arXiv subjects

Otfried Gühne

Publications and source records attributed to Otfried Gühne.

At least 127 records · Page 7Linked to original sources

arXiv2019

Quantifying quantum resources with conic programming

Resource theories can be used to formalize the quantification and manipulation of resources in quantum information processing such as entanglement, asymmetry and coherence of quantum states, and incompatibility of quantum measurements. Given a certain state or measurement, one can ask whether there is a task in which it performs better than any resourceless state or measurement. Using conic programming, we prove that any general robustness measure (with respect to a convex set of free states or measurements) can be seen as a quantifier of such outperformance in some discrimination task. We apply the technique to various examples, e.g. joint measurability, POVMs simulable by projective measurements, and state assemblages preparable with a given Schmidt number.

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arXiv2019

Entanglement detection with scrambled data

In the usual entanglement detection scenario the possible measurements and the corresponding data are assumed to be fully characterized. We consider the situation where the measurements are known, but the data is scrambled, meaning the assignment of the probabilities to the measurement outcomes is unknown. We investigate in detail the two-qubit scenario with local measurements in two mutually unbiased bases. First, we discuss the use of entropies to detect entanglement from scrambled data, showing that Tsallis- and Rényi entropies can detect entanglement in our scenario, while the Shannon entropy cannot. Then, we introduce and discuss scrambling-invariant families of entanglement witnesses. Finally, we show that the set of non-detectable states in our scenario is non-convex and therefore in general hard to characterize.

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arXiv2019

The thermodynamical cost of some interpretations of quantum theory. Reply to Prunkl and Timpson, and Davidsson

Here we clarify the assumptions made and conclusions reached in our paper "The thermodynamical cost of some interpretations of quantum theory" [Phys. Rev. A 94, 052127 (2016)], at the light of the criticisms of Prunkl and Timpson [Stud. Hist. Philos. Sci. Part B 63, 114 (2018)], and Davidsson (Master thesis, Stockholm University, 2018). We point out some misunderstandings and some weaknesses of the counterexample Prunkl and Timpson present to challenge our conclusion. We thus conclude, once more, that interpretations of quantum theory which consider the probabilities of measurement outcomes to be determined by objective properties of the measured system and satisfy the assumption that the measured system only has finite memory have a thermodynamical cost.

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arXiv2018

Characterizing multipartite entanglement with moments of random correlations

The experimental detection of multipartite entanglement usually requires a number of appropriately chosen local quantum measurements which are aligned with respect to a previously shared common reference frame. The latter, however, can be a challenging prerequisite e.g. for satellite-based photonic quantum communication, making the development of alternative detection strategies desirable. One possibility for avoiding the distribution of classical reference frames is to perform a number of local measurements with settings distributed uniformly at random. In this work we follow such a treatment and show that an improved detection and characterization of multipartite entanglement is possible by combining statistical moments of different order. To do so, we make use of designs which are pseudo-random processes allowing to link the present entanglement criteria to ordinary reference frame independent ones. The strengths of our methods are illustrated in various cases starting with two qubits and followed by more involved multipartite scenarios.

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arXiv2018

Steering criteria from general entropic uncertainty relations

The effect of steering describes a possible action at a distance via measurements but characterizing the quantum states that can be used for this task remains difficult. We provide a method to derive sufficient criteria for steering from entropic uncertainty relations using generalized entropies. We demonstrate that the resulting criteria outperform existing criteria in several scenarios; moreover, they allow one to detect weakly steerable states.

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arXiv2018

Proving genuine multiparticle entanglement from separable nearest-neighbor marginals

We address the question of whether or not global entanglement of a quantum state can be inferred from local properties. Specifically, we are interested in genuinely multiparticle entangled states whose two-body marginals are all separable, but where the entanglement can be proven using knowledge of a subset of the marginals only. Using an iteration of semidefinite programs we prove that for any possible marginal configuration up to six particles multiqubit states with the desired properties can be found. We then present a method to construct states with the same properties for more particles in higher dimensions.

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arXiv2018

Structure of temporal correlations of a qubit

In quantum mechanics, spatial correlations arising from measurements at separated particles are well studied. This is not the case, however, for the temporal correlations arising from a single quantum system subjected to a sequence of generalized measurements. We first characterize the polytope of temporal quantum correlations coming from the most general measurements. We then show that if the dimension of the quantum system is bounded, only a subset of the most general correlations can be realized and identify the correlations in the simplest scenario that can not be reached by two-dimensional systems. This leads to a temporal inequality for a dimension test, and we discuss a possible implementation using nitrogen-vacancy centers in diamond.

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arXiv2018

Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems

The effect of quantum steering describes a possible action at a distance via local measurements. Whereas many attempts on characterizing steerability have been pursued, answering the question as to whether a given state is steerable or not remains a difficult task. Here, we investigate the applicability of a recently proposed method for building steering criteria from generalized entropic uncertainty relations. This method works for any entropy which satisfy the properties of (i) (pseudo-) additivity for independent distributions; (ii) state independent entropic uncertainty relation (EUR); and (iii) joint convexity of a corresponding relative entropy. Our study extends the former analysis to Tsallis and Rényi entropies on bipartite and tripartite systems. As examples, we investigate the steerability of the three-qubit GHZ and W states.

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arXiv2018

Entanglement properties of quantum grid states

Grid states form a discrete set of mixed quantum states that can be described by graphs. We characterize the entanglement properties of these states and provide methods to evaluate entanglement criteria for grid states in a graphical way. With these ideas we find bound entangled grid states for two-particle systems of any dimension and multiparticle grid states that provide examples for the different aspects of genuine multiparticle entanglement. Our findings suggest that entanglement theory for grid states, although being a discrete set, has already a complexity similar to the one for general states.

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arXiv2018

Enhanced entanglement criterion via symmetric informationally complete measurements

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.

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arXiv2018

The structure of ultrafine entanglement witnesses

An entanglement witness is an observable with the property that a negative expectation value signals the presence of entanglement. The question arises how a witness can be improved if the expectation value of a second observable is known, and methods for doing this have recently been discussed as so-called ultrafine entanglement witnesses. We present several results on the characterization of entanglement given the expectation values of two observables. First, we explain that this problem can naturally be tackled with the method of the Legendre transformation, leading even to a quantification of entanglement. Second, we present necessary and sufficient conditions that two product observables are able to detect entanglement. Finally, we explain some fallacies in the original construction of ultrafine entanglement witnesses [F. Shahandeh et al., Phys. Rev. Lett. 118, 110502 (2017)].

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arXiv2018

Exponentially many entanglement and correlation constraints for multipartite quantum states

We present a family of correlations constraints that apply to all multipartite quantum systems of finite dimension. The size of this family is exponential in the number of subsystems. We obtain these relations by defining and investigating the generalized state inversion map. This map provides a systematic way to generate local unitary invariants of degree two in the state and is directly linked to the shadow inequalities proved by Rains [IEEE Trans. Inf. Theory 46, 54 (2000)]. The constraints are stated in terms of linear inequalities for the linear entropies of the subsystems. For pure quantum states they turn into monogamy relations that constrain the distribution of bipartite entanglement among the subsystems of the global state.

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arXiv2018

Optimal classical simulation of state-independent quantum contextuality

Simulating quantum contextuality with classical systems requires memory. A fundamental yet open question is what is the minimum memory needed and, therefore, the precise sense in which quantum systems outperform classical ones. Here, we make rigorous the notion of classically simulating quantum state-independent contextuality (QSIC) in the case of a single quantum system submitted to an infinite sequence of measurements randomly chosen from a finite QSIC set. We obtain the minimum memory needed to simulate arbitrary QSIC sets via classical systems under the assumption that the simulation should not contain any oracular information. In particular, we show that, while classically simulating two qubits tested with the Peres-Mermin set requires $\log_2 24 \approx 4.585$ bits, simulating a single qutrit tested with the Yu-Oh set requires, at least, $5.740$ bits.

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arXiv2018

Characterizing Genuine Multilevel Entanglement

Entanglement of high-dimensional quantum systems has become increasingly important for quantum communication and experimental tests of nonlocality. However, many effects of high-dimensional entanglement can be simulated by using multiple copies of low-dimensional systems. We present a general theory to characterize those high-dimensional quantum states for which the correlations cannot simply be simulated by low-dimensional systems. Our approach leads to general criteria for detecting multilevel entanglement in multiparticle quantum states, which can be used to verify these phenomena experimentally.

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arXiv2018

Convex optimization over classes of multiparticle entanglement

A well-known strategy to characterize multiparticle entanglement utilizes the notion of stochastic local operations and classical communication (SLOCC), but characterizing the resulting entanglement classes is difficult. Given a multiparticle quantum state, we first show that Gilbert's algorithm can be adapted to prove separability or membership in a certain entanglement class. We then present two algorithms for convex optimization over SLOCC classes. The first algorithm uses a simple gradient approach, while the other one employs the accelerated projected-gradient method. For demonstration, the algorithms are applied to the likelihood-ratio test using experimental data on bound entanglement of a noisy four-photon Smolin state [Phys. Rev. Lett. 105, 130501 (2010)].

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arXiv2017

Bounds on absolutely maximally entangled states from shadow inequalities, and the quantum MacWilliams identity

A pure multipartite quantum state is called absolutely maximally entangled (AME), if all reductions obtained by tracing out at least half of its parties are maximally mixed. Maximal entanglement is then present across every bipartition. The existence of such states is in many cases unclear. With the help of the weight enumerator machinery known from quantum error correction and the generalized shadow inequalities, we obtain new bounds on the existence of AME states in dimensions larger than two. To complete the treatment on the weight enumerator machinery, the quantum MacWilliams identity is derived in the Bloch representation. Finally, we consider AME states whose subsystems have different local dimensions, and present an example for a $2 \times3 \times 3 \times 3$ system that shows maximal entanglement across every bipartition.

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arXiv2017

Estimation of gradients in quantum metrology

We develop a general theory to estimate magnetic field gradients in quantum metrology. We consider a system of $N$ particles distributed on a line whose internal degrees of freedom interact with a magnetic field. Usually gradient estimation is based on precise measurements of the magnetic field at two different locations, performed with two independent groups of particles. This approach, however, is sensitive to fluctuations of the off-set field determining the level-splitting of the particles and results in collective dephasing. In this work we use the framework of quantum metrology to assess the maximal accuracy for gradient estimation. For arbitrary positioning of particles, we identify optimal entangled and separable states allowing the estimation of gradients with the maximal accuracy, quantified by the quantum Fisher information. We also analyze the performance of states from the decoherence-free subspace (DFS), which are insensitive to the fluctuations of the magnetic offset field. We find that these states allow to measure a gradient directly, without the necessity of estimating the magnetic offset field. Moreover, we show that DFS states attain a precision for gradient estimation comparable to the optimal entangled states. Finally, for the above classes of states we find simple and feasible measurements saturating the quantum Cramér-Rao bound.

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arXiv2017

Unified picture for spatial, temporal and channel steering

Quantum steering describes how local actions on a quantum system can affect another, space-like separated, quantum state. Lately, quantum steering has been formulated also for time-like scenarios and for quantum channels. We approach all the three scenarios as one using tools from Stinespring dilations of quantum channels. By applying our technique we link all three steering problems one-to-one with the incompatibility of quantum measurements, a result formerly known only for spatial steering. We exploit this connection by showing how measurement uncertainty relations can be used as tight steering inequalities for all three scenarios. Moreover, we show that certain notions of temporal and spatial steering are fully equivalent and prove a hierarchy between temporal steering and macrorealistic hidden variable models.

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