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Physical Review A

Experimental investigation of contextual robustness and coherence in state discrimination

Jingyan Lin, Kunkun Wang, Lei Xiao, Dengke Qu, Gaoyan Zhu, Yong Zhang, Peng Xue

Published May 8, 2024• 3 citations
Publisher

Abstract

Given that contextuality and coherence are significant resources in quantum physics, exploring the intricate interplay between these two factors presents a compelling avenue for research. Here, an experiment is presented to investigate the nuanced relationship between contextual robustness and coherence in a scenario of state discrimination. Specifically, two types of noises---depolarizing and dephasing---are introduced in the measurement procedure to assess the robustness of contextuality. By varying the overlap between the states to be discriminated, we explore the variations in contextual robustness across different levels of coherence. Importantly, our findings demonstrate that contextuality can persist under any degree of coherence. Notably, when coherence approaches zero (while remaining nonzero), contextuality can still endure under arbitrary amounts of partial dephasing. These results underscore the pivotal role of coherence in contextual phenomena, offering significant insights into the intricate interplay between coherence and contextuality.

DOI
10.1103/physreva.109.052208

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Given that contextuality and coherence are significant resources in quantum physics, exploring the intricate interplay between these two factors presents a compelling avenue for research. Here, an experiment is presented to investigate the nuanced relationship between contextual robustness and coherence in a scenario of state discrimination. Specifically, two types of noises---depolarizing and dephasing---are introduced in the measurement procedure to assess the robustness of contextuality. By varying the overlap between the states to be discriminated, we explore the variations in contextual robustness across different levels of coherence. Importantly, our findings demonstrate that contextuality can persist under any degree of coherence. Notably, when coherence approaches zero (while remaining nonzero), contextuality can still endure under arbitrary amounts of partial dephasing. These results underscore the pivotal role of coherence in contextual phenomena, offering significant insights into the intricate interplay between coherence and contextuality.
Generalized contextuality is a resource for a wide range of communication and information processing protocols. However, contextuality is not possible without coherence, and so can be destroyed by dephasing noise. Here, we explore the robustness of contextuality to partially dephasing noise in a scenario related to state discrimination (for which contextuality is a resource). We find that a vanishing amount of coherence is sufficient to demonstrate the failure of noncontextuality in this scenario, and we give a proof of contextuality that is robust to arbitrary amounts of partially dephasing noise. This is in stark contrast to partially depolarizing noise, which is always sufficient to destroy contextuality.
Exploring quantum phenomena beyond predictions of any classical model has fundamental importance to understand the boundary of classical and quantum descriptions of nature. As a typical property that a quantum system behaves distinctively from a classical counterpart, contextuality has been studied extensively and verified experimentally in systems composed of at least three levels (qutrit). Here we extend the scope of experimental test of contextuality to a minimal quantum system of only two states (qubit) by implementing the minimum error state discrimination on a single 171Yb+ ion. We observe a substantial violation of a no-go inequality derived by assuming non-contextuality, and firmly conclude that the measured results of state discrimination cannot be reconciled with any non-contextual description. We also quantify the contextual advantage of state discrimination and the tolerance against quantum noises.
Contextuality provides a unifying paradigm for nonclassical aspects of quantum probabilities and resources of quantum information. Unfortunately, most forms of quantum contextuality remain experimentally unexplored due to the difficulty of performing sequences of projective measurements on individual quantum systems. Here we show that two-point correlations between binary compatible observables are sufficient to reveal any form of contextuality. This allows us to design simple experiments that are more robust against imperfections and easier to analyze, thus opening the door for observing interesting forms of contextuality, including those requiring quantum systems of high dimensions. In addition, it allows us to connect contextuality to communication complexity scenarios and reformulate a recent result relating contextuality and quantum computation.
Quantum non-locality and quantum contextuality result from the impossibility of explain- ing the probabilities of measurement outcomes in quantum systems using theoretical mod- els that assume that observables have well-defined values prior to the measurement, and that these values do not depend on which other compatible measurements are performed simultaneously to the measurement. These two features are not only of foundational im- portance for quantum theory, but are also recognized as resources for quantum computing and other applications. The experimental verification of contextuality has garnered significant attention, and its recognition as an operational resource for quantum information is expected to further fuel this interest. Developing a robust theoretical framework for contextuality that is both operationally grounded and experimentally applicable is crucial. Particularly, real-world experiments often violate the non-disturbance assumption, requiring alternative frame- works that remain effective under such conditions. This dissertation builds upon a recent work by Renou et.al, which explores how dif- ferent variants of a Bell inequality, despite being equivalent under the condition of no- signaling, are not equally robust in real experiments. In order to do so, they propose a method which employs the group of symmetries of a Bell scenario to analyze and op- timize the robustness of Bell inequalities. The primary goal of this dissertation is to generalize this method to contextuality scenarios, exploring the role of group representa- tion theory in optimizing inequalities, and enhancing both theoretical understanding and experimental applicability.
The emergence of classicality is fundamentally driven by the interaction between a quantum system and its environment. Foundational open-system approaches, notably the Caldeira-Leggett model, successfully captured how these interactions lead to macroscopic effects like quantum dissipation and decoherence. However, these approaches often leave the precise definitions of classicality and quantumness ambiguous. In quantum information theory, this boundary is a heavily scrutinized question, and Kochen-Specker contextuality emerges as a hallmark of nonclassicality. It is therefore natural to investigate whether decoherence can actually suppress this property. Taking this path creates an apparent conundrum, once there exist two distinct manifestations of quantum contextuality: state-dependent and state-independent ones. While state-dependent contextuality naturally vanishes under state degradation, state-independent contextuality could persist for any quantum state, since it shows up even for the maximally mixed state! In this paper, we resolve this apparent paradox by analyzing sequential measurement implementations of the paradigmatic Klyachko, Can, Binicioğlu, and Shumovsky (KCBS) and Peres-Mermin prepare-and-measure scenarios under the influence of depolarizing channels. By introducing noise both prior to and in between measurements, and by analyzing the resulting sequential correlators in both the Schrödinger and Heisenberg pictures, we show how open-system dynamics suppress the correlations required to witness contextuality, leading to classicalization.
Contextuality provides a unifying paradigm for nonclassical aspects of quantum probabilities and resources of quantum information. Unfortunately, most forms of quantum contextuality remain experimentally unexplored due to the difficulty of performing sequences of projective measurements on individual quantum systems. Here we show that two-point correlations between binary compatible observables are sufficient to reveal any form of contextuality. This allows us to design simple experiments that are more robust against imperfections and easier to analyze, thus opening the door for observing interesting forms of contextuality, including those requiring quantum systems of high dimensions. In addition, it allows us to connect contextuality to communication complexity scenarios and reformulate a recent result relating contextuality and quantum computation.