arXiv subjects

Otfried Gühne

Publications and source records attributed to Otfried Gühne.

At least 91 records · Page 5Linked to original sources

arXiv2022

Statistically significant tests of multiparticle quantum correlations based on randomized measurements

We consider statistical methods based on finite samples of locally randomized measurements in order to certify different degrees of multiparticle entanglement in intermediate-scale quantum systems. We first introduce hierarchies of multi-qubit criteria, satisfied by states which are separable with respect to partitions of different size, involving only second moments of the underlying probability distribution. Then, we analyze in detail the statistical error of the estimation in experiments and present several approaches for estimating the statistical significance based on large deviation bounds. The latter allows us to characterize the measurement resources required for the certification of multiparticle correlations, as well as to analyze given experimental data in detail.

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arXiv2022

Statistical Methods for Quantum State Verification and Fidelity Estimation

The efficient and reliable certification of quantum states is essential for various quantum information processing tasks as well as for the general progress on the implementation of quantum technologies. In the last few years several methods have been introduced which use advanced statistical methods to certify quantum states in a resource-efficient manner. In this article we present a review of the recent progress in this field. We first explain how the verification and fidelity estimation of a quantum state can be discussed in the language of hypothesis testing. Then, we explain in detail various strategies for the verification of entangled states with local measurements or measurements assisted by local operations and classical communication. Finally, we discuss several extensions of the problem, such as the certification of quantum channels and the verification of entanglement.

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arXiv2022

Quantum-Inspired Hierarchy for Rank-Constrained Optimization

Many problems in information theory can be reduced to optimizations over matrices, where the rank of the matrices is constrained. We establish a link between rank-constrained optimization and the theory of quantum entanglement. More precisely, we prove that a large class of rank-constrained semidefinite programs can be written as a convex optimization over separable quantum states and, consequently, we construct a complete hierarchy of semidefinite programs for solving the original problem. This hierarchy not only provides a sequence of certified bounds for the rank-constrained optimization problem, but also gives pretty good and often exact values in practice when the lowest level of the hierarchy is considered. We demonstrate that our approach can be used for relevant problems in quantum information processing, such as the optimization over pure states, the characterization of mixed unitary channels and faithful entanglement, and quantum contextuality, as well as in classical information theory including the maximum cut problem, pseudo-Boolean optimization, and the orthonormal representation of graphs. Finally, we show that our ideas can be extended to rank-constrained quadratic and higher-order programming.

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arXiv2022

Structure of dimension-bounded temporal correlations

We analyze the structure of the space of temporal correlations generated by quantum systems. We show that the temporal correlation space under dimension constraints can be nonconvex. For the general case, we provide the necessary and sufficient dimension of a quantum system needed to generate a convex correlation space for a given scenario. We further prove that this dimension coincides with the dimension necessary to generate any point in the temporal correlation polytope. As an application of our results, we derive nonlinear inequalities to witness the nonconvexity for qubits and qutrits in the simplest scenario, and present an algorithm which can help to find the minimum for a certain type of nonlinear expressions under dimension constraints.

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arXiv2022

Symmetries in quantum networks lead to no-go theorems for entanglement distribution and to verification techniques

Quantum networks are promising tools for the implementation of long-range quantum communication. The characterization of quantum correlations in networks and their usefulness for information processing is therefore central for the progress of the field, but so far only results for small basic network structures or pure quantum states are known. Here we show that symmetries provide a versatile tool for the analysis of correlations in quantum networks. We provide an analytical approach to characterize correlations in large network structures with arbitrary topologies. As examples, we show that entangled quantum states with a bosonic or fermionic symmetry can not be generated in networks; moreover, cluster and graph states are not accessible. Our methods can be used to design certification methods for the functionality of specific links in a network and have implications for the design of future network structures.

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arXiv2021

Optimal Entanglement Certification from Moments of the Partial Transpose

For the certification and benchmarking of medium-size quantum devices efficient methods to characterize entanglement are needed. In this context, it has been shown that locally randomized measurements on a multiparticle quantum system can be used to obtain valuable information on the so-called moments of the partially transposed quantum state. This allows one to infer some separability properties of a state, but how to use the given information in an optimal and systematic manner has yet to be determined. We propose two general entanglement detection methods based on the moments of the partially transposed density matrix. The first method is based on the Hankel matrices and provides a family of entanglement criteria, of which the lowest order reduces to the known $p_3$-PPT criterion proposed in A. Elben et al. [Phys. Rev. Lett. 125, 200501 (2020)]. The second method is optimal and gives necessary and sufficient conditions for entanglement based on some moments of the partially transposed density matrix.

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arXiv2021

Genuine Multipartite Entanglement in Time

While spatial quantum correlations have been studied in great detail, much less is known about the genuine quantum correlations that can be exhibited by temporal processes. Employing the quantum comb formalism, processes in time can be mapped onto quantum states, with the crucial difference that temporal correlations have to satisfy causal ordering, while their spatial counterpart is not constrained in the same way. Here, we exploit this equivalence and use the tools of multipartite entanglement theory to provide a comprehensive picture of the structure of correlations that (causally ordered) temporal quantum processes can display. First, focusing on the case of a process that is probed at two points in time -- which can equivalently be described by a tripartite quantum state -- we provide necessary as well as sufficient conditions for the presence of bipartite entanglement in different splittings. Next, we connect these scenarios to the previously studied concepts of quantum memory, entanglement breaking superchannels, and quantum steering, thus providing both a physical interpretation for entanglement in temporal quantum processes, and a determination of the resources required for its creation. Additionally, we construct explicit examples of W-type and GHZ-type genuinely multipartite entangled two-time processes and prove that genuine multipartite entanglement in temporal processes can be an emergent phenomenon. Finally, we show that genuinely entangled processes across multiple times exist for any number of probing times.

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arXiv2021

Bound entanglement from randomized measurements

If only limited control over a multiparticle quantum system is available, a viable method to characterize correlations is to perform random measurements and consider the moments of the resulting probability distribution. We present systematic methods to analyze the different forms of entanglement with these moments in an optimized manner. First, we find the optimal criteria for different forms of multiparticle entanglement in three-qubit systems using the second moments of randomized measurements. Second, we present the optimal inequalities if entanglement in a bipartition of a multi-qubit system shall be analyzed in terms of these moments. Finally, for higher-dimensional two-particle systems and higher moments, we provide criteria that are able to characterize various examples of bound entangled states, showing that detection of such states is possible in this framework.

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arXiv2021

Finding optimal Bell inequalities using the cone-projection technique

Bell inequalities are relevant for many problems in quantum information science, but finding them for many particles is computationally hard. Recently, a computationally feasible method called cone-projection technique has been developed to find all optimal Bell inequalities under some constraints, which may be given by some symmetry or other linear conditions. In this paper we extend this work in several directions. We use the method to generalize the I4422 inequality to three particles and a so-called GYNI inequality to four particles. Additionally, we find Bell inequalities for three particles that generalize the I3322 inequality and the CHSH inequality at the same time. We discuss the obtained inequalities in some detail and characterize their violation in quantum mechanics.

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arXiv2021

Geometry of faithful entanglement

A typical concept in quantum state analysis is based on the idea that states in the vicinity of some pure entangled state share the same properties; implying that states with a high fidelity must be entangled. States whose entanglement can be detected in this way are also called faithful. We prove a structural result on the corresponding fidelity-based entanglement witnesses, resulting in a simple condition for faithfulness of a two-party state. For the simplest case of two qubits faithfulness can directly be decided and for higher dimensions accurate analytical criteria are given. Finally, our results show that faithful entanglement is, in a certain sense, useful entanglement; moreover, they establish connections to computational complexity and simplify several results in entanglement theory.

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arXiv2021

Quantum measurement incompatibility in subspaces

We consider the question of characterising the incompatibility of sets of high-dimensional quantum measurements. We introduce the concept of measurement incompatibility in subspaces. That is, starting from a set of measurements that is incompatible, one considers the set of measurements obtained by projection onto any strict subspace of fixed dimension. We identify three possible forms of incompatibility in subspaces: (i) incompressible incompatibility: measurements that become compatible in every subspace, (ii) fully compressible incompatibility: measurements that remain incompatible in every subspace, and (iii) partly compressible incompatibility: measurements that are compatible in some subspace and incompatible in another. For each class we discuss explicit examples. Finally, we present some applications of these ideas. First we show that joint measurability and coexistence are two inequivalent notions of incompatibility in the simplest case of qubit systems. Second we highlight the implications of our results for tests of quantum steering.

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arXiv2021

Exploring the relationship between the faithfulness and entanglement of two qubits

A conceptually simple and experimentally prevalent class of entanglement witnesses, known as fidelity witnesses, detect entanglement via a state's fidelity with a pure reference state. While existence proofs guarantee that a suitable witness can be constructed for every entangled state, such assurances do not apply to fidelity witnesses. Recent results have found that entangled states that cannot be detected by a fidelity witness, known as unfaithful states, are exceedingly common among bipartite states. In this paper, we show that even among two-qubit states, the simplest of all entangled states, unfaithful states can be created through a suitable application of decoherence and filtering to a Bell state. We also show that the faithfulness is not monotonic to entanglement, as measured by the concurrence. Finally, we experimentally verify our predictions using polarization-entangled photons and specifically demonstrate a situation where an unfaithful state is brought to faithfulness at the expense of further reducing the entanglement of the state.

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arXiv2021

A complete hierarchy for the pure state marginal problem in quantum mechanics

Clarifying the relation between the whole and its parts is crucial for many problems in science. In quantum mechanics, this question manifests itself in the quantum marginal problem, which asks whether there is a global pure quantum state for some given marginals. This problem arises in many contexts, ranging from quantum chemistry to entanglement theory and quantum error correcting codes. In this paper, we prove a correspondence of the marginal problem to the separability problem. Based on this, we describe a sequence of semidefinite programs which can decide whether some given marginals are compatible with some pure global quantum state. As an application, we prove that the existence of multiparticle absolutely maximally entangled states for a given dimension is equivalent to the separability of an explicitly given two-party quantum state. Finally, we show that the existence of quantum codes with given parameters can also be interpreted as a marginal problem, hence, our complete hierarchy can also be used.

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arXiv2021

Quantum entanglement in the triangle network

Beyond future applications, quantum networks open interesting fundamental perspectives, notably novel forms of quantum correlations. In this work we discuss quantum correlations in networks from the perspective of the underlying quantum states and their entanglement. We address the questions of which states can be prepared in the so-called triangle network, consisting of three nodes connected pairwise by three sources. We derive necessary criteria for a state to be preparable in such a network, considering both the cases where the sources are statistically independent and classically correlated. This shows that the network structure imposes strong and non-trivial constraints on the set of preparable states, fundamentally different from the standard characterization of multipartite quantum entanglement.

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arXiv2020

Some quantum measurements with three outcomes can reveal nonclassicality where all two-outcome measurements fail to do so

Measurements serve as the intermediate communication layer between the quantum world and our classical perception. So, the question which measurements efficiently extract information from quantum systems is of central interest. Using quantum steering as a nonclassical phenomenon, we show that there are instances, where the results of all two-outcome measurements can be explained in a classical manner, while the results of some three-outcome measurements cannot. This points at the important role of the number of outcomes in revealing the nonclassicality hidden in a quantum system. Moreover, our methods allow to improve the understanding of quantum correlations by delivering novel criteria for quantum steering and improved ways to construct local hidden variable models.

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arXiv2020

Generalizing optimal Bell inequalities

Bell inequalities are central tools for studying nonlocal correlations and their applications in quantum information processing. Identifying inequalities for many particles or measurements is, however, difficult due to the computational complexity of characterizing the set of local correlations. We develop a method to characterize Bell inequalities under constraints, which may be given by symmetry or other linear conditions. This allows to search systematically for generalizations of given Bell inequalities to more parties. As an example, we find all possible generalizations of the two-particle inequality by Froissart [Il Nuovo Cimento B64, 241 (1981)], also known as I3322 inequality, to three particles. For the simplest of these inequalities, we study their quantum mechanical properties and demonstrate that they are relevant, in the sense that they detect nonlocality of quantum states, for which all two-setting inequalities fail to do so.

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arXiv2020

Simulating extremal temporal correlations

The correlations arising from sequential measurements on a single quantum system form a polytope. This is defined by the arrow-of-time (AoT) constraints, meaning that future choices of measurement settings cannot influence past outcomes. We discuss the resources needed to simulate the extreme points of the AoT polytope, where resources are quantified in terms of the minimal dimension, or "internal memory" of the physical system. First, we analyze the equivalence classes of the extreme points under symmetries. Second, we characterize the minimal dimension necessary to obtain a given extreme point of the AoT polytope, including a lower scaling bound in the asymptotic limit of long sequences. Finally, we present a general method to derive dimension-sensitive temporal inequalities for longer sequences, based on inequalities for shorter ones, and investigate their robustness to imperfections.

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arXiv2020

Entanglement characterization using quantum designs

We present in detail a statistical approach for the reference-frame-independent detection and characterization of multipartite entanglement based on moments of randomly measured correlation functions. We start by discussing how the corresponding moments can be evaluated with designs, linking methods from group and entanglement theory. Then, we illustrate the strengths of the presented framework with a focus on the multipartite scenario. We discuss a condition for characterizing genuine multipartite entanglement for three qubits, and we prove criteria that allow for a discrimination of $W$-type entanglement for an arbitrary number of qubits.

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