Entanglement detection beyond the local bound with coarsely calibrated measurements

We generalize the scheme for detection of qubit-environment entanglement to qudit-environment systems. This is of relevance for many-qubit systems and the quantification of the operation of quantum algorithms under the influence of external noise, since only decoherence that is not entangling in its nature can be effectively described by quantum channels and similar methods in more complicated scenarios. The generalization involves an increase in the class of entangled states which are not detected by the scheme, but the type of entanglement which cannot be detected is also least likely to qualitatively influence decoherence. We exemplify the operation of the scheme on a realistically modeled nitrogen-vacancy-center spin qutrit interacting with an environment of nuclear spins.

Entanglement detection is one of the most fundamental tasks in quantum information science, playing vital roles in theoretical studies and quantum system benchmarking. Researchers have proposed many powerful entanglement criteria with high detection capabilities and small observable numbers. Nonetheless, entanglement criteria only represent mathematical rules deciding the existence of entanglement. The relationship between a good entanglement criterion and an effective experimental entanglement detection protocol (EDP) is poorly understood. In this study, we introduce postulates for EDPs about their detection capabilities and robustness and use them to show the difference between entanglement criteria and EDPs. Specifically, we design an entanglement detection task for unknown pure bipartite states and demonstrate that the sample complexity of any EDP and the number of observables for a good entanglement criterion can have exponential separation. Furthermore, we discover that the optimal EDP with the lowest sample complexity does not necessarily correspond to an entanglement criterion constructed by a small number of observables. Our results can be used to prove the exponential speedups achieved through quantum memory and be generalized to multipartite entanglement detection. By highlighting the significance and independence of EDP design, our work holds practical implications for entanglement detection experiments.

Quantum entanglement is a critical physical process in quantum mechanics and quantum information theory. It is a required process in quantum computing, quantum teleportation, and quantum cryptography. Entanglement detection affects the performance of quantum information processing tasks. Entanglement detection has grown in popularity over the years, and various entanglement detection methods are available, though some have application and system scale limitations. This scoping review sought to identify various measurement methods for entanglement detection in both bipartite and multipartite entanglement systems. Secondary resource indexed literatures were selected based on specific keywords from literatures published between 2017 and 2021. The goal of this study is to present a proposed conceptual framework of entanglement detection based on previous work as a guidance and reference founded on one’s specific requirements.

Nonlocal operation enhanced entanglement detection and classification

This work presents a machine learning approach based on support vector machines (SVMs) for quantum entanglement detection. Particularly, we focus on bipartite systems of dimensions $$3\times 3$$ 3 × 3 , $$4\times 4$$ 4 × 4 , and $$5\times 5$$ 5 × 5 , where the positive partial transpose criterion (PPT) provides only partial characterization. Using SVMs with quantum-inspired kernels, we develop a classification scheme that distinguishes between separable and entangled states, including PPT-detectable entangled states, and entangled states that evade PPT detection. Our method achieves increasing accuracy with system dimension, reaching $$80\%$$ 80 % , $$90\%$$ 90 % , and nearly $$100\%$$ 100 % for $$3\times 3$$ 3 × 3 , $$4\times 4$$ 4 × 4 , and $$5\times 5$$ 5 × 5 systems, respectively. Our results show that principal component analysis significantly enhances performance for small training sets. The study reveals important practical considerations regarding purity biases in the generation of data for this problem and examines the challenges of implementing these techniques on near-term quantum hardware. Our results demonstrate that machine learning can be an effective alternative to entanglement detection of higher-dimensional systems where conventional entanglement detection methods struggle. Our approach provides improved data generation protocols and can be readily implemented in hybrid classical-quantum architectures, overcoming current limitations.

In this paper, we introduce a supervised learning technique that harnesses artificial neural networks, along with the outcomes of collective entanglement measurements, to estimate the negativity of quantum states in two-qubit and qubit-qutrit systems. The resulting deep-learned collective entanglement witnesses offer the unique capability of continuous sensitivity and selectivity tuning. This instrument enables us to explore the tradeoff between sensitivity and selectivity in entanglement detection, a dimension not accessible to previously employed analytical witnesses. In particular, we demonstrate that there are experimentally cost-effective methods (in terms of the number of measurements) where sensitivity can be significantly improved at a slight expense of the selectivity of entanglement detection. This chosen approach is also favored due to its high generality and potential for superior performance compared to other types of entanglement witnesses. Our findings may pave the way for the development of more efficient and accurate entanglement detection methods in complex quantum systems, especially when considering realistic experimental imperfections. Published by the American Physical Society 2024

Entanglement detection and classification of different kinds of entangled states in quantum many-body systems have always been a key topic in quantum information and quantum computation. In this work, we investigate the entanglement detection and classification of three special entangled states: 4-qubit GHZ state, 4-qubit <inline-formula><tex-math id="M6">\begin{document}$ {\mathrm{W}}\overline{{\mathrm{W}}} $\end{document}</tex-math></inline-formula> state, and 4-qubit SGT state, which cannot be distinguished by the general quantum Fisher information (QFI) under the usual local operations. By utilizing the experimentally mature and controllable one-axis twisting model, along with optimized rotations and adjustable interaction strength, we successfully classify the three states by QFI. Additionally, we also study the effects of four types of environmental noise on entanglement detection, namely, bit-flip channel, amplitude-damping channel, phase-damping channel, and depolarizing channel. The results show that under local operations, the changes of the QFI from the 4-qubit GHZ state with decoherence parameter <i>p</i> in four noise channels are significantly different from those of the <inline-formula><tex-math id="M7">\begin{document}$ {\mathrm{W}}\overline{{\mathrm{W}}} $\end{document}</tex-math></inline-formula> state and SGT state, and thus making them distinguished. However, the QFI about the <inline-formula><tex-math id="M8">\begin{document}$ {\mathrm{W}}\overline{{\mathrm{W}}} $\end{document}</tex-math></inline-formula> state and the QFI about the SGT state exhibit the same variations and cannot be classified. In the one-axis twisting model, the variation curves of the QFI of the three states under the four noise channels are different from each other, which can be clearly observed. It should be noted that in the bit-flip channel, the QFI curves of the <inline-formula><tex-math id="M9">\begin{document}$ {\mathrm{W}}\overline{{\mathrm{W}}} $\end{document}</tex-math></inline-formula> state and the SGT state overlaps in the middle region (<inline-formula><tex-math id="M10">\begin{document}$ p\approx0.5 $\end{document}</tex-math></inline-formula>), which prevents their classification. Our work provides a new method for entanglement detection and classification in quantum many-body systems, which will contribute to future research in quantum science and technology.

Progress in multiphoton interferometry allows us now to observe even six-photon interference of a very high contrast. Also, it is possible to observe interference of two photons originating from truly independent sources. Non-classical effects may violate Bell inequalities, or reveal quantum non-separability. Methods of producing non-classical states of few photons, and the detection of entanglement via Bell inequalities, or via nor-separability criteria will be presented. Implications of violations of Bell inequalities will be discussed, with a special stress on over-interpretations of this fact.

We propose a criterion for the detection of genuine entanglement of pure multiqubit states. To this aim, we define an operator called the losing one qubit operator, which is different from the reduced density operator. The states obtained from a multiqubit state by applying the losing one qubit operator are referred to as its projected states. We show that all of the projected states of a pure product n-qubit state are pure product states provided that it cannot be written as a product of a single qubit state and a genuinely entangled (\(n-1\))-qubit state. We also show that a pure n-qubit state is genuinely entangled provided that the state has at least two genuinely entangled (\(n-1\))-qubit projected states. By repeating the losing process, we reduce the detection of entanglement of pure n-qubit states to the one of pure two-qubit states. Also we write a LISP program for the reduction process.

In this paper, we discuss some general connections between the notions of positive map, weak majorization and entropic inequalities in the context of detection of entanglement among bipartite quantum systems. First, basing on the fact that any positive map can be written as the difference between two completely positive maps Λ=Λ1−Λ2, we propose a possible way to generalize the Nielsen–Kempe majorization criterion. Then, we present two methods of derivation of some general classes of entropic inequalities useful for the detection of entanglement. While the first one follows from the aforementioned generalized majorization relation and the concept of Schur-concave decreasing functions, the second is based on some functional inequalities. What is important is that, contrary to the Nielsen–Kempe majorization criterion and entropic inequalities, our criteria allow for the detection of entangled states with positive partial transposition when using indecomposable positive maps. We also point out that if a state with at least one maximally mixed subsystem is detected by some necessary criterion based on the positive map Λ, then there exist entropic inequalities derived from Λ (by both procedures) that also detect this state. In this sense, they are equivalent to the necessary criterion [I⊗Λ](ϱAB)⩾0. Moreover, our inequalities provide a way of constructing multi-copy entanglement witnesses and therefore are promising from the experimental point of view. Finally, we discuss some of the derived inequalities in the context of the recently introduced protocol of state merging and the possibility of approximating the mean value of a linear entanglement witness.

Detection of polarization-spatial classical optical entanglement through implementation of partial transpose on measured intensities is explored. A sufficient criterion for polarization-spatial entanglement in partially coherent light fields based on intensities measured at various orientations of the polarizer, as implied through partial transpose, is outlined. Detection of polarization-spatial entanglement using the outlined method is demonstrated experimentally through a Mach-Zehnder interferometer setup.

We formulate some properties of a set of several mutually unbiased measurements. These properties are used for deriving entropic uncertainty relations. Applications of mutually unbiased measurements in entanglement detection are also revisited. First, we estimate from above the sum of the indices of coincidence for several mutually unbiased measurements. Further, we derive entropic uncertainty relations in terms of the Rényi and Tsallis entropies. Both the state-dependent and state-independent formulations are obtained. Using the two sets of local mutually unbiased measurements, a method of entanglement detection in bipartite finite-dimensional systems may be realized. A certain trade-off between a sensitivity of the scheme and its experimental complexity is discussed.

We show that a special type of measurements, called symmetric informationally complete positive operator-valued measures (SIC POVMs), provide a stronger entanglement detection criterion than the computable cross-norm or realignment criterion based on local orthogonal observables. As an illustration, we demonstrate the enhanced entanglement detection power in simple systems of qubit and qutrit pairs. This observation highlights the significance of SIC POVMs for entanglement detection.

Recent research on parallel functional programming has culminated in a provably efficient (in work and space) parallel memory manager, which has been incorporated into the MPL (MaPLe) compiler for Parallel ML and shown to deliver practical efficiency and scalability. The memory manager exploits a property of parallel programs called disentanglement, which restricts computations from accessing concurrently allocated objects. Disentanglement is closely related to race-freedom, but subtly differs from it. Unlike race-freedom, however, no known techniques exists for ensuring disentanglement, leaving the task entirely to the programmer. This is a challenging task, because it requires reasoning about low-level memory operations (e.g., allocations and accesses), which is especially difficult in functional languages. In this paper, we present techniques for detecting entanglement dynamically, while the program is running. We first present a dynamic semantics for a functional language with references that checks for entanglement by consulting parallel and sequential dependency relations in the program. Notably, the semantics requires checks for mutable objects only. We prove the soundness of the dynamic semantics and present several techniques for realizing it efficiently, in particular by pruning away a large number of entanglement checks. We also provide bounds on the work and space of our techniques. We show that the entanglement detection techniques are practical by implementing them in the MPL compiler for Parallel ML. Considering a variety of benchmarks, we present an evaluation and measure time and space overheads of less than 5% on average with up to 72 cores. These results show that entanglement detection has negligible cost and can therefore remain deployed with little or no impact on efficiency, scalability, and space.

Uncertainty relations and quantum entanglement are pivotal concepts in quantum theory. Beyond their fundamental significance in shaping our understanding of the quantum world, they also underpin crucial applications in quantum information theory. In this article, we investigate entropic uncertainty relations and entanglement detection with an emphasis on quantum measurements with design structures. On the one hand, we derive improved Rényi entropic uncertainty relations for design-structured measurements, exploiting the property that the sum of powered (e.g., squared) probabilities of obtaining different measurement outcomes is now invariant under unitary transformations of the measured system and can be easily computed. On the other hand, the above property essentially imposes a state-independent upper bound, which is achieved at all pure states, on one’s ability to predict local outcomes when performing a set of design-structured measurements on quantum systems. Realizing this, we also obtain criteria for detecting multi-partite entanglement with design-structured measurements.