Kirkwood-Dirac Quasiprobability Approach To The Statistics Of Incompatible Observables

Matteo Lostaglio¹, Alessio Belenchia^2,3, Amikam Levy⁴, Santiago Hernández-Gómez^5,6,7, Nicole Fabbri^5,7, and Stefano Gherardini^8,5

¹Korteweg-de Vries Institute for Mathematics and QuSoft, University of Amsterdam, The Netherlands
²Institut für Theoretische Physik, Eberhard-Karls-Universität Tübingen, 72076 Tübingen, Germany
³Centre for Theoretical Atomic, Molecular and Optical Physics, School of Mathematics and Physics, Queen’s University Belfast, Belfast BT7 1NN, United Kingdom
⁴Department of Chemistry and Center for Quantum Entanglement Science and Technology, Bar-Ilan University, Ramat-Gan 52900, Israel
⁵European Laboratory for Non-linear Spectroscopy (LENS), Università di Firenze, I-50019 Sesto Fiorentino, Italy
⁶Dipartimento di Fisica e Astronomia, Università di Firenze, I-50019, Sesto Fiorentino, Italy
⁷Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (CNR-INO), I-50019 Sesto Fiorentino, Italy
⁸Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (CNR-INO), Area Science Park, Basovizza, I-34149 Trieste, Italy

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Abstract

Recent work has revealed the central role played by the Kirkwood-Dirac quasiprobability (KDQ) as a tool to properly account for non-classical features in the context of condensed matter physics (scrambling, dynamical phase transitions) metrology (standard and post-selected), thermodynamics (power output and fluctuation theorems), foundations (contextuality, anomalous weak values) and more. Given the growing relevance of the KDQ across the quantum sciences, our aim is two-fold: First, we highlight the role played by quasiprobabilities in characterizing the statistics of quantum observables and processes in the presence of measurement incompatibility. In this way, we show how the KDQ naturally underpins and unifies quantum correlators, quantum currents, Loschmidt echoes, and weak values. Second, we provide novel theoretical and experimental perspectives by discussing a wide variety of schemes to access the KDQ and its non-classicality features.

Popular summary

The study explores the manifold ways in which a quasiprobability introduced by Kirkwood and Dirac enters disparate physical concepts and fields. The main focus of the work is twofold: First, to show how this quasiprobability can be used to characterize the statistics of incompatible quantum observables during quantum dynamical processes and, second, to provide schemes to access the non-classicality encoded in this quasiprobability.

► BibTeX data

@article{Lostaglio2023kirkwooddirac, doi = {10.22331/q-2023-10-09-1128}, url = {https://doi.org/10.22331/q-2023-10-09-1128}, title = {Kirkwood-{D}irac quasiprobability approach to the statistics of incompatible observables}, author = {Lostaglio, Matteo and Belenchia, Alessio and Levy, Amikam and Hern{‘{a}}ndez-G{‘{o}}mez, Santiago and Fabbri, Nicole and Gherardini, Stefano}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {1128}, month = oct, year = {2023}<br /> }

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[1] Philipp Strasberg, “Classicality with(out) decoherence: Concepts, relation to Markovianity, and a random matrix theory approach”, SciPost Physics 15 1, 024 (2023).

[2] Santiago Hernández-Gómez, Stefano Gherardini, Alessio Belenchia, Matteo Lostaglio, Amikam Levy, and Nicole Fabbri, “Projective measurements can probe non-classical work extraction and time-correlations”, arXiv:2207.12960, (2022).

[3] Twesh Upadhyaya, William F. Braasch, Gabriel T. Landi, and Nicole Yunger Halpern, “What happens to entropy production when conserved quantities fail to commute with each other”, arXiv:2305.15480, (2023).

[4] Loris Maria Cangemi, Chitrak Bhadra, and Amikam Levy, “Quantum Engines and Refrigerators”, arXiv:2302.00726, (2023).

[5] Ilaria Gianani, Alessio Belenchia, Stefano Gherardini, Vincenzo Berardi, Marco Barbieri, and Mauro Paternostro, “Diagnostics of quantum-gate coherences deteriorated by unitary errors via end-point-measurement statistics”, Quantum Science and Technology 8 4, 045018 (2023).

[6] Alessandro Santini, Andrea Solfanelli, Stefano Gherardini, and Mario Collura, “Work statistics, quantum signatures, and enhanced work extraction in quadratic fermionic models”, Physical Review B 108 10, 104308 (2023).

[7] Rafael Wagner, Zohar Schwartzman-Nowik, Ismael L. Paiva, Amit Te’eni, Antonio Ruiz-Molero, Rui Soares Barbosa, Eliahu Cohen, and Ernesto F. Galvão, “Quantum circuits measuring weak values, Kirkwood–Dirac quasiprobability distributions, and state spectra”, arXiv:2302.00705, (2023).

[8] M. S. Leifer, “Uncertainty from the Aharonov-Vaidman Identity”, arXiv:2301.08679, (2023).

[9] Agung Budiyono and Hermawan K. Dipojono, “Quantifying quantum coherence via Kirkwood-Dirac quasiprobability”, Physical Review A 107 2, 022408 (2023).

[10] Santiago Hernández-Gómez, Stefano Gherardini, Alessio Belenchia, Andrea Trombettoni, Mauro Paternostro, and Nicole Fabbri, “Experimental signature of initial quantum coherence on entropy production”, npj Quantum Information 9, 86 (2023).

[11] Agung Budiyono, “Operational interpretation and estimation of quantum trace-norm asymmetry based on weak-value measurement and some bounds”, Physical Review A 108 1, 012431 (2023).

[12] Agung Budiyono, Mohammad K. Agusta, Bagus E. B. Nurhandoko, and Hermawan K. Dipojono, “Quantum coherence as asymmetry from complex weak values”, Journal of Physics A Mathematical General 56 23, 235304 (2023).

[13] Pengfei Wang, Hyukjoon Kwon, Chun-Yang Luan, Wentao Chen, Mu Qiao, Zinan Zhou, Kaizhao Wang, M. S. Kim, and Kihwan Kim, “Demonstration of multi-time quantum statistics without measurement back-action”, arXiv:2207.06106, (2022).

[14] Jianwei Xu, “Kirkwood-Dirac classical pure states”, arXiv:2210.02876, (2022).

[15] Gianluca Francica, “Most general class of quasiprobability distributions of work”, Physical Review E 106 5, 054129 (2022).

[16] Rafael Wagner and Ernesto F. Galvão, “Anomalous weak values require coherence”, arXiv:2303.08700, (2023).

[17] Gianluca Francica, “What is the most general class of quasiprobabilities of work?”, arXiv:2209.02527, (2022).

[18] Agung Budiyono, Joel F. Sumbowo, Mohammad K. Agusta, and Bagus E. B. Nurhandoko, “Characterizing quantum coherence based on the nonclassicality of the Kirkwood-Dirac quasiprobability”, arXiv:2309.09162, (2023).

[19] Ji-Hui Pei, Jin-Fu Chen, and H. T. Quan, “Exploring quasiprobability approach to quantum work in the presence of initial coherence: Advantages of the Margenau-Hill distribution”, arXiv:2306.10917, (2023).

The above citations are from SAO/NASA ADS (last updated successfully 2023-10-10 01:25:21). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2023-10-10 01:25:19).

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

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Kirkwood-Dirac quasiprobability approach to the statistics of incompatible observables

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Kirkwood-Dirac quasiprobability approach to the statistics of incompatible observables

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