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Otfried Gühne

Publications and source records attributed to Otfried Gühne.

At least 73 records · Page 4Linked to original sources
arXiv2023

Complete characterization of quantum correlations by randomized measurements

The fact that quantum mechanics predicts stronger correlations than classical physics is an essential cornerstone of quantum information processing. Indeed, these quantum correlations are a valuable resource for various tasks, such as quantum key distribution or quantum teleportation, but characterizing these correlations in an experimental setting is a formidable task, especially in scenarios where no shared reference frames are available. By definition, quantum correlations are reference-frame independent, i.e., invariant under local transformations; this physically motivated invariance implies, however, a dedicated mathematical structure and, therefore, constitutes a roadblock for an efficient analysis of these correlations in experiments. Here we provide a method to directly measure any locally invariant property of quantum states using locally randomized measurements, and we present a detailed toolbox to analyze these correlations for two quantum bits. We implement these methods experimentally using pairs of entangled photons, characterizing their usefulness for quantum teleportation and their potential to display quantum nonlocality in its simplest form. Our results can be applied to various quantum computing platforms, allowing simple analysis of correlations between arbitrary distant qubits in the architecture.

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arXiv2023

Covariance matrix-based criteria for network entanglement

Quantum networks offer a realistic and practical scheme for generating multiparticle entanglement and implementing multiparticle quantum communication protocols. However, the correlations that can be generated in networks with quantum sources and local operations are not yet well understood. Covariance matrices, which are powerful tools in entanglement theory, have been also applied to the network scenario. We present simple proofs for the decomposition of such matrices into the sum of positive semidefinite block matrices and, based on that, develop analytical and computable necessary criteria for preparing states in quantum networks. These criteria can be applied to networks in which any two nodes share at most one source, such as all bipartite networks.

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arXiv2023

Uncertainty relations from graph theory

Quantum measurements are inherently probabilistic and quantum theory often forbids to precisely predict the outcomes of simultaneous measurements. This phenomenon is captured and quantified through uncertainty relations. Although studied since the inception of quantum theory, the problem of determining the possible expectation values of a collection of quantum measurements remains, in general, unsolved. By constructing a close connection between observables and graph theory, we derive uncertainty relations valid for any set of dichotomic observables. These relations are, in many cases, tight, and related to the size of the maximum clique of the associated graph. As applications, our results can be straightforwardly used to formulate entropic uncertainty relations, separability criteria and entanglement witnesses.

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arXiv2023

Characterizing entanglement dimensionality from randomized measurements

We consider the problem of detecting the dimensionality of entanglement with the use of correlations between measurements in randomized directions. First, exploiting the recently derived covariance matrix criterion for the entanglement dimensionality [S. Liu et al., arXiv:2208.04909], we derive an inequality that resembles well-known entanglement criteria, but contains different bounds for the different dimensionalities of entanglement. This criterion is invariant under local changes of $su(d)$ bases and can be used to find regions in the space of moments of randomized correlations, generalizing the results of [S. Imai et al., Phys. Rev. Lett. 126, 150501 (2021)] to the case of entanglement-dimensionality detection. In particular, we find analytical boundary curves for the different entanglement dimensionalities in the space of second- and fourth-order moments of randomized correlations for all dimensions $d_a = d_b = d$ of a bipartite system. We then show how our method works in practice, also considering a finite statistical sample of correlations, and we also show that it can detect more states than other entanglement-dimensionality criteria available in the literature, thus providing a method that is both very powerful and potentially simpler in practical scenarios. We conclude by discussing the partly open problem of the implementation of our method in the multipartite scenario.

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arXiv2023

Scalable generation and detection of on-demand W states in nanophotonic circuits

Quantum physics phenomena, entanglement and coherence, are crucial for quantum information protocols, but understanding these in systems with more than two parts is challenging due to increasing complexity. The W state, a multipartite entangled state, is notable for its robustness and benefits in quantum communication. Here, we generate an 8-mode on-demand single photon W states, using nanowire quantum dots and a silicon nitride photonic chip. We demonstrate a reliable, scalable technique for reconstructing W-state in photonic circuits using Fourier and real-space imaging, supported by the Gerchberg-Saxton phase retrieval algorithm. Additionally, we utilize an entanglement witness to distinguish between mixed and entangled states, thereby affirming the entangled nature of our generated state. The study provides a new imaging approach of assessing multipartite entanglement in W-states, paving the way for further progress in image processing and Fourier-space analysis techniques for complex quantum systems.

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arXiv2023

Experimental verification of bound and multiparticle entanglement with the randomized measurement toolbox

In recent years, analysis methods for quantum states based on randomized measurements have been investigated extensively. Still, in the experimental implementations these methods were typically used for characterizing strongly entangled states and not to analyze the different families of multiparticle or weakly entangled states. In this work, we experimentally prepare various entangled states with path-polarization hyper-entangled photon pairs, and study their entanglement properties using the full toolbox of randomized measurements. First, we successfully characterize the correlations of a series of GHZ-W mixed states using the second moments of the random outcomes, and demonstrate the advantages of this method by comparing it with the well-known three-tangle and squared concurrence. Second, we generate bound entangled chessboard states of two three-dimensional systems and verify their weak entanglement with a criterion derived from moments of randomized measurements.

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arXiv2023

Randomness Certification from Multipartite Quantum Steering for Arbitrary Dimensional Systems

Entanglement in bipartite systems has been applied for the generation of secure random numbers, which are playing an important role in cryptography or scientific numerical simulations. Here, we propose to use multipartite entanglement distributed between trusted and untrusted parties for generating randomness of arbitrary dimensional systems. We show that the distributed structure of several parties leads to additional protection against possible attacks by an eavesdropper, resulting in more secure randomness generated than in the corresponding bipartite scenario. Especially, randomness can be certified in the group of untrusted parties, even there is no randomness exists in either of them individually. We prove that the necessary and sufficient resource for quantum randomness in this scenario is multipartite quantum steering when two measurement settings are performed on the untrusted parties. However, the sufficiency no longer holds with more measurement settings. Finally, we apply our analysis to some experimentally realized states and show that more randomness can be extracted in comparison to the existing analysis.

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arXiv2023

Generalized Iterative Formula for Bell Inequalities

Bell inequalities are a vital tool to detect the nonlocal correlations, but the construction of them for multipartite systems is still a complicated problem. In this work, inspired via a decomposition of $(n+1)$-partite Bell inequalities into $n$-partite ones, we present a generalized iterative formula to construct nontrivial $(n+1)$-partite ones from the $n$-partite ones. Our iterative formulas recover the well-known Mermin-Ardehali-Belinski{\uı}-Klyshko (MABK) and other families in the literature as special cases. Moreover, a family of ``dual-use'' Bell inequalities is proposed, in the sense that for the generalized Greenberger-Horne-Zeilinger states these inequalities lead to the same quantum violation as the MABK family and, at the same time, the inequalities are able to detect the non-locality in the entire entangled region. Furthermore, we present generalizations of the the I3322 inequality to any $n$-partite case which are still tight, and of the $46$ Śliwa's inequalities to the four-partite tight ones, by applying our iteration method to each inequality and its equivalence class.

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arXiv2023

Fate of multiparticle entanglement when one particle becomes classical

We study the change of multiparticle entanglement if one particle becomes classical, in the sense that this particle is destructed by a measurement, but the gained information is encoded into a new register. We present an estimation of this change for different entanglement measures and ways of encoding. We first simplify the numerical calculation to analyze the change of entanglement under classicalization in special cases. Second, we provide general upper and lower bounds on the entanglement change. Third, we show that the entanglement change caused by classicalization of one qubit only can still be arbitrarily large. Finally, we discuss cases where no entanglement is left under classicalization for any possible measurement. Our results shed light on the storage of quantum resources and help to develop a novel direction in the field of quantum resource theories.

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arXiv2023

No-go theorem based on incomplete information of Wigner about his friend

The notion of measurements is central for many debates in quantum mechanics. One critical point is whether a measurement can be regarded as an absolute event, giving the same result for any observer in an irreversible manner. Using ideas from the gedankenexperiment of Wigner's friend it has been argued that, when combined with the assumptions of locality and no-superdeterminism, regarding a measurement as an absolute event is incompatible with the universal validity of quantum mechanics. We consider a weaker assumption: is the measurement event realised relatively to the observer when he only partially observed the outcome. We proposed a protocol to show that this assumption putting in conjunction with the natural assumptions of no-superdeterminism and locality is also not compatible with the universal validity of quantum mechanics.

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arXiv2023

Work fluctuations and entanglement in quantum batteries

We consider quantum batteries given by composite interacting quantum systems in terms of the thermodynamic work cost of local random unitary processes. We characterize quantum correlations by monitoring the average energy change and its fluctuations in the high-dimensional bipartite systems. We derive a hierarchy of bounds on high-dimensional entanglement (the so-called Schmidt number) from the work fluctuations and thereby show that larger work fluctuations can verify the presence of stronger entanglement in the system. Finally, we develop two-point measurement protocols with noisy detectors that can estimate work fluctuations, showing that the dimensionality of entanglement can be probed in this manner.

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arXiv2023

Incompatible measurements in quantum information science

Some measurements in quantum mechanics disturb each other. This has puzzled physicists since the formulation of the theory, but only in recent decades has the incompatibility of measurements been analyzed in depth and detail, using the notion of joint measurability of generalized measurements. In this Colloquium joint measurability and incompatibility are reviewed from the perspective of quantum information science. The Colloquium starts by discussing the basic definitions and concepts. An overview on applications of incompatibility, such as in measurement uncertainty relations, the characterization of quantum correlations, or information processing tasks like quantum state discrimination, is then presented. Finally, emerging directions of research, such as a resource theory of incompatibility as well as other concepts to grasp the nature of measurements in quantum mechanics, are discussed.

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arXiv2023

Bell inequalities for nonlocality depth

When three or more particles are considered, quantum correlations can be stronger than the correlations generated by so-called hybrid local hidden variable models, where some of the particles are considered as a single block inside which communication and signaling is allowed. We provide an exhaustive classification of Bell inequalities to characterize various hybrid scenarios in four- and five-particle systems. In quantum mechanics, these inequalities provide device-independent witnesses for the entanglement depth. In addition, we construct a family of inequalities to detect a non-locality depth of (n-1) in n-particle systems. Moreover, we present two generalizations of the original Svetlichny inequality, which was the first Bell inequality designed for hybrid models. Our results are based on the cone-projection technique, which can be used to completely characterize Bell inequalities under affine constraints; even for many parties, measurements, and outcomes.

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arXiv2023

Kochen-Specker Contextuality

A central result in the foundations of quantum mechanics is the Kochen-Specker theorem. In short, it states that quantum mechanics is in conflict with classical models in which the result of a measurement does not depend on which other compatible measurements are jointly performed. Here compatible measurements are those that can be implemented simultaneously or, more generally, those that are jointly measurable. This conflict is generically called quantum contextuality. In this review, an introduction to this subject and its current status is presented. Several proofs of the Kochen-Specker theorem and different notions of contextuality are reviewed. How to experimentally test some of these notions is explained and connections between contextuality and nonlocality or graph theory are discussed. Finally, some applications of contextuality in quantum information processing are reviewed.

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arXiv2022

Complete hierarchy for high-dimensional steering certification

High-dimensional quantum steering can be seen as a test for the dimensionality of entanglement, where the devices at one side are not characterized. As such, it is an important component in quantum informational protocols that make use of high-dimensional entanglement. Although it has been recently observed experimentally, the phenomenon of high-dimensional steering is lacking a general certification procedure. We provide necessary and sufficient conditions to certify the entanglement dimension in a steering scenario. These conditions are stated in terms of a hierarchy of semidefinite programs, which can also be used to quantify the phenomenon using the steering dimension robustness. To demonstrate the practical viability of our method, we characterize the dimensionality of entanglement in steering scenarios prepared with maximally entangled states measured in mutually unbiased bases. Our methods give significantly stronger bounds on the noise robustness necessary to experimentally certify high-dimensional entanglement.

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arXiv2022

Exact Entanglement Dynamics of Two Spins in Finite Baths

We consider the buildup and decay of two-spin entanglement through phase interactions in a finite environment of surrounding spins, as realized in quantum computing platforms based on arrays of atoms, molecules, or nitrogen vacancy centers. The non-Markovian dephasing caused by the spin environment through Ising-type phase interactions can be solved exactly and compared to an effective Markovian treatment based on collision models. In a first case study on a dynamic lattice of randomly hopping spins, we find that non-Markovianity boosts the dephasing rate caused by nearest neighbour interactions with the surroundings, degrading the maximum achievable entanglement. However, we also demonstrate that additional three-body interactions can mitigate this degradation, and that randomly timed reset operations performed on the two-spin system can help sustain a finite average amount of steady-state entanglement. In a second case study based on a model nuclear magnetic resonance system, we elucidate the role of bath correlations at finite temperature on non-Markovian dephasing. They speed up the dephasing at low temperatures while slowing it down at high temperatures, compared to an uncorrelated bath, which is related to the number of thermally accessible spin configurations with and without interactions.

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arXiv2022

Optimising shadow tomography with generalised measurements

Advances in quantum technology require scalable techniques to efficiently extract information from a quantum system, such as expectation values of observables or its entropy. Traditional tomography is limited to a handful of qubits and shadow tomography has been suggested as a scalable replacement for larger systems. Shadow tomography is conventionally analysed based on outcomes of ideal projective measurements on the system upon application of randomised unitaries. Here, we suggest that shadow tomography can be much more straightforwardly formulated for generalised measurements, or positive operator valued measures. Based on the idea of the least-square estimator, shadow tomography with generalised measurements is both more general and simpler than the traditional formulation with randomisation of unitaries. In particular, this formulation allows us to analyse theoretical aspects of shadow tomography in detail. For example, we provide a detailed study of the implication of symmetries in shadow tomography. Shadow tomography with generalised measurements is also indispensable in realistic implementation of quantum mechanical measurements, when noise is unavoidable. Moreover, we also demonstrate how the optimisation of measurements for shadow tomography tailored toward a particular set of observables can be carried out.

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arXiv2022

Characterizing generalized axisymmetric quantum states in $d\times d$ systems

We introduce a family of highly symmetric bipartite quantum states in arbitrary dimensions. It consists of all states that are invariant under local phase rotations and local cyclic permutations of the basis. We solve the separability problem for a subspace of these states and show that a sizable part of the family is bound entangled. We also calculate some of the Schmidt numbers for the family in $d = 3$, thereby characterizing the dimensionality of entanglement. Our results allow us to estimate entanglement properties of arbitrary states, as general states can be symmetrized to the considered family by local operations.

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