Quantum Mechanics and Symmetry/Asymmetry: Review Paper on Quantum Nonlinear Interferometers

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (31 July 2023) | Viewed by 5483

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Department of Physics, Faculty of Science, Paderborn University, Warburger Strasse 100, 33098 Paderborn, Germany
Interests: laser; atomic physics; quantum mechanics; quantum optics; quantum entanglement; nonlinear optics

Special Issue Information

Dear Colleagues,

In metrology, nonlinear interferometers present a versatile technique for sensitive phase measurements and form the basis for detecting gravitational waves. Such interferometers contain nonlinear elements (parametric down-conversion, four-wave mixing) instead of conventional beam splitters, and have many advantages over their linear counterparts in terms of measurement accuracy, state engineering and loss resistance. Nonlinear interferometers can be realized in different geometries and produce quantum light with various spectral and spatial profiles, mode structure and orbital angular momenta. At the same time, due to strong correlations between signal and idler photons generated within such interferometers, they are promissing tools for testing the symmetry of objects, their chirality, and can be used in many quantum applications, from quantum imaging to quantum communication and quantum cryptography.

This Special Issue, “Quantum nonlinear interferometers”, will feature articles with a broad scope of research on the properties of nonlinear interferometers and their applications in metrology and other branches of science.

Dr. Polina Sharapova
Guest Editor

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Keywords

  • quantum optics
  • metrology
  • nonlinear interferometers
  • quantum imaging
  • state engineering
  • parametric down-conversion
  • four-wave-mixing
  • entanglement
  • orbital angular momentum
  • chirality

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Published Papers (3 papers)

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Research

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18 pages, 524 KiB  
Article
A Symmetric Extensible Protocol for Quantum Secret Sharing
by Michael Ampatzis and Theodore Andronikos
Symmetry 2022, 14(8), 1692; https://doi.org/10.3390/sym14081692 - 15 Aug 2022
Cited by 9 | Viewed by 1601
Abstract
This paper introduces the Symmetric Extensible Quantum Secret Sharing protocol, a novel quantum protocol for secret sharing. At its heart, it is an entanglement-based protocol that relies on the use of maximally entangled GHZ tuples, evenly distributed among the players, endowing the spymaster [...] Read more.
This paper introduces the Symmetric Extensible Quantum Secret Sharing protocol, a novel quantum protocol for secret sharing. At its heart, it is an entanglement-based protocol that relies on the use of maximally entangled GHZ tuples, evenly distributed among the players, endowing the spymaster with the ability to securely share a secret message with the agents. Its security stems from the fact that it is highly improbable for a malicious eavesdropper or a rogue double agent to disrupt its successful execution. It is characterized by symmetry, since all agents are treated indiscriminately, utilizing identical quantum circuits. Furthermore, it can be seamlessly extended to an arbitrary number of agents. Finally, after the completion of the quantum part of the protocol, the spymaster will have to publicly transmit some information, in order to allow the agents to unlock the secret message. This part of the protocol can be considered as an additional advantage, due to the fact that it gives the spymaster the privilege of deciding if, or when, it is the right time for the agents to unlock the secret message, after the completion of the quantum part of the protocol. Full article
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Review

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26 pages, 534 KiB  
Review
Sensitivity of Quantum-Enhanced Interferometers
by Dariya Salykina and Farid Khalili
Symmetry 2023, 15(3), 774; https://doi.org/10.3390/sym15030774 - 22 Mar 2023
Cited by 3 | Viewed by 2059
Abstract
We review various schemes of quantum-enhanced optical interferometers, both linear (SU(2)) and non-linear (SU(1,1)) ones, as well as hybrid SU(2)/SU(1,1) options, using the unified modular approach based on the Quantum Cramèr–Rao bound (QCRB), and taking into account the practical limitations pertinent to all [...] Read more.
We review various schemes of quantum-enhanced optical interferometers, both linear (SU(2)) and non-linear (SU(1,1)) ones, as well as hybrid SU(2)/SU(1,1) options, using the unified modular approach based on the Quantum Cramèr–Rao bound (QCRB), and taking into account the practical limitations pertinent to all real-world highly-sensitive interferometers. We focus on three important cases defined by the interferometer symmetry: (i) the asymmetric single-arm interferometer; (ii) the symmetric two-arm interferometer with the antisymmetric phase shifts in the arms; and (iii) the symmetric two-arm interferometer with the symmetric phase shifts in the arms. We show that while the optimal regimes for these cases differ significantly, their QCRBs asymptotically correspond to the same squeezing-enhanced shot noise limit (2), which first appeared in the pioneering work by C. Caves in 1981.We show also that in all considered cases the QCRB can be asymptotically saturated by the standard (direct or homodyne) detection schemes. Full article
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26 pages, 9142 KiB  
Review
Phase Sensitivity Improvement in Correlation-Enhanced Nonlinear Interferometers
by Xinyun Liang, Zhifei Yu, Chun-Hua Yuan, Weiping Zhang and Liqing Chen
Symmetry 2022, 14(12), 2684; https://doi.org/10.3390/sym14122684 - 19 Dec 2022
Cited by 5 | Viewed by 2608
Abstract
Interferometers are widely used as sensors in precision measurement. Compared with a conventional Mach–Zehnder interferometer, the sensitivity of a correlation-enhanced nonlinear interferometer can break the standard quantum limit. Phase sensitivity plays a significant role in the enhanced performance. In this paper, we review [...] Read more.
Interferometers are widely used as sensors in precision measurement. Compared with a conventional Mach–Zehnder interferometer, the sensitivity of a correlation-enhanced nonlinear interferometer can break the standard quantum limit. Phase sensitivity plays a significant role in the enhanced performance. In this paper, we review improvement in phase estimation technologies in correlation-enhanced nonlinear interferometers, including SU(1,1) interferometer and SU(1,1)-SU(2) hybrid interferometer, and so on, and the applications in quantum metrology and quantum sensing networks. Full article
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