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Certifying the Dimension of Classical and Quantum Systems in a Prepare-and-Measure Scenario with Independent Devices
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We consider the problem of testing the dimension of uncharacterized classical and quantum systems in a prepare-and-measure setup. Here we assume the preparation and measurement devices to be independent, thereby making the problem nonconvex. We present a simple method for generating nonlinear dimension witnesses for systems of arbitrary dimension. The simplest of our witnesses is highly robust to technical imperfections, and can certify the use of qubits in the presence of arbitrary noise and arbitrarily low detection efficiency. Finally, we show that this witness can be used to certify the presence of randomness, suggesting applications in quantum information processing.
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“A positive value of this dimension witness could certify randomness in this scenario, similar to the fact that a violation of the Bell inequality could certify randomness of self-testing QRNG in Section ' Self-testing QRNG ' .”
From Quantum random number generation (2016) · cites this paper as [86]
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“The randomness can be estimated by adopting a dimension witness. 86”
From Quantum random number generation (2016) · cites this paper as [86]
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Quantum random number generators
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“…QRNG of (Lunghi et al., 2015) where randomness from a quantum origin is separated from technical noise using the 31 dimension witness of (Bowles et al., 2014) defined as W = ∣∣∣∣∣ p (1 | 0, 0) − p (1 | 1, 0) p (1 | 2, 0) − p (1 | 3, 0) p (1 | 0, 1) − p (1 | 1, 1) p (1 | 2, 1) − p (1 |…”
Quantum random number generation
Ma, X., Yuan, X., Cao, Z., Qi, B., & Zhang, Z. (2016) · npj Quantum Information · doi:10.1038/npjqi.2016.21 · Cited by 445
“The randomness can be estimated by adopting a dimension witness.(86) A positive value of this dimension witness could certify randomness in this scenario, similar to the fact that a violation of the Bell inequality could certify randomness of self-testing QRNG in Section ‘Self-testing QRNG’.”
Self-testing of quantum systems: a review
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BackgroundSelf-Testing Quantum Random Number Generator
Lunghi, T., Brask, J. B., Lim, C. C. W., Lavigne, Q., Bowles, J., Martin, A., Zbinden, H., & Brunner, N. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.150501 · Cited by 206
Self-citationBrask, J. B., Martin, A., Esposito, W., Houlmann, R., Bowles, J., Zbinden, H., & Brunner, N. (2017) · Physical Review Applied · doi:10.1103/physrevapplied.7.054018 · Cited by 127
Self-citationOptimal randomness certification in the quantum steering and prepare-and-measure scenarios
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Semi-device-independent framework based on natural physical assumptions
Himbeeck, T. V., Woodhead, E., Cerf, N. J., García−Patrón, R., & Pironio, S. (2017) · Quantum · doi:10.22331/q-2017-11-18-33 · Cited by 124
Mannalath, V., Mishra, S., & Pathak, A. (2023) · Quantum Information Processing · doi:10.1007/s11128-023-04175-y · Cited by 125
“They used a function presented in [192], which acts as a ‘dimension witness’.”
MethodBounding the Set of Finite Dimensional Quantum Correlations
Navascués, M., & Vértesi, T. (2015) · Physical Review Letters · doi:10.1103/physrevlett.115.020501 · Cited by 95
Quantum Cryptography: Key Distribution and Beyond
Akshata Shenoy, H., Pathak, A., & Radhakrishna, S. (2017) · Quanta · doi:10.12743/quanta.v6i1.57 · Cited by 86
“enario. This uses the notion of bounding the classical or quantum dimension required to reproduce the observed quantum correlations by measurements on transmitted particles prepared in specific states [177,183]. Let P(yj;b) = Tr(ˆ y b ) (9) denote Bob’s probability for getting outcome ygiven measurement b acting on sta…”
BackgroundCharacterising the correlations of prepare-and-measure quantum networks
Wang, Y., Primaatmaja, I. W., Lavie, E., Varvitsiotis, A., & Lim, C. C. W. (2019) · npj Quantum Information · doi:10.1038/s41534-019-0133-3 · Cited by 73
“Semi-device-independent security of one-way quantum key distribution, Physical Review A 84, 010302(R) (2011) [22] Bowles, J.”
BackgroundSemidefinite programming relaxations for quantum correlations
Tavakoli, A., Pozas-Kerstjens, A., Brown, P. J., & Araújo, M. (2024) · Reviews of Modern Physics · doi:10.1103/revmodphys.96.045006 · Cited by 98
Identifying nonconvexity in the sets of limited-dimension quantum correlations
Donohue, J. M., & Wolfe, E. (2015) · Physical Review A · doi:10.1103/physreva.92.062120 · Cited by 55
“[33] recently reanalyzed prepare-and-measure signalling scenarios without the assumption of unlimited shared randomness [34].”
BackgroundSemi-device-independent framework based on natural physical assumptions
van Himbeeck, T., Woodhead, E., Cerf, N. J., García−Patrón, R., & Pironio, S. (2017) · Dépôt institutionnel de l'Université libre de Bruxelles (Université Libre de Bruxelles) · Cited by 54
Causal Modeling the Delayed-Choice Experiment
Chaves, R., Lemos, G. B., & Pienaar, J. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.190401 · Cited by 45
“where the statistics produced by a √ k + 1 dimensional quantum system can only be reproduced by a classical system of at least k + 1 dimensions [14].”
BackgroundMethodCertifying an Irreducible 1024-Dimensional Photonic State Using Refined Dimension Witnesses
Aguilar, E. A., Farkas, M., Martínez, D., Alvarado, M., Cariñe, J., XAVIER, G. B., Barra, J. F., Cañas, G., Pawłowski, M., & Lima, G. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.230503 · Cited by 38
Superactivation of quantum steering
Quintino, M. T., Brunner, N., & Huber, M. (2016) · Physical Review A · doi:10.1103/physreva.94.062123 · Cited by 39
“First of all, the fact that every entangled 2× 2 state is steerable for some number of copies k, together with the fact that there are numerous 2× 2 entangled state admitting a LHS model [5, 27–32] is sufficient to show super-activation.”
BackgroundResultSelf-citationPhysical security in the post-quantum era
Chowdhury, S., Covic, A., Acharya, R. Y., Dupee, S., Ganji, F., & Forte, D. J. (2021) · Journal of Cryptographic Engineering · doi:10.1007/s13389-021-00255-w · Cited by 60
“mension witnesses [Gallego et al. 2010]. Although this allows non-entangled devices to be used, the efficiency of the protocol should be verified experimentally. This shortcoming has been tackled in [Bowles et al. 2014] by showing that if (a) the preparation and measuring device share no correlations, and (b) devices…”
BackgroundActivating Hidden Metrological Usefulness
Tóth, G., Vértesi, T., Horodecki, P., & Horodecki, R. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.020402 · Cited by 36
Testing dimension and nonclassicality in communication networks
Bowles, J., Brunner, N., & Pawłowski, M. (2015) · Physical Review A · doi:10.1103/physreva.92.022351 · Cited by 35
Self-citationDevice-independent certification of the Hilbert-space dimension using a family of Bell expressions
Pan, A. K., & Mahato, S. S. (2020) · Physical Review A · doi:10.1103/physreva.102.052221 · Cited by 29
Li, Y., Fei, Y., Wang, W., Meng, X., Wang, H., Duan, Q., & Ma, Z. (2021) · Scientific Reports · doi:10.1038/s41598-021-03286-9 · Cited by 34
Semi-Device-Independent Certification of Independent Quantum State and Measurement Devices
Tavakoli, A. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.150503 · Cited by 26
“[20] J.”
BackgroundDevice-independent test of a delayed choice experiment
Polino, E., Agresti, I., Poderini, D., Carvacho, G., Milani, G., Lemos, G. B., Chaves, R., & Sciarrino, F. (2019) · Physical Review A · doi:10.1103/physreva.100.022111 · Cited by 29
“in the DCE can be tested via well developed dimensional witness inequalities [19, 20] that, if violated, prove that”
BackgroundA new device-independent dimension witness and its experimental implementation
Cai, Y., Bancal, J.-D., Romero, J., & Scarani, V. (2016) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/49/30/305301 · Cited by 22
Sarkar, S., Borkała, J. J., Jebarathinam, C., Makuta, O., Saha, D., & Augusiak, R. (2023) · Physical Review Applied · doi:10.1103/physrevapplied.19.034038 · Cited by 27
Realization of a causal-modeled delayed-choice experiment using single photons
Yu, S., Sun, Y.-N., Liu, W., Liu, Z., Ke, Z., Wang, Y., Tang, J., Li, C., & Guo, G. (2019) · Physical Review A · doi:10.1103/physreva.100.012115 · Cited by 21
“Consider a scenario with 2k preparations and k binary measurements, we construct the k × k matrix [20]”
MethodInfluentialGenuine temporal correlations can certify the quantum dimension
Spee, C., Siebeneich, H., Gloger, T. F., Kaufmann, P., Johanning, M., Kleinmann, M., Wunderlich, C., & Gühne, O. (2020) · New Journal of Physics · doi:10.1088/1367-2630/ab6d42 · Cited by 21
Mukherjee, S., & Pan, A. K. (2021) · Physical Review A · doi:10.1103/physreva.104.062214 · Cited by 21
Sharing nonlocality in a quantum network by unbounded sequential observers
Mahato, S. S., & Pan, A. K. (2022) · Physical Review A · doi:10.1103/physreva.106.042218 · Cited by 20
Compatibility of causal hidden-variable theories with a delayed-choice experiment
Huang, H.-L., Luo, Y.-H., Bai, B., Deng, Y.-H., Wang, H., Zhao, Q., Zhong, H.-S., Nie, Y.-Q., Jiang, W., Wang, X., et al. (2019) · Physical Review A · doi:10.1103/physreva.100.012114 · Cited by 19
Shared randomness and device-independent dimension witnessing
de Vicente, J. I. (2017) · Physical Review A · doi:10.1103/physreva.95.012340 · Cited by 18
Quantum Random Number Generation
Kollmitzer, C., Schauer, S., Raß, S., & Rainer, B. (2020) · Quantum science and technology · doi:10.1007/978-3-319-72596-3 · Cited by 22
Sun, Y.-N., Liu, Z., Bowles, J., Chen, G., Xu, X.-Y., Tang, J., Li, C., & Guo, G. (2020) · Optica · doi:10.1364/optica.396932 · Cited by 16
Self-citationClassical Cost of Transmitting a Qubit
Renner, M. J., Tavakoli, A., & Quintino, M. T. (2023) · Physical Review Letters · doi:10.1103/physrevlett.130.120801 · Cited by 16
Self-citationThree-observer classical dimension witness violation with weak measurement
Li, H.-W., Zhang, Y.-S., An, X.-B., Han, Z., & Guo, G. (2018) · Communications Physics · doi:10.1038/s42005-018-0011-x · Cited by 17
Device-independent dimension tests in the prepare-and-measure scenario
Sikora, J., Varvitsiotis, A., & Wei, Z. (2016) · Physical Review A · doi:10.1103/physreva.94.042125 · Cited by 15
Practical randomness amplification and privatisation with implementations on quantum computers
Foreman, C., Wright, S., Edgington, A., Berta, M., & Curchod, F. J. (2023) · Quantum · doi:10.22331/q-2023-03-30-969 · Cited by 20
Detection efficiency and noise in a semi-device-independent randomness-extraction protocol
Li, H.-W., Yin, Z., Pawłowski, M., Guo, G., & Han, Z. (2015) · Physical Review A · doi:10.1103/physreva.91.032305 · Cited by 15
An, X.-B., Li, H.-W., Yin, Z., Hu, M., Huang, W., Xu, B., Wang, S., Chen, W., Guo, G., & Han, Z. (2018) · Optics Letters · doi:10.1364/ol.43.003437 · Cited by 14
Semi-device-independent characterization of quantum measurements under a minimum overlap assumption
Shi, W., Cai, Y., Brask, J. B., Zbinden, H., & Brunner, N. (2019) · Physical Review A · doi:10.1103/physreva.100.042108 · Cited by 14
Self-citationCommunication tasks in operational theories
Heinosaari, T., Kerppo, O., & Leppäjärvi, L. (2020) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/abb5dc · Cited by 14
“This topic connects to several active research areas, including self-testing (see e.g. [1, 2]), dimension witnesses (see e.g. [3, 4, 5, 6]) and foundational principles of quantum theory (see e.g. [7, 8]).”
BackgroundGeneral Method for Classicality Certification in the Prepare and Measure Scenario
de Gois, C., Moreno, G., Nery, R., Brito, S., Chaves, R., & Rabelo, R. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.030311 · Cited by 14
Shaleena, A. S., Mukherjee, S., & Pan, A. K. (2023) · Physical Review A · doi:10.1103/physreva.107.012411 · Cited by 14
Practical Quantum Key Distribution with Non-Phase-Randomized Coherent States
Liu, L., Wang, Y., Lavie, E., Wang, C., Ricou, A., Guo, F. Z., & Lim, C. C. W. (2019) · Physical Review Applied · doi:10.1103/physrevapplied.12.024048 · Cited by 13
Sharing preparation contextuality in a Bell experiment by an arbitrary pair of sequential observers
Kumari, A., & Pan, A. K. (2023) · Physical Review A · doi:10.1103/physreva.107.012615 · Cited by 13
Criteria for nonclassicality in the prepare-and-measure scenario
Poderini, D., Brito, S., Nery, R., Sciarrino, F., & Chaves, R. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.043106 · Cited by 12
Classical model of a delayed-choice quantum eraser
Cour, B. R. L., & Yudichak, T. W. (2021) · Physical Review A · doi:10.1103/physreva.103.062213 · Cited by 11
Xiao, H., & Zhang, Z. (2016) · Quantum Information Processing · doi:10.1007/s11128-016-1474-x · Cited by 11
“In the dependentdevices model [45], Alice’s (Bob’s) state could be described as the input number x(y) and hidden variable λA(λB); neither of them can be controlled or known by Eve’s device.”
MethodPractical source-independent quantum random number generation with detector efficiency mismatch
Ma, D., Wang, Y., & Wei, K. (2020) · Quantum Information Processing · doi:10.1007/s11128-020-02865-5 · Cited by 10
Semi device independence of the BB84 protocol
Woodhead, E. (2016) · New Journal of Physics · doi:10.1088/1367-2630/18/5/055010 · Cited by 11
Experimental quantum randomness generation invulnerable to the detection loopholePreprint
Cañas, G., Cariñe, J., Gómez, E. S., Barra, J. F., Cabello, A., XAVIER, G. B., Lima, G., & Pawłowski, M. (2014) · arXiv (Cornell University) · Cited by 10
Closing the detection loophole in nonlinear entanglement witnesses
Sen, K., Das, S., & Sen, U. (2019) · Physical Review A · doi:10.1103/physreva.100.062333 · Cited by 9
Thenabadu, M., & Reid, M. D. (2022) · Physical Review A · doi:10.1103/physreva.105.062209 · Cited by 9
More randomness from a prepare-and-measure scenario with independent devices
Han, Y.-G., Yin, Z., Li, H.-W., Chen, W., Wang, S., Guo, G., & Han, Z. (2016) · Physical Review A · doi:10.1103/physreva.93.032332 · Cited by 9
Interplays between classical and quantum entanglement-assisted communication scenarios
Vieira, C., de Gois, C., Pollyceno, L. D. S., & Rabelo, R. (2023) · New Journal of Physics · doi:10.1088/1367-2630/ad0526 · Cited by 8
Effect of external magnetic fields on practical quantum random number generator
Li, Y., Fei, Y., Wang, W., Meng, X., Wang, H., Duan, Q.-H., Han, Y., & Ma, Z. (2023) · EPJ Quantum Technology · doi:10.1140/epjqt/s40507-023-00206-w · Cited by 8
“To trade off between generation rate and practical security, the semi-device-independent QRNG (SDI-QRNG) protocols are proposed, which mainly include source-device-independent [42–44], measurement-device-independent [45, 46] and dimension witness violation based QRNG protocols [15, 47–49].”
MethodPhase-Coding Self-Testing Quantum Random Number Generator
Song, X., Li, H.-W., Yin, Z., Liang, W.-Y., Zhang, C., Han, Y.-G., Chén, W., & Han, Z. (2015) · Chinese Physics Letters · doi:10.1088/0256-307x/32/8/080302 · Cited by 8
A general bound for the dimension of quantum behaviours in the prepare-and-measure scenario
de Vicente, J. I. (2019) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/aafde7 · Cited by 8
Certified randomness from a remote-state-preparation dimension witness
Xing, C., Redeker, K., Garthoff, R., Rosenfeld, W., Wrachtrup, J., & Gerhardt, I. (2021) · Physical Review A · doi:10.1103/physreva.103.042211 · Cited by 8
Wei, S., Guo, F., Gao, F., & Wen, Q. (2021) · New Journal of Physics · doi:10.1088/1367-2630/abf614 · Cited by 8
“This dimension witness can be used to estimate the genuine randomness generated if the quantum random number generator system satisfied two assumptions [5, 39, 40].”
BackgroundHybrid quantum random number generator for cryptographic algorithms
Iavich, M., Kuchukhidze, T., Iashvili, G., & Gnatyuk, S. O. (2021) · RADIOELECTRONIC AND COMPUTER SYSTEMS · doi:10.32620/reks.2021.4.09 · Cited by 9
Optimal classical and quantum real and complex dimension witness
Batle, J. A. I., & Bednorz, A. (2022) · Physical Review A · doi:10.1103/physreva.105.042433 · Cited by 8
“to make it equivalent to the previous one, with all odd preparations being identical [7].”
BackgroundStructure of dimension-bounded temporal correlations
Mao, Y., Spee, C., Xu, Z., & Gühne, O. (2022) · Physical Review A · doi:10.1103/physreva.105.l020201 · Cited by 7
Novel Certification Method for Quantum Random Number Generators
Iavich, M., Kuchukhidze, T., Gnatyuk, S. O., & Fesenko, A. (2021) · International Journal of Computer Network and Information Security · doi:10.5815/ijcnis.2021.03.03 · Cited by 7
“In order to obtain the final random bit string, sufficient post processing of the raw data is performed based on the entropy bound [7, 8]. pr (o | s, m) gives the conditional probability of finding the result of o (from ± 1) for a condition that is one of the defined probabilities s = 0, 1, 2, 3.”
MethodEvidence-Based Certification of Quantum Dimensions
Teo, Y. S., Shringarpure, S. U., Jeong, H., Prasannan, N., Brecht, B., Silberhorn, C., Evans, M. J., Mogilevtsev, D. S., & Sánchez-Soto, L. L. (2024) · Physical Review Letters · doi:10.1103/physrevlett.133.050204 · Cited by 7
Tighter bound of quantum randomness certification for independent-devices scenario
Fei, X.-W., Yin, Z., Huang, W., Xu, B., Wang, S., Chen, W., Han, Y.-G., Guo, G., & Han, Z. (2017) · Scientific Reports · doi:10.1038/s41598-017-15318-4 · Cited by 6
“34 proposed the so-called dimension witness to bound the quantumness of a prepare-and-measure scenario could behave, with the assumption that the state preparation and measurement devices share no correlations.”
BackgroundMethodInfluentialAlves, G. P., Gigena, N., & Kaniewski, J. (2023) · Physical Review A · doi:10.1103/physreva.108.042608 · Cited by 7
Generalized measurements on qubits in quantum randomness certification and expansion
Mironowicz, P., Grünfeld, M., & Bourennane, M. (2024) · Physical Review Applied · doi:10.1103/physrevapplied.22.044041 · Cited by 6
Measurement-Device-Independent Quantum Random-Number Generator With Source Flaws
Wu, T., Zhang, C., Zhou, X., Li, J., & Wang, Q. (2023) · IEEE photonics journal · doi:10.1109/jphot.2023.3331547 · Cited by 5
“Usually, there are three types of SDI-QRNGs, the source-independent QRNG (SI-QRNG) [18], [19], [20], the measurement-device-independent QRNG (MDI-QRNG) [21], [24], and the SDI-QRNG based on dimension witness [16], [17].”
BackgroundMethodDetection loophole attacks on semi-device-independent quantum and classical protocols
Dall’Arno, M., Passaro, E., Gallego, R., Pawłowski, M., & Acín, A. (2015) · Quantum Information and Computation · doi:10.26421/qic15.1-2-3 · Cited by 7
“[30].”
BackgroundRoy, A. K., Srivastava, V., Mahanti, S., Giarmatzi, C., & Gilchrist, A. (2024) · Physical Review A · doi:10.1103/physreva.110.012608 · Cited by 4
Quantum discord witness with uncharacterized devices
Wang, R., Yao, Y., & Yin, Z.-Q. (2025) · Physical Review Applied · doi:10.1103/hht6-mvyz · Cited by 4
Novel Quantum Random Number Generator with the Improved Certification Method
Iavich, M., Kuchukhidze, T., Iashvili, G., Gnatyuk, S. O., & Bocu, R. (2021) · International Journal of Mathematical Sciences and Computing · doi:10.5815/ijmsc.2021.03.05 · Cited by 4
“In order to obtain the final random bit string, sufficient post processing of the raw data is performed based on the entropy bound [18, 19].”
MethodExperimental certification of nonprojective quantum measurements under a minimum overlap assumption
Fan, Q., Ma, M.-Y., Sun, Y.-N., Su, Q.-P., & Yang, C. (2022) · Optics Express · doi:10.1364/oe.469225 · Cited by 4
Self-testing of an unbounded number of mutually commuting local observables
Munshi, S., & Pan, A. K. (2023) · Physical Review A · doi:10.1103/physreva.108.062607 · Cited by 4
Testing the accuracy of qubit rotations on a public quantum computer
Białecki, T., Rybotycki, T., Tworzydło, J., & Bednorz, A. (2024) · Frontiers in Physics · doi:10.3389/fphy.2024.1360080 · Cited by 4
Experimental test of nonclassicality with arbitrarily low detection efficiency
Hameedi, A., Marques, B., Mironowicz, P., Saha, D., Pawłowski, M., & Bourennane, M. (2020) · Physical Review A · doi:10.1103/physreva.102.032621 · Cited by 5
“With this added assumption, it was shown [22, 23] that any experimental setup with a non-zero detection efficiency can be used to prove nonclassicality.”
MethodModified quantum delayed-choice experiment without quantum control or entanglement assistance
Guo, Q., Zhang, W.-J., Li, G., Zhang, T., Wang, H.-F., & Zhang, S. (2021) · Physical Review A · doi:10.1103/physreva.104.022210 · Cited by 4
“In that work, the authors treated the WDC experiment as a device-independent prepare-and-measure (PAM) scenario [40], and suggested a slight modification for the WDC experiment can exclude any two-dimensional nonretrocausal hidden classical model in a device-independent manner by violating the dimension witness inequa…”
BackgroundMethodInfluentialDetection Efficiency Bounds in (Semi-)Device-Independent Scenarios
Sarubi, T. S., Zamora, S., Alves, M., Alves, V. F., Viswanathan, G. M., & Chaves, R. (2026) · Brazilian Journal of Physics · doi:10.1007/s13538-026-02008-8 · Cited by 4
“This leads to a nonconvex set of correlations, making the analysis of such models more subtle [118, 119].”
Optimality of quantum randomness certification with independent devices
Fei, X.-W., Yin, Z., Cui, C., Huang, W., Xu, B., Wang, S., Chen, W., Han, Y.-G., Guo, G., & Han, Z. (2018) · Journal of the Optical Society of America B · doi:10.1364/josab.35.002186 · Cited by 3
An, X.-B., Han, Y.-G., Yin, Z., Huang, W., Chen, W., Wang, S., Guo, G., & Han, Z. (2017) · Optics Letters · doi:10.1364/ol.42.004139 · Cited by 3
Practical decoy-state quantum random number generator with weak coherent sources
Han, S.-S., Ding, H.-J., Zhang, C., Zhou, X., Zhang, C.-M., & Wang, Q. (2020) · Quantum Information Processing · doi:10.1007/s11128-020-02902-3 · Cited by 3
Jebarathinam, C., & Das, D. (2023) · Quantum Information and Computation · doi:10.26421/qic23.5-6-2 · Cited by 5
“[41] serve as the certification of quantumness of sequential correlations arising in the prepare and measure scenario in a semi-device-independent way.”
BackgroundPrecise certification of a qubit space
Białecki, T., Rybotycki, T., Batle, J. A. I., Tworzydło, J., & Bednorz, A. (2024) · EPJ Quantum Technology · doi:10.1140/epjqt/s40507-024-00230-4 · Cited by 4
“A good witness certifies the linear independence of specific dichotomic outcome probability p ( M | N ) for the preparation N and measurement M and so it is expressed by a suitable determinant [23–25].”
BackgroundTowards minimal self-testing of qubit states and measurements in prepare-and-measure scenarios
Drótos, G., Pál, K. F., Taoutioui, A., & Vértesi, T. (2024) · New Journal of Physics · doi:10.1088/1367-2630/ad4e5c · Cited by 3
“[47] for how to generate them.”
Estimating the privacy of quantum-random numbers
Seiler, J., Strohm, T., & Schleich, W. P. (2020) · OPen Access Repositorium der Universität Ulm (OPARU) (Ulm University) · doi:10.18725/oparu-34102 · Cited by 3
The role of entanglement in energy-restricted communication and randomness generation
Carceller, C. R. I., & Tavakoli, A. (2026) · Quantum Science and Technology · doi:10.1088/2058-9565/ae4d80 · Cited by 2
“Common to all these frameworks for semi-device-independent PM scenarios is that they suppose that Alice and Bob do not share entanglement, and sometimes not even classical random variables [ 23–25 ] .”
Semi-device-independent randomness certification on discretized continuous-variable platforms
Alves, M., Sena, V. L. O., Zamora, S., Sarubi, T. S., de Oliveira, A., Tacla, A. B., & Chaves, R. (2026) · Physical Review A · doi:10.1103/z3s5-bhb7 · Cited by 5
Theory-independent randomness generation from spatial symmetries
Jones, C. L., Ludescher, S. L., Aloy, A., & Müller, M. P. (2026) · Quantum · doi:10.22331/q-2026-01-16-1966 · Cited by 9
“This has often been implemented with a bound on the dimension of the Hilbert space of the transmitted sys-tem, restricting the communication to qubits or qutrits, as in [14, 21, 27, 28], although this is arguably not very well-motivated for non-idealized physical scenarios.”
Single- and two-photon wave-particle superpositions: Theory and experiment
Xue, Q.-F., Zhuang, X.-C., An, N. B., Duan, D., Ma, R., Pan, W., Wang, Q., Xia, Y., & Man, Z. (2023) · Physical Review A · doi:10.1103/physreva.108.022223 · Cited by 2
Null dimension witness based on single measurements
Batle, J. A. I., & Bednorz, A. (2023) · Physical Review A · doi:10.1103/physreva.108.062202 · Cited by 2
“In previous works, a witness of dimension d needed 2k preparations and k measurements with binary outcomes, with d ≤ k for the classical system and d(2) ≤ k for the quantum system [6].”
BackgroundMethodInfluentialQuantum null-hypothesis device-independent Schmidt number witness
Batle, J. A. I., Białecki, T., Rybotycki, T., Tworzydło, J., & Bednorz, A. (2024) · EPJ Quantum Technology · doi:10.1140/epjqt/s40507-024-00273-7 · Cited by 3
“The quantum dimension can also be tested by null hypotheses [30–32], demonstrated experimentally [33, 34].”
BackgroundNoise-resilient quantum random access codes
Karthik, H. S., Gómez, S., Quinteros, F., Akshata Shenoy, H., Pawłowski, M., Walborn, S. P., Lima, G., & Gómez, E. S. (2025) · Physical Review A · doi:10.1103/physreva.111.032613 · Cited by 2
Experimental Implementation of Dimension-Dependent Contextuality Inequality
Håkansson, E., Piveteau, A., Seguinard, A., Muhammad, S., Bourennane, M., Gühne, O., & Plávala, M. (2025) · Physical Review Letters · doi:10.1103/physrevlett.134.200202 · Cited by 2
Experimental device-independent tests of classical and quantum entropy
Zhu, F., Zhang, W., Chen, S., You, L., Wang, Z., & Huang, Y. (2016) · Physical Review A · doi:10.1103/physreva.94.062340 · Cited by 2
Quantum dimension witness with a single repeated operation
Białecki, T., Rybotycki, T., Batle, J. A. I., & Bednorz, A. (2024) · Physical Review A · doi:10.1103/physreva.109.l020201 · Cited by 2
Characterizing high-dimensional quantum contextuality
Yu, X., Veeren, I., & Gühne, O. (2024) · Physical Review A · doi:10.1103/physreva.109.l030201 · Cited by 3
“[ 36 – 39 ] for some examples and their applications.”
BackgroundMethodSun, Y., Ma, M.-Y., Su, Q.-P., Sun, Z., Yang, C.-P., & Nori, F. (2026) · Physical Review Letters · doi:10.1103/q85z-wl38 · Cited by 2
“As discussed in [36, 37], it is more natural to assume that all devices are not correlated in a practical setup, i.e., they are independent.”
Metadata
- Authors
- Bowles, J., Quintino, M. T., & Brunner, N.
- Affiliations
- University of Geneva (CH)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2014-04-11
- Volume
- 112
- Issue
- 14
- Pages
- 140407-140407
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2070059557
- Cited by
- 116
- References
- 22
- Citations by year
- 2026: 7 · 2025: 4 · 2024: 13 · 2023: 16 · 2022: 7 · 2021: 13 · 2020: 13 · 2019: 9 · 2018: 5 · 2017: 9 · 2016: 10 · 2015: 8 · 2014: 1
- FWCI
- 9.30
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- Archive ouverte UNIGE (University of Geneva) (publishedVersion, other-oa)
- arXiv (Cornell University) (submittedVersion)
- Archive ouverte UNIGE (University of Geneva) (submittedVersion, cc-by)
- arXiv (Cornell University)
- Funders
- National Science Foundation (PP00P2_138917)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- dimension witness, prepare-and-measure scenario, noise robustness, randomness certification, non-convex optimization
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