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

arXiv:1012.3660 · Physical Review A

Hybrid methods for witnessing entanglement in a microscopic-macroscopic system

Nicolò Spagnolo, Chiara Vitelli, Mauro Paternostro, F. De Martini, Fabio Sciarrino

Published Sep 2, 2011• 29 citations
arXivHTMLPDF

Abstract

We propose a hybrid approach to the experimental assessment of the genuine quantum features of a general system consisting of microscopic and macroscopic parts. We infer entanglement by combining dichotomic measurements on a bidimensional system and phase-space inference through the Wigner distribution associated with the macroscopic component of the state. As a benchmark, we investigate the feasibility of our proposal in a bipartite-entangled state composed of a single-photon and a multiphoton field. Our analysis shows that, under ideal conditions, maximal violation of a Clauser-Horne-Shimony-Holt-based inequality is achievable regardless of the number of photons in the macroscopic part of the state. The difficulty in observing entanglement when losses and detection inefficiency are included can be overcome by using a hybrid entanglement witness that allows efficient correction for losses in the few-photon regime.

DOI
10.1103/physreva.84.032102

Related papers

Hybrid non-locality test in a microscopic-macroscopic system

Nicolò Spagnolo, Chiara Vitelli, Mauro Paternostro +2 more

We investigate the feasibility of a non-locality test in a bipartite system composed of a single-photon and a multi-photon field that embodies the paradigm of a microscopic-macroscopic entangled state. We run an intrinsically hybrid test requiring polarization measurements on the microscopic part of the state and phase-space ones on the macroscopic counterpart. Our analysis shows that, under ideal conditions, maximal violation of a Bell-CHSH inequality is achievable regardless of the number of photons in the macroscopic part of the state. The difficulty in observing non-locality when losses and detection inefficiency are included can be overcome using a hybrid entanglement witness that allows to efficiently correct for losses in the few photon regime.

•Dec 16, 2010•2 citations

Witnessing Entanglement

Marisol N. Beck, M. Beck

An entangled state of a two-particle system is a quantum state that cannot be separated-it cannot be written as the product of states of the individual particles.One way to tell if a system is entangled is to use it to violate a Bell inequality (such as the Clauser-Horne-Shimony-Holt, CHSH, inequality), because entanglement is necessary to violate these inequalities.However, there are other, more efficient measurements that determine whether or not a system is entangled; an operator that corresponds to such a measurement is referred to as an entanglement witness.We present the theory of witness operators, and an undergraduate experiment that measures an entanglement witness for the joint polarization state of two photons.We are able to produce states for which the expectation value of the witness operator is entangled by more than 160 standard deviations.

Conference on Laboratory Instruction Beyond the First Year (BFY)•Nov 17, 2015•0 citations

CHSH Bell tests for optical hybrid entanglement

Morteza Moradi, Juan Camilo López Carreño, Adam Buraczewski +4 more

Abstract Optical hybrid entanglement can be created between two qubits, one encoded in a single photon and another one in coherent states with opposite phases. It opens the path to a variety of quantum technologies, such as heterogeneous quantum networks, merging continuous- and discrete-variable encoding, and enabling the transport and interconversion of information. However, reliable characterization of the non-local nature of this quantum state is limited so far to full quantum state tomography. Here, we perform a thorough study of Clauser–Horne–Shimony–Holt Bell inequality tests, enabling practical verification of quantum nonlocality for optical hybrid entanglement. We show that a practical violation of this inequality is possible with simple photon number on/off measurements if detection efficiencies stay above 82%. Another approach, based on photon-number parity measurements, requires 94% efficiency but works well in the limit of higher photon populations. Both tests use no postselection of the measurement outcomes and they are free of the fair-sampling hypothesis. Our proposal paves the way to performing loophole-free tests using feasible experimental tasks such as coherent state interference and photon counting.

arXiv:2406.04736•New Journal of Physics•Feb 26, 2024•5 citations

Witnessing entanglement in an undergraduate laboratory

Marisol N. Beck, M. Beck

An entangled state of a two-particle system is a quantum state that cannot be separated, meaning it cannot be written as the product of states of the individual particles. One way to tell if a system is entangled is to use it to violate a Bell inequality (such as the Clauser-Horne-Shimony-Holt, CHSH, inequality), because entanglement is necessary for such a violation. However, there are other, easier-to-perform measurements that determine whether or not a system is entangled. An operator that corresponds to such a measurement is referred to as an entanglement witness. Here, we present the theory of witness operators and an undergraduate experiment that measures entanglement witnesses for the joint polarization state of two photons. We are able to produce states for which the expectation value of a witness operator is entangled by more than 300 standard deviations. In order to further examine the performance of these witness operators, we present a simple way to generate states that closely approximate Werner states, which have a controllable degree of entanglement.

American Journal of Physics•Jan 21, 2016•13 citations

Experimental amplification of an entangled photon: what if the detection loophole is ignored?

Enrico Pomarico, Bruno Sanguinetti, Pavel Sekatski +2 more

The experimental verification of quantum features, such as entanglement, at large scales is extremely challenging because of environment-induced decoherence. Indeed, measurement techniques for demonstrating the quantumness of multiparticle systems in the presence of losses are difficult to define, and if they are not sufficiently accurate they can provide wrong conclusions. We present a Bell test where one photon of an entangled pair is amplified and then detected by threshold detectors, whose signals undergo postselection. The amplification is performed by a classical machine, which produces a fully separable micro–macro state. However, by adopting such a technique one can surprisingly observe a violation of the Clauser–Horne–Shimony–Holt inequality. This is due to the fact that ignoring the detection loophole opened by the postselection and the system losses can lead to misinterpretations, such as claiming micro–macro entanglement in a setup where evidently it is not present. By using threshold detectors and postselection, one can only infer the entanglement of the initial pair of photons, and so micro–micro entanglement, as is further confirmed by the violation of a nonseparability criterion for bipartite systems. How to detect photonic micro–macro entanglement in the presence of losses with the currently available technology remains an open question.

arXiv:1104.2212•New Journal of Physics•Jun 17, 2011•36 citations

Single-photon quantum nonlocality: Violation of the Clauser-Horne-Shimony-Holt inequality using feasible measurement setups

Su‐Yong Lee, Jiyong Park, Jaewan Kim +1 more

We investigate quantum nonlocality of a single-photon entangled state under feasible measurement techniques consisting of on-off and homodyne detections along with unitary operations of displacement and squeezing. We test for a potential violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality, in which each of the bipartite party has a freedom to choose between two measurement settings, with each measurement yielding a binary outcome. We find that single-photon quantum nonlocality can be detected when two or less of the four total measurements are carried out by homodyne detection. The largest violation of the CHSH inequality is obtained when all four measurements are squeezed-and-displaced on-off detections. We test the robustness of violations against imperfections in on-off detectors and single-photon sources, finding that the squeezed-and-displaced measurement schemes perform better than the displacement-only measurement schemes.

arXiv:1612.02920•Physical Review A•Jan 26, 2017•11 citations
We propose a hybrid approach to the experimental assessment of the genuine quantum features of a general system consisting of microscopic and macroscopic parts. We infer entanglement by combining dichotomic measurements on a bidimensional system and phase-space inference through the Wigner distribution associated with the macroscopic component of the state. As a benchmark, we investigate the feasibility of our proposal in a bipartite-entangled state composed of a single-photon and a multiphoton field. Our analysis shows that, under ideal conditions, maximal violation of a Clauser-Horne-Shimony-Holt-based inequality is achievable regardless of the number of photons in the macroscopic part of the state. The difficulty in observing entanglement when losses and detection inefficiency are included can be overcome by using a hybrid entanglement witness that allows efficient correction for losses in the few-photon regime.
We investigate the feasibility of a non-locality test in a bipartite system composed of a single-photon and a multi-photon field that embodies the paradigm of a microscopic-macroscopic entangled state. We run an intrinsically hybrid test requiring polarization measurements on the microscopic part of the state and phase-space ones on the macroscopic counterpart. Our analysis shows that, under ideal conditions, maximal violation of a Bell-CHSH inequality is achievable regardless of the number of photons in the macroscopic part of the state. The difficulty in observing non-locality when losses and detection inefficiency are included can be overcome using a hybrid entanglement witness that allows to efficiently correct for losses in the few photon regime.
An entangled state of a two-particle system is a quantum state that cannot be separated-it cannot be written as the product of states of the individual particles.One way to tell if a system is entangled is to use it to violate a Bell inequality (such as the Clauser-Horne-Shimony-Holt, CHSH, inequality), because entanglement is necessary to violate these inequalities.However, there are other, more efficient measurements that determine whether or not a system is entangled; an operator that corresponds to such a measurement is referred to as an entanglement witness.We present the theory of witness operators, and an undergraduate experiment that measures an entanglement witness for the joint polarization state of two photons.We are able to produce states for which the expectation value of the witness operator is entangled by more than 160 standard deviations.
Abstract Optical hybrid entanglement can be created between two qubits, one encoded in a single photon and another one in coherent states with opposite phases. It opens the path to a variety of quantum technologies, such as heterogeneous quantum networks, merging continuous- and discrete-variable encoding, and enabling the transport and interconversion of information. However, reliable characterization of the non-local nature of this quantum state is limited so far to full quantum state tomography. Here, we perform a thorough study of Clauser–Horne–Shimony–Holt Bell inequality tests, enabling practical verification of quantum nonlocality for optical hybrid entanglement. We show that a practical violation of this inequality is possible with simple photon number on/off measurements if detection efficiencies stay above 82%. Another approach, based on photon-number parity measurements, requires 94% efficiency but works well in the limit of higher photon populations. Both tests use no postselection of the measurement outcomes and they are free of the fair-sampling hypothesis. Our proposal paves the way to performing loophole-free tests using feasible experimental tasks such as coherent state interference and photon counting.
An entangled state of a two-particle system is a quantum state that cannot be separated, meaning it cannot be written as the product of states of the individual particles. One way to tell if a system is entangled is to use it to violate a Bell inequality (such as the Clauser-Horne-Shimony-Holt, CHSH, inequality), because entanglement is necessary for such a violation. However, there are other, easier-to-perform measurements that determine whether or not a system is entangled. An operator that corresponds to such a measurement is referred to as an entanglement witness. Here, we present the theory of witness operators and an undergraduate experiment that measures entanglement witnesses for the joint polarization state of two photons. We are able to produce states for which the expectation value of a witness operator is entangled by more than 300 standard deviations. In order to further examine the performance of these witness operators, we present a simple way to generate states that closely approximate Werner states, which have a controllable degree of entanglement.
The experimental verification of quantum features, such as entanglement, at large scales is extremely challenging because of environment-induced decoherence. Indeed, measurement techniques for demonstrating the quantumness of multiparticle systems in the presence of losses are difficult to define, and if they are not sufficiently accurate they can provide wrong conclusions. We present a Bell test where one photon of an entangled pair is amplified and then detected by threshold detectors, whose signals undergo postselection. The amplification is performed by a classical machine, which produces a fully separable micro–macro state. However, by adopting such a technique one can surprisingly observe a violation of the Clauser–Horne–Shimony–Holt inequality. This is due to the fact that ignoring the detection loophole opened by the postselection and the system losses can lead to misinterpretations, such as claiming micro–macro entanglement in a setup where evidently it is not present. By using threshold detectors and postselection, one can only infer the entanglement of the initial pair of photons, and so micro–micro entanglement, as is further confirmed by the violation of a nonseparability criterion for bipartite systems. How to detect photonic micro–macro entanglement in the presence of losses with the currently available technology remains an open question.
We investigate quantum nonlocality of a single-photon entangled state under feasible measurement techniques consisting of on-off and homodyne detections along with unitary operations of displacement and squeezing. We test for a potential violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality, in which each of the bipartite party has a freedom to choose between two measurement settings, with each measurement yielding a binary outcome. We find that single-photon quantum nonlocality can be detected when two or less of the four total measurements are carried out by homodyne detection. The largest violation of the CHSH inequality is obtained when all four measurements are squeezed-and-displaced on-off detections. We test the robustness of violations against imperfections in on-off detectors and single-photon sources, finding that the squeezed-and-displaced measurement schemes perform better than the displacement-only measurement schemes.