arXiv subjects

Nikolai Miklin

Publications and source records attributed to Nikolai Miklin.

29 records · Page 2Linked to original sources

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

Information Causality without concatenation

Information Causality is a physical principle which states that the amount of randomly accessible data over a classical communication channel cannot exceed its capacity, even if the sender and the receiver have access to a source of nonlocal correlations. This principle can be used to bound the nonlocality of quantum mechanics without resorting to its full formalism, with a notable example of reproducing the Tsirelson's bound of the Clauser-Horne-Shimony-Holt inequality. Despite being promising, the latter result found little generalization to other Bell inequalities because of the limitations imposed by the process of concatenation, in which several nonsignaling resources are put together to produce tighter bounds. In this work, we show that concatenation can be successfully replaced by limits on the communication channel capacity. It allows us to re-derive and, in some cases, significantly improve all the previously known results in a simpler manner and apply the Information Causality principle to previously unapproachable Bell scenarios.

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arXiv2020

Experimental characterisation of unsharp qubit observables and sequential measurement incompatibility via quantum random access codes

Unsharp measurements are increasingly important for foundational insights in quantum theory and quantum information applications. Here, we report an experimental implementation of unsharp qubit measurements in a sequential communication protocol, based on a quantum random access code. The protocol involves three parties; the first party prepares a qubit system, the second party performs operations which return both a classical and quantum outcome, and the latter is measured by the third party. We demonstrate a nearly-optimal sequential quantum random access code that outperforms both the best possible classical protocol and any quantum protocol which utilises only projective measurements. Furthermore, while only assuming that the involved devices operate on qubits and that detected events constitute a fair sample, we demonstrate the noise-robust characterisation of unsharp measurements based on the sequential quantum random access code. We apply this characterisation towards quantifying the degree of incompatibility of two sequential pairs of quantum measurements.

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arXiv2020

Semi-device-independent self-testing of unsharp measurements

Unsharp quantum measurements provide a resource in scenarios where one faces the trade-off between information gain and disturbance. In this work we introduce a prepare-transform-measure scenario in which two-outcome unsharp measurements outperform their sharp counterparts, as well as any stochastic strategy involving dichotomic projective measurements. Based on that, we propose a scheme for semi-device-independent self-testing of unsharp measurements and show that all two-outcome qubit measurements can be characterized in a robust way. Along with the main result, in this work we introduce a method, based on semidefinite programming, for bounding quantum correlations in scenarios with sequential measurements of length two. This method can also be applied to refine security analysis of the semi-device-independent one-way quantum key distribution. We also present new information gain-disturbance relation for pairs of dichotomic measurements.

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arXiv2020

Quantifying causal influences in the presence of a quantum common cause

Quantum mechanics challenges our intuition on the cause-effect relations in nature. Some fundamental concepts, including Reichenbach's common cause principle or the notion of local realism, have to be reconsidered. Traditionally, this is witnessed by the violation of a Bell inequality. But are Bell inequalities the only signature of the incompatibility between quantum correlations and causality theory? Motivated by this question we introduce a general framework able to estimate causal influences between two variables, without the need of interventions and irrespectively of the classical, quantum, or even post-quantum nature of a common cause. In particular, by considering the simplest instrumental scenario -- for which violation of Bell inequalities is not possible -- we show that every pure bipartite entangled state violates the classical bounds on causal influence, thus answering in negative to the posed question and opening a new venue to explore the role of causality within quantum theory.

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arXiv2019

The entropic approach to causal correlations

The existence of a global causal order between events places constraints on the correlations that parties may share. Such "causal correlations" have been the focus of recent attention, driven by the realization that some extensions of quantum mechanics may violate so-called causal inequalities. In this paper we study causal correlations from an entropic perspective, and we show how to use this framework to derive entropic causal inequalities. We consider two different ways to derive such inequalities. Firstly, we consider a method based on the causal Bayesian networks describing the causal relations between the parties. In contrast to the Bell-nonlocality scenario, where this method has previously been shown to be ineffective, we show that it leads to several interesting entropic causal inequalities. Secondly, we consider an alternative method based on counterfactual variables that has previously been used to derive entropic Bell inequalities. We compare the inequalities obtained via these two methods and discuss their violation by noncausal correlations. As an application of our approach, we derive bounds on the quantity of information - which is more naturally expressed in the entropic framework - that parties can communicate when operating in a definite causal order.

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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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arXiv2017

Qudit Hypergraph States

We generalize the class of hypergraph states to multipartite systems of qudits, by means of constructions based on the d-dimensional Pauli group and its normalizer. For simple hypergraphs, the different equivalence classes under local operations are shown to be governed by a greatest common divisor hierarchy. Moreover, the special cases of three qutrits and three ququarts is analysed in detail.

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arXiv2016

Indistinguishability of causal relations from limited marginals

We investigate the possibility of distinguishing among different causal relations starting from a limited set of marginals. Our main tool is the notion of adhesivity, that is, the extension of probability or entropies defined only on subsets of variables, which provides additional independence constraints among them. Our results provide a criterion for recognizing which causal structures are indistinguishable when only limited marginal information is accessible. Furthermore, the existence of such extensions greatly simplifies the characterization of a marginal scenario, a result that facilitates the derivation of Bell inequalities both in the probabilistic and entropic frameworks, and the identification of marginal scenarios where classical, quantum, and postquantum probabilities coincide.

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arXiv2016

Multiparticle entanglement as an emergent phenomenon

The question whether global entanglement of a multiparticle quantum system can be inferred from local properties is of great relevance for the theory of quantum correlations as well as for experimental implementations. We present a method to systematically find quantum states, for which the two- or three-body marginals do not contain any entanglement, nevertheless, the knowledge of these reduced states is sufficient to prove genuine multiparticle entanglement of the global state. With this, we show that the emergence of global entanglement from separable local quantum states occurs frequently and for an arbitrary number of particles. We discuss various extensions of the phenomenon and present examples where global entanglement can be proven from marginals, even if entanglement cannot be localized in the marginals with measurements on the other parties.

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arXiv2013

Schmidt modes and entanglement of biphoton polarization qutrits

Polarization features and entanglement of biphoton polarization qutrits are briefly outlined. Schmidt modes of qutrits are found analytically and in a general form by the method different from the standard one and based on the original approach of Erhard Schmidt (1906)

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