© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:2408.03398 · Proceedings of the National Academy of Sciences

Variable-strength nonlocal measurements reveal quantum violations of classical counting principles

Noah Lupu-Gladstein, Ou Teen Arthur Pang, Hugo Ferretti, Weng-Kian Tham, Aephraim M. Steinberg, Kent Bonsma-Fisher, Aharon Brodutch

Published Feb 14, 2025• 0 citations

Abstract

We implement a variant of the quantum pigeonhole paradox thought experiment to study whether classical counting principles survive in the quantum domain. We observe strong measurements significantly violate the pigeonhole principle (that among three pigeons in two holes, at least one pair must be in the same hole) and the sum rule (that the number of pigeon pairs in the same hole is the sum of the number of pairs across each of the holes) in an ensemble that is pre- and postselected into particular separable states. To investigate whether measurement disturbance is a viable explanation for these counterintuitive phenomena, we employ a we employ variable-strength nonlocal measurements. As we decrease the measurement strength, we find the violation of the sum rule decreases, yet the pigeonhole principle remains violated. In the weak limit, the sum rule is restored due to the cancellation between two weak values with equal and opposite imaginary parts. We observe the same kind of cancellation at higher measurement strengths, thus raising the question: do strong measurements have imaginary parts?

DOI: 10.1073/pnas.2416331122

Related papers

Quantum violation of the pigeonhole principle and the nature of quantum correlations

Yakir Aharonov, Fabrizio Colombo, Sandu Popescu +3 more

The pigeonhole principle: "If you put three pigeons in two pigeonholes, at least two of the pigeons end up in the same hole," is an obvious yet fundamental principle of nature as it captures the very essence of counting. Here however we show that in quantum mechanics this is not true! We find instances when three quantum particles are put in two boxes, yet no two particles are in the same box. Furthermore, we show that the above "quantum pigeonhole principle" is only one of a host of related quantum effects, and points to a very interesting structure of quantum mechanics that was hitherto unnoticed. Our results shed new light on the very notions of separability and correlations in quantum mechanics and on the nature of interactions. It also presents a new role for entanglement, complementary to the usual one. Finally, interferometric experiments that illustrate our effects are proposed.

Proceedings of the National Academy of Sciences•Jan 4, 2016•76 citations

Experimental demonstration of quantum pigeonhole paradox

Ming-Cheng Chen, Chang Liu, Yi-Han Luo +7 more

We experimentally demonstrate that when three single photons transmit through two polarization channels, in a well-defined pre- and postselected ensemble, there are no two photons in the same polarization channel by weak-strength measurement, a counterintuitive quantum counting effect called the quantum pigeonhole paradox. We further show that this effect breaks down in second-order measurement. These results indicate the existence of the quantum pigeonhole paradox and its operating regime.

arXiv:2103.15070•Proceedings of the National Academy of Sciences•Jan 11, 2019•20 citations

Quantum Measurements are Disturbing: Experiments studying the role of disturbance in postselected metrology, quantum pigeonholes, and entangled sheep

Noah Lupu-Gladstein

This thesis details two experiments and one theoretical manuscript that explore the nature of measurement disturbance in quantum mechanics. The first experiment exploits measurement disturbance to enhance measurement precision by two orders of magnitude, and in principle even more. The second experiment investigates a paradox where three quantum pigeons seem to occupy two pigeonholes without any pair belonging to the same hole. It finds that measurement disturbance accounts for some, but not all of the counter-intuitive phenomena at play in the paradox. The final manuscript develops a new theoretical framework for studying quantum measurement and disturbance from the viewpoint of quantum agents. Our framework reveals how agents endowed with quantum memories might view measurement not as a stochastic collapse, but as a continuous flow of quantum information.

•Nov 1, 2024•0 citations

Non-Local Parity Measurements and the Quantum Pigeonhole Effect

Gheorghe Sorin Paraoanu

The pigeonhole principle upholds the idea that by ascribing to three different particles either one of two properties, we necessarily end up in a situation when at least two of the particles have the same property. In quantum physics, this principle is violated in experiments involving postselection of the particles in appropriately-chosen states. Here, we give two explicit constructions using standard gates and measurements that illustrate this fact. Intriguingly, the procedures described are manifestly non-local, which demonstrates that the correlations needed to observe the violation of this principle can be created without direct interactions between particles.

arXiv:1902.05854•Entropy•Aug 16, 2018•8 citations

Linear optics for direct observation of quantum violation of pigeonhole principle by joint weak measurement

Kazuhiro Yokota, Nobuyuki Imoto

When three pigeons are in two pigeonholes, at least two of them should be in the same pigeonhole, which is called pigeonhole principle. Recently Aharonov el al have shown that the principle can be violated in a pre-postselected quantum system. This violation sheds light on a new aspect of quantum correlations, as both of the pre and postselected states are separable states. To prove this kind of quantum correlations, a measurement apparatus must be arranged in entanglement to perform a joint measurement on the quantum system. In this paper we discuss how to design the state of entangled meters to achieve such a measurement. We also propose an experimental setup composed of linear optics for direct observation of violation of pigeonhole principle.

arXiv:1812.04887•Dec 12, 2018•2 citations

Statistical Mechanics for Weak Measurements and Quantum Inseparability

Salwa Al Saleh

In weak measurement thought experiment, an ensemble consists of M quantum particles and N states. We observe that separability of the particles is lost, and hence we have fuzzy occupation numbers for the particles in the ensemble. Without sharply measuring each particle state, quantum interferences add extra possible configurations of the ensemble, this explains the Quantum Pigeonhole Principle. This principle adds more entropy to the system; hence the particles seem to have a new kind of correlations emergent from particles not having a single, well-defined state. We formulated the Quantum Pigeonhole Principle in the language of abstract Hilbert spaces, then generalized it to systems consisting of mixed states. This insight into the fundamentals of quantum statistical mechanics could help us understand the interpretation of quantum mechanics more deeply, and possibly have implication on quantum computing and information theory.

Journal of Quantum Information Science•Jan 1, 2016•2 citations

We implement a variant of the quantum pigeonhole paradox thought experiment to study whether classical counting principles survive in the quantum domain. We observe strong measurements significantly violate the pigeonhole principle (that among three pigeons in two holes, at least one pair must be in the same hole) and the sum rule (that the number of pigeon pairs in the same hole is the sum of the number of pairs across each of the holes) in an ensemble that is pre- and postselected into particular separable states. To investigate whether measurement disturbance is a viable explanation for these counterintuitive phenomena, we employ a we employ variable-strength nonlocal measurements. As we decrease the measurement strength, we find the violation of the sum rule decreases, yet the pigeonhole principle remains violated. In the weak limit, the sum rule is restored due to the cancellation between two weak values with equal and opposite imaginary parts. We observe the same kind of cancellation at higher measurement strengths, thus raising the question: do strong measurements have imaginary parts?

The pigeonhole principle: "If you put three pigeons in two pigeonholes, at least two of the pigeons end up in the same hole," is an obvious yet fundamental principle of nature as it captures the very essence of counting. Here however we show that in quantum mechanics this is not true! We find instances when three quantum particles are put in two boxes, yet no two particles are in the same box. Furthermore, we show that the above "quantum pigeonhole principle" is only one of a host of related quantum effects, and points to a very interesting structure of quantum mechanics that was hitherto unnoticed. Our results shed new light on the very notions of separability and correlations in quantum mechanics and on the nature of interactions. It also presents a new role for entanglement, complementary to the usual one. Finally, interferometric experiments that illustrate our effects are proposed.

This thesis details two experiments and one theoretical manuscript that explore the nature of measurement disturbance in quantum mechanics. The first experiment exploits measurement disturbance to enhance measurement precision by two orders of magnitude, and in principle even more. The second experiment investigates a paradox where three quantum pigeons seem to occupy two pigeonholes without any pair belonging to the same hole. It finds that measurement disturbance accounts for some, but not all of the counter-intuitive phenomena at play in the paradox. The final manuscript develops a new theoretical framework for studying quantum measurement and disturbance from the viewpoint of quantum agents. Our framework reveals how agents endowed with quantum memories might view measurement not as a stochastic collapse, but as a continuous flow of quantum information.

The pigeonhole principle upholds the idea that by ascribing to three different particles either one of two properties, we necessarily end up in a situation when at least two of the particles have the same property. In quantum physics, this principle is violated in experiments involving postselection of the particles in appropriately-chosen states. Here, we give two explicit constructions using standard gates and measurements that illustrate this fact. Intriguingly, the procedures described are manifestly non-local, which demonstrates that the correlations needed to observe the violation of this principle can be created without direct interactions between particles.

When three pigeons are in two pigeonholes, at least two of them should be in the same pigeonhole, which is called pigeonhole principle. Recently Aharonov el al have shown that the principle can be violated in a pre-postselected quantum system. This violation sheds light on a new aspect of quantum correlations, as both of the pre and postselected states are separable states. To prove this kind of quantum correlations, a measurement apparatus must be arranged in entanglement to perform a joint measurement on the quantum system. In this paper we discuss how to design the state of entangled meters to achieve such a measurement. We also propose an experimental setup composed of linear optics for direct observation of violation of pigeonhole principle.

In weak measurement thought experiment, an ensemble consists of M quantum particles and N states. We observe that separability of the particles is lost, and hence we have fuzzy occupation numbers for the particles in the ensemble. Without sharply measuring each particle state, quantum interferences add extra possible configurations of the ensemble, this explains the Quantum Pigeonhole Principle. This principle adds more entropy to the system; hence the particles seem to have a new kind of correlations emergent from particles not having a single, well-defined state. We formulated the Quantum Pigeonhole Principle in the language of abstract Hilbert spaces, then generalized it to systems consisting of mixed states. This insight into the fundamentals of quantum statistical mechanics could help us understand the interpretation of quantum mechanics more deeply, and possibly have implication on quantum computing and information theory.