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Kuroiwa K, Takagi R, Adesso G, Yamasaki H. Every Quantum Helps: Operational Advantage of Quantum Resources beyond Convexity. PHYSICAL REVIEW LETTERS 2024; 132:150201. [PMID: 38682983 DOI: 10.1103/physrevlett.132.150201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2023] [Accepted: 02/05/2024] [Indexed: 05/01/2024]
Abstract
Identifying what quantum-mechanical properties are useful to untap a superior performance in quantum technologies is a pivotal question. Quantum resource theories provide a unified framework to analyze and understand such properties, as successfully demonstrated for entanglement and coherence. While these are examples of convex resources, for which quantum advantages can always be identified, many physical resources are described by a nonconvex set of free states and their interpretation has so far remained elusive. Here we address the fundamental question of the usefulness of quantum resources without convexity assumption, by providing two operational interpretations of the generalized robustness measure in general resource theories. First, we characterize the generalized robustness in terms of a nonlinear resource witness and reveal that any state is more advantageous than a free one in some multicopy channel discrimination task. Next, we consider a scenario where a theory is characterized by multiple constraints and show that the generalized robustness coincides with the worst-case advantage in a single-copy channel discrimination setting. Based on these characterizations, we conclude that every quantum resource state shows a qualitative and quantitative advantage in discrimination problems in a general resource theory even without any specification on the structure of the free states.
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Affiliation(s)
- Kohdai Kuroiwa
- Institute for Quantum Computing and Department of Combinatorics and Optimization, University of Waterloo, Ontario N2L 3G1, Canada
- Perimeter Institute for Theoretical Physics, Ontario N2L 2Y5, Canada
| | - Ryuji Takagi
- Department of Basic Science, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
| | - Gerardo Adesso
- School of Mathematical Sciences and Centre for the Mathematical and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Hayata Yamasaki
- Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
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Giordani T, Wagner R, Esposito C, Camillini A, Hoch F, Carvacho G, Pentangelo C, Ceccarelli F, Piacentini S, Crespi A, Spagnolo N, Osellame R, Galvão EF, Sciarrino F. Experimental certification of contextuality, coherence, and dimension in a programmable universal photonic processor. SCIENCE ADVANCES 2023; 9:eadj4249. [PMID: 37922346 PMCID: PMC10624346 DOI: 10.1126/sciadv.adj4249] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2023] [Accepted: 10/02/2023] [Indexed: 11/05/2023]
Abstract
Quantum superposition of high-dimensional states enables both computational speed-up and security in cryptographic protocols. However, the exponential complexity of tomographic processes makes certification of these properties a challenging task. In this work, we experimentally certify coherence witnesses tailored for quantum systems of increasing dimension using pairwise overlap measurements enabled by a six-mode universal photonic processor fabricated with a femtosecond laser writing technology. In particular, we show the effectiveness of the proposed coherence and dimension witnesses for qudits of dimensions up to 5. We also demonstrate advantage in a quantum interrogation task and show it is fueled by quantum contextuality. Our experimental results testify to the efficiency of this approach for the certification of quantum properties in programmable integrated photonic platforms.
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Affiliation(s)
- Taira Giordani
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Roma, Italy
| | - Rafael Wagner
- International Iberian Nanotechnology Laboratory (INL), Av. Mestre José Veiga s/n, 4715-330 Braga, Portugal
- Centro de Física, Universidade do Minho, Campus de Gualtar, 4710-057 Braga, Portugal
| | - Chiara Esposito
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Roma, Italy
| | - Anita Camillini
- International Iberian Nanotechnology Laboratory (INL), Av. Mestre José Veiga s/n, 4715-330 Braga, Portugal
- Centro de Física, Universidade do Minho, Campus de Gualtar, 4710-057 Braga, Portugal
| | - Francesco Hoch
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Roma, Italy
| | - Gonzalo Carvacho
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Roma, Italy
| | - Ciro Pentangelo
- Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci, 32, I-20133 Milano, Italy
- Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche (IFN-CNR), Piazza Leonardo da Vinci, 32, I-20133 Milano, Italy
| | - Francesco Ceccarelli
- Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche (IFN-CNR), Piazza Leonardo da Vinci, 32, I-20133 Milano, Italy
| | - Simone Piacentini
- Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche (IFN-CNR), Piazza Leonardo da Vinci, 32, I-20133 Milano, Italy
| | - Andrea Crespi
- Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci, 32, I-20133 Milano, Italy
- Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche (IFN-CNR), Piazza Leonardo da Vinci, 32, I-20133 Milano, Italy
| | - Nicolò Spagnolo
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Roma, Italy
| | - Roberto Osellame
- Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche (IFN-CNR), Piazza Leonardo da Vinci, 32, I-20133 Milano, Italy
| | - Ernesto F. Galvão
- International Iberian Nanotechnology Laboratory (INL), Av. Mestre José Veiga s/n, 4715-330 Braga, Portugal
- Instituto de Física, Universidade Federal Fluminense, Av. Gal. Milton Tavares de Souza s/n, Niterói, RJ, 24210-340, Brazil
| | - Fabio Sciarrino
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Roma, Italy
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Wang P, Guo Z, Cao H. Quantum Incoherence Based Simultaneously on k Bases. ENTROPY 2022; 24:e24050659. [PMID: 35626544 PMCID: PMC9141266 DOI: 10.3390/e24050659] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/29/2022] [Revised: 05/06/2022] [Accepted: 05/06/2022] [Indexed: 02/01/2023]
Abstract
Quantum coherence is known as an important resource in many quantum information tasks, which is a basis-dependent property of quantum states. In this paper, we discuss quantum incoherence based simultaneously on k bases using Matrix Theory Method. First, by defining a correlation function m(e,f) of two orthonormal bases e and f, we investigate the relationships between sets I(e) and I(f) of incoherent states with respect to e and f. We prove that I(e)=I(f) if and only if the rank-one projective measurements generated by e and f are identical. We give a necessary and sufficient condition for the intersection I(e)⋂I(f) to include a state except the maximally mixed state. Especially, if two bases e and f are mutually unbiased, then the intersection has only the maximally mixed state. Secondly, we introduce the concepts of strong incoherence and weak coherence of a quantum state with respect to a set B of k bases and propose a measure for the weak coherence. In the two-qubit system, we prove that there exists a maximally coherent state with respect to B when k=2 and it is not the case for k=3.
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