these limitations, we propose a family of sub-symmetric witnesses (SSWs), which are tractable both theoretically and experimentally. Analytically, we establish a connection between SSWs and the cut space of graph theory, enabling several powerful detection criteria tailored to practical quantum networks. Numerically, we show that the optimal detection can be formulated as a linear program, offering a significant efficiency advantage over the semidefinite programs commonly employed in quantum certification. Experimentally, SSWs can be evaluated via local measurements, with resource requirements independent of the local dimension in general, and even independent of the overall network size in many practical networks.
Characterizing large noisy multiparty quantum states using genuine multipartite entanglement is a challenging task. In this paper, we calculate lower bounds of genuine multipartite entanglement localized over a chosen multiparty subsystem of multiqubit stabilizer states in the noiseless and noisy scenarios. In the absence of noise, adopting a graph-based technique, we perform the calculation for arbitrary graph states as representatives of the stabilizer states and show that the graph operations required for the calculation have a polynomial scaling with the system size. As demonstrations, we compute the localized genuine multipartite entanglement over subsystems of large graphs having linear, ladder, and square structures. We also extend the calculation for graph states subjected to single-qubit Markovian or non-Markovian Pauli noise on all qubits and demonstrate, for a specific lower bound of the localizable genuine multipartite entanglement corresponding to a specific Pauli measurement setup, the existence of a critical noise strength beyond which all of the postmeasured states are biseparable. The calculation is also useful for arbitrary large stabilizer states under noise due to the local unitary connection between stabilizer states and graph states. We demonstrate this by considering a toric code defined on a square lattice and computing a lower bound of localizable genuine multipartite entanglement over a nontrivial loop of the code. Similar to the graph states, we show the existence of the critical noise strength in this case also and discuss its interesting features.
Abstract Genuine multipartite entanglement (GME) is arguably the most valuable form of entanglement in the multipartite case with application for instance in quantum metrology. In order to detect that form of entanglement in multipartite quantum states, one typically uses entanglement witnesses. The aim of this paper is to generalize the results of Tóth and Gühne (2005 Phys. Rev. A 72 022340) in order to provide a construction of witnesses of GME tailored to entangled subspaces originating from the multi-qudit stabilizer formalism—a framework well known for its role in quantum error correction, which also provides a very convenient description of a broad class of entangled multipartite states (both pure and mixed). Our construction includes graph states of arbitrary local dimension. We then show that in certain situations, the obtained witnesses detecting GME in quantum systems of higher local dimension are superior in terms of noise robustness to those derived for multiqubit states.
Abstract Suppose we have an unknown multipartite quantum state, how can we experimentally find out whether it is genuine multipartite entangled or not? Recall that even for a bipartite quantum state whose density matrix is known, it is already NP-Hard to determine whether it is entangled or not. Therefore, it is hard to efficiently solve the above problem generally. However, since genuine multipartite entanglement (GME) is such a fundamental concept that plays a crucial role in many-body physics and quantum information processing tasks, finding realistic approaches to certify GME is undoubtedly necessary. In this work, we show that neural networks can provide a nice solution to this problem, where measurement statistics data produced by measuring involved quantum states with local measurement devices serve as input features of neural networks. By testing our models on many specific multipartite quantum states, we show that they can certify GME very accurately, even including some new results unknown before. We also exhibit a possible way to improve the efficiency of our models by reducing the size of features. Lastly, we show that our models enjoy remarkable robustness against flaws in measurement devices, implying that they are very experiment-friendly.