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arXiv:2302.10159 · Scientific Reports

Experimental hierarchy of two-qubit quantum correlations without state tomography

Shilan Abo, Jan Soubusta, Kateřina Jiráková, Karol Bartkiewicz, Antonín Černoch, Karel Lemr, Adam Miranowicz

Published May 26, 2023• 17 citations
arXivHTMLPDF

Abstract

A Werner state, which is the singlet Bell state affected by white noise, is a prototype example of states, which can reveal a hierarchy of quantum entanglement, steering, and Bell nonlocality by controlling the amount of noise. However, experimental demonstrations of this hierarchy in a sufficient and necessary way (i.e., by applying measures or universal witnesses of these quantum correlations) have been mainly based on full quantum state tomography, corresponding to measuring at least 15 real parameters of two-qubit states. Here we report an experimental demonstration of this hierarchy by measuring only six elements of a correlation matrix depending on linear combinations of two-qubit Stokes parameters. We show that our experimental setup can also reveal the hierarchy of these quantum correlations of generalized Werner states, which are any two-qubit pure states affected by white noise.

DOI
10.1038/s41598-023-35015-9

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A Werner state, which is the singlet Bell state affected by white noise, is a prototype example of states, which can reveal a hierarchy of quantum entanglement, steering, and Bell nonlocality by controlling the amount of noise. However, experimental demonstrations of this hierarchy in a sufficient and necessary way (i.e., by applying measures or universal witnesses of these quantum correlations) have been mainly based on full quantum state tomography, corresponding to measuring at least 15 real parameters of two-qubit states. Here we report an experimental demonstration of this hierarchy by measuring only six elements of a correlation matrix depending on linear combinations of two-qubit Stokes parameters. We show that our experimental setup can also reveal the hierarchy of these quantum correlations of generalized Werner states, which are any two-qubit pure states affected by white noise.
We demonstrate a hierarchy of various classes of quantum correlations on experimentally prepared two-qubit Werner-like states with controllable white noise. Werner states, which are white-noise-affected Bell states, are prototypal examples for studying such a hierarchy as a function of the amount of white noise. We experimentally generate Werner states and their generalizations, i.e., partially entangled pure states affected by white noise. These states enable us to study the hierarchy of the following classes of correlations: separability, entanglement, steering in three- and two-measurement scenarios, and Bell nonlocality. We show that the generalized Werner states (GWSs) reveal fundamentally different aspects of the hierarchy compared to the Werner states. In particular, we find five different parameter regimes of the GWSs, including those steerable in a two-measurement scenario but not violating Bell inequalities. This regime cannot be observed for the usual Werner states. Moreover, we find threshold curves separating different regimes of the quantum correlations and find the optimal states which allow for the largest amount of white noise which does not destroy their specific quantum correlations (e.g., unsteerable entanglement). Thus, we could identify the optimal Bell-nondiagonal GWSs which are, for this specific meaning, more robust against the white noise compared to the Bell-diagonal GWSs (i.e., Werner states).
Entanglement, quantum steering and Bell nonlocality can be used to describe the distinct quantum correlations of quantum systems. Because of their different characteristics and application fields, how to divide them quantitatively and accurately becomes particularly important. Based on the sufficient and necessary criterion for quantum steering of an arbitrary two-qubit T-state, we derive the inequality relations between quantum steering and entanglement as well as between quantum steering and Bell nonlocality for the T-state. Additionally, we have verified those relations experimentally.
Abstract Steering, a quantum property stronger than entanglement but weaker than non-locality in the quantum correlation hierarchy, is a key resource for one-sided device-independent quantum key distribution applications, in which only one of the communicating parties is trusted. A fine-grained steering inequality was introduced in (2014 Phys. Rev. A 90 050305), enabling for the first time the detection of steering in all steerable two-qubit Werner states using only two measurement settings. Here, we numerically and experimentally investigate this inequality for generalized Werner states and successfully detect steerability in a wide range of two-photon polarization-entangled Bell local states generated by a parametric down-conversion source.
Quantum entanglement as a special resource inspires various distinct applications in quantum information processing. Unfortunately, it is NP-hard to detect general quantum entanglement using Bell testing. Our goal is to investigate quantum entanglement with white noises that appear frequently in experiment and quantum simulations. Surprisingly, for almost all multipartite generalized Greenberger-Horne-Zeilinger states there are entangled noisy states that satisfy all linear Bell inequalities consisting of full correlations with dichotomic inputs and outputs of each local observer. This result shows generic undetectability of mixed entangled states in contrast to Gisin's theorem of pure bipartite entangled states in terms of Bell nonlocality. We further provide an accessible method to show a nontrivial set of noisy entanglement with small number of parties satisfying all general linear Bell inequalities. These results imply typical incompleteness of special Bell theory in explaining entanglement.
Quantum correlation between two parties serves as an important resource in the surging applications of quantum information. The Bell nonlocality and quantum steering have been proposed to describe non-classical correlations against local-hidden-variable and local-hidden-state theories, respectively. To characterize the two types of non-classical correlations, various nonlocality and steering inequalities have been established, and the amount of inequality violation serves as an important indicator for many entanglement-based tasks. Quantum state tomography has been employed for measuring quantum states, while the method requires intensive computation and does not directly verify either nonlocality or steering over the full domain independent of established theories. Here, we experimentally map the full-domain correlation with bipartite states for nonlocality and quantum steering in CHSH scenarios. The measurement of the maps automatically accounts for detection imperfections. Furthermore, we demonstrate the application of the correlation maps in the entanglement-based quantum key distribution protocol with arbitrary bipartite states. The correlation maps show direct measurements and simple interpretations that can answer fundamental questions about nonlocality and quantum steering as well as contribute to quantum information applications in a straightforward manner.
Entanglement potentials are a promising way to quantify the nonclassicality of single-mode states. They are defined by the amount of entanglement (expressed by, e.g., the Wootters concurrence) obtained after mixing the examined single-mode state with a purely classical state; such as the vacuum or a coherent state. We generalize the idea of entanglement potentials to other quantum correlations: the EPR steering and Bell nonlocality, thus enabling us to study mutual hierarchies of these nonclassicality potentials. Instead of the usual vacuum and one-photon superposition states, we experimentally test this concept using specially tailored polarization-encoded single-photon states. One polarization encodes a given nonclassical single-mode state, while the other serves as the vacuum place-holder. This technique proves to be experimentally more convenient in comparison to the vacuum and a one-photon superposition as it does not require the vacuum detection.