Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Hardy-like Quantum Pigeonhole Effects and Projected-Coloring Graphs.

Weidong Tang

Published Mar 15, 2021• 0 citations
OpenAlex

Abstract

Hardy-like proofs for some quantum mechanical properties, such as Hardy-like nonlocality and Hardy-like contextuality, provide us two probabilistic no-go theorems by logical contradictions. Inspired by this, one may conjure that there are some other nonclassical properties which can also be revealed by Hardy-like arguments. In this work, we present an unconventional kind of quantum pigeonhole effects using Hardy-like arguments and show how to systematically construct them. Besides, we introduce a kind of ``projected-stabilizer state, say projected-coloring graph states, associated with a special type of coloring graphs called projected-coloring graph states. We build a one-to-one connection between a given projected-coloring graph (state) and a Hardy-like quantum pigeonhole In this sense a Hardy-like quantum pigeonhole paradox may also be referred to as a ``quantum coloring paradox.

Related papers

Hardy-like quantum pigeonhole paradox and the projected-coloring graph state

Weidong Tang

A Hardy-like version of the quantum pigeonhole paradox is proposed, which can also be considered as a special kind of Hardy's paradox. Besides an example induced from the minimal system, a general construction of this paradox from an $n$-qubit quantum state is also discussed. Moreover, by introducing the projected-coloring graph and the projected-coloring graph state, a pictorial representation of the Hardy-like quantum pigeonhole paradox can be presented. This Hardy-like version of the quantum pigeonhole paradox can be implemented more directly in experiment than the original one, since it does not require some sophisticated techniques such as weak measurements. In addition, from the angle of Hardy's paradox, some Hardy-like quantum pigeonhole paradoxes may be able to set a new record for the success probability of demonstrating Bell nonlocality.

arXiv:2103.08194•Physical Review A•Mar 31, 2022•5 citations

Experimental implementation of Hardy-like quantum pigeonhole paradoxes

Shihao Ru, Cen-Xiao Huang, Xiao‐Min Hu +7 more

The general Hardy-like quantum pigeonhole paradoxes for n-qubit states were presented by Tang [W. Tang, Phys. Rev. A 105, 032457 (2022)]. It has been shown that each of such paradoxes can be associated with an uncolorable solution of a specific vertex-coloring problem induced from the projected-coloring graph (a kind of unconventional graph). The Hardy-like quantum pigeonhole paradoxes can even give rise to a higher suc- cess probability in demonstrating the conflict between quantum mechanics and local or noncontextual realism than the previous Hardy's paradoxes. Moreover, multiqubit states and high-dimensional states can exhibit paradoxes. In contrast to only one type of contradiction presented in the original quantum pigeonhole paradox, we discussed two kinds of three-qubit projected-coloring graph states as the minimal illustration in our work. An optical experiment to verify such a stronger paradox is performed. This quantum paradox provides innovative thoughts and methods for exploring new types of stronger multiparty quantum nonlocality. It may have potential applications in untrusted multiparty communications and device-independent random number generation.

arXiv:2206.02324•Physical Review A•Feb 9, 2023•3 citations

Hardy's Paradox for Yu-Oh Set Constructed by Logically Contextual Quantum States

Chang He, Yongjun Wang, Baoshan Wang +2 more

Quantum contextuality is a fundamental nonclassical property of quantum systems, regarded as a key resource that demonstrates the computational and informational advantages of quantum over classical systems. Our present work aims to construct Hardy's paradoxes, a set of possibilistic conditions witnessing contextuality, for Yu-Oh set, which is the state-independent contextual quantum system with the least number of vectors. To achieve the aim, we systematically enumerate all logically contextual pure states on Yu-Oh set, and theoretically prove that no mixed states in this scenario are logically contextual. Based on the identified logically contextual quantum states, we construct 12 Hardy's paradoxes with identical success probability SP=11.1%. Furthermore, we present corresponding observables to experimentally witness these Hardy's paradoxes.

quant-pharXiv:2603.12738•Mar 16, 2026•0 citations

A Logical Formalism of Hardy-type Paradox

Songyi Liu, Yongjun Wang, Baoshan Wang +2 more

Hardy-type paradoxes provide elegant, inequality-free proofs of quantum contextuality. We introduce a unified logical formalism for these paradoxes, termed logical Hardy-type paradoxes. For any finite quantum scenario of ideal measurements, we prove that the existence of a logical Hardy-type paradox is equivalent to logical contextuality. Specifically, strong contextuality is equivalent to logical Hardy-type paradoxes with success probability SP = 1. These results generalize prior work on (2,k,2), (2,2,d), and n-cycle scenarios. We analyze logical Hardy-type paradoxes in the Mansfield and Klyachko-Can-Binicioglu-Shumovsky (KCBS) scenarios. In the KCBS scenario, we show that there is exactly one type of logical Hardy-type paradox, achieving SP\approx 10.56% for a specific parameter setting.

quant-pharXiv:2601.01445•Jan 6, 2026•0 citations

Quantum pigeonhole effect, Cheshire cat and contextuality

Sixia Yu, C. H. Oh

A kind of paradoxical effects has been demonstrated that the pigeonhole principle, i.e., if three pigeons are put in two pigeonholes then at least two pigeons must stay in the same hole, fails in certain quantum mechanical scenario. Here we shall show how to associate a proof of Kochen-Specker theorem with a quantum pigeonhole effect and vise versa, e.g., from state-independent proofs of Kochen-Specker theorem some kind of state-independent quantum pigeonhole effects can be demonstrated. In particular, a state-independent version of the quantum Cheshire cat, which can be rendered as a kind of quantum pigeonhole effect about the trouble of putting two pigeons in two or more pigeonholes, arises from Peres-Mermin's magic square proof of contextuality.

arXiv:1408.2477•Aug 11, 2014•6 citations

Stronger Hardy-type paradox based on the Bell inequality and its experimental test

Mu Yang, Hui-Xian Meng, Jie Zhou +7 more

Local realistic models cannot completely describe all predictions of quantum mechanics. This is known as Bell's theorem that can be revealed either by violations of Bell inequality, or all-versus-nothing proof of nonlocality. Hardy's paradox is an important all-versus-nothing proof and is considered as ``the simplest form of Bell's theorem.'' In this work, we advance the study of Hardy's paradox based on Bell's inequality. Our formalism is essentially equivalent to the ``logical Bell inequality'' formalism developed by Abramsky and Hardy, but ours is more easily applied to experimental tests. Remarkably, we find that not only for a two-qubit two-setting case but also for a two-qubit four-setting case, we can construct stronger Hardy-type paradoxes based on Bell's inequality, whose successful probabilities can attain four times and seven times larger than the original one, respectively, thus providing more friendly tests for experiment. Meanwhile, we experimentally test the stronger Hardy-type paradoxes in a two-qubit system. Within the experimental errors, the experimental results coincide with the theoretical predictions.

arXiv:1809.04289•Physical Review A•Mar 5, 2019•26 citations
Hardy-like proofs for some quantum mechanical properties, such as Hardy-like nonlocality and Hardy-like contextuality, provide us two probabilistic no-go theorems by logical contradictions. Inspired by this, one may conjure that there are some other nonclassical properties which can also be revealed by Hardy-like arguments. In this work, we present an unconventional kind of quantum pigeonhole effects using Hardy-like arguments and show how to systematically construct them. Besides, we introduce a kind of projected-stabilizer state, say projected-coloring graph states, associated with a special type of coloring graphs called projected-coloring graph states. We build a one-to-one connection between a given projected-coloring graph (state) and a Hardy-like quantum pigeonhole In this sense a Hardy-like quantum pigeonhole paradox may also be referred to as a quantum coloring paradox.
A Hardy-like version of the quantum pigeonhole paradox is proposed, which can also be considered as a special kind of Hardy's paradox. Besides an example induced from the minimal system, a general construction of this paradox from an nnn-qubit quantum state is also discussed. Moreover, by introducing the projected-coloring graph and the projected-coloring graph state, a pictorial representation of the Hardy-like quantum pigeonhole paradox can be presented. This Hardy-like version of the quantum pigeonhole paradox can be implemented more directly in experiment than the original one, since it does not require some sophisticated techniques such as weak measurements. In addition, from the angle of Hardy's paradox, some Hardy-like quantum pigeonhole paradoxes may be able to set a new record for the success probability of demonstrating Bell nonlocality.
The general Hardy-like quantum pigeonhole paradoxes for n-qubit states were presented by Tang [W. Tang, Phys. Rev. A 105, 032457 (2022)]. It has been shown that each of such paradoxes can be associated with an uncolorable solution of a specific vertex-coloring problem induced from the projected-coloring graph (a kind of unconventional graph). The Hardy-like quantum pigeonhole paradoxes can even give rise to a higher suc- cess probability in demonstrating the conflict between quantum mechanics and local or noncontextual realism than the previous Hardy's paradoxes. Moreover, multiqubit states and high-dimensional states can exhibit paradoxes. In contrast to only one type of contradiction presented in the original quantum pigeonhole paradox, we discussed two kinds of three-qubit projected-coloring graph states as the minimal illustration in our work. An optical experiment to verify such a stronger paradox is performed. This quantum paradox provides innovative thoughts and methods for exploring new types of stronger multiparty quantum nonlocality. It may have potential applications in untrusted multiparty communications and device-independent random number generation.
Quantum contextuality is a fundamental nonclassical property of quantum systems, regarded as a key resource that demonstrates the computational and informational advantages of quantum over classical systems. Our present work aims to construct Hardy's paradoxes, a set of possibilistic conditions witnessing contextuality, for Yu-Oh set, which is the state-independent contextual quantum system with the least number of vectors. To achieve the aim, we systematically enumerate all logically contextual pure states on Yu-Oh set, and theoretically prove that no mixed states in this scenario are logically contextual. Based on the identified logically contextual quantum states, we construct 12 Hardy's paradoxes with identical success probability SP=11.1%. Furthermore, we present corresponding observables to experimentally witness these Hardy's paradoxes.
Hardy-type paradoxes provide elegant, inequality-free proofs of quantum contextuality. We introduce a unified logical formalism for these paradoxes, termed logical Hardy-type paradoxes. For any finite quantum scenario of ideal measurements, we prove that the existence of a logical Hardy-type paradox is equivalent to logical contextuality. Specifically, strong contextuality is equivalent to logical Hardy-type paradoxes with success probability SP = 1. These results generalize prior work on (2,k,2), (2,2,d), and n-cycle scenarios. We analyze logical Hardy-type paradoxes in the Mansfield and Klyachko-Can-Binicioglu-Shumovsky (KCBS) scenarios. In the KCBS scenario, we show that there is exactly one type of logical Hardy-type paradox, achieving SP\approx 10.56% for a specific parameter setting.
A kind of paradoxical effects has been demonstrated that the pigeonhole principle, i.e., if three pigeons are put in two pigeonholes then at least two pigeons must stay in the same hole, fails in certain quantum mechanical scenario. Here we shall show how to associate a proof of Kochen-Specker theorem with a quantum pigeonhole effect and vise versa, e.g., from state-independent proofs of Kochen-Specker theorem some kind of state-independent quantum pigeonhole effects can be demonstrated. In particular, a state-independent version of the quantum Cheshire cat, which can be rendered as a kind of quantum pigeonhole effect about the trouble of putting two pigeons in two or more pigeonholes, arises from Peres-Mermin's magic square proof of contextuality.
Local realistic models cannot completely describe all predictions of quantum mechanics. This is known as Bell's theorem that can be revealed either by violations of Bell inequality, or all-versus-nothing proof of nonlocality. Hardy's paradox is an important all-versus-nothing proof and is considered as ``the simplest form of Bell's theorem.'' In this work, we advance the study of Hardy's paradox based on Bell's inequality. Our formalism is essentially equivalent to the ``logical Bell inequality'' formalism developed by Abramsky and Hardy, but ours is more easily applied to experimental tests. Remarkably, we find that not only for a two-qubit two-setting case but also for a two-qubit four-setting case, we can construct stronger Hardy-type paradoxes based on Bell's inequality, whose successful probabilities can attain four times and seven times larger than the original one, respectively, thus providing more friendly tests for experiment. Meanwhile, we experimentally test the stronger Hardy-type paradoxes in a two-qubit system. Within the experimental errors, the experimental results coincide with the theoretical predictions.