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Quantum illumination

December 20, 2023

Quantum illumination is a paradigm for target detection that employs quantum entanglement between a signal electromagnetic mode and an idler electromagnetic mode, as well as joint measurement of these modes. The signal mode is propagated toward a region of space, and it is either lost or reflected, depending on whether a target is absent or present, respectively. In principle, quantum illumination can be beneficial even if the original entanglement is completely destroyed by a lossy and noisy environment.

Introduction edit

Many quantum information applications, such as quantum teleportation,[1] quantum error correction, and superdense coding, rely on entanglement. However, entanglement is a fragile quantum property between particles and can be easily destroyed by loss and noise arising from interaction with the environment, leading to quantum decoherence.

Lloyd, Shapiro, Sacchi and others showed that, even though entanglement itself may not survive, the residual correlation between the two initially-entangled systems remains much higher than any initial classical states can provide. This implies that the use of entanglement should not be dismissed in entanglement-breaking scenarios.

Quantum illumination takes advantage of this stronger-than-classical residual correlations between two systems to achieve a performance enhancement over all schemes based on transmitting classical states with comparable power levels. Quantum illumination has been proven to be particularly useful in very noisy environments.

History edit

Theory edit

The concept of quantum illumination was introduced by Seth Lloyd and collaborators at MIT in 2008. This included a discrete-variable version[2] and a continuous-variable version developed in collaboration with Jeffrey Shapiro, Stefano Pirandola, Saikat Guha and others,[3] the latter version being based on Gaussian states.[4]

The basic setup of quantum illumination is target detection. Here the sender prepares two entangled systems, called signal and idler. The idler is retained while the signal is sent to probe the presence of a low-reflectivity object in a region with bright background noise. The reflection from the object is then combined with the retained idler system in a joint quantum measurement providing two possible outcomes: object present or object absent. More precisely, the probing process is repeated many times so that many pairs of signal-idler systems are collected at the receiver for the joint quantum detection.

The advantage of the scheme is evident at low energies where the mean number of photons in each signal system is very low (of the order of one photon or less). In this case, at fixed low energy, the probability of success in detecting a target has a remarkable improvement with respect to classical detection schemes, where entanglement is not used and signal systems are prepared in coherent states (technically, there is a 6 dB improvement in the error exponent [3]). A key feature of quantum illumination is that the entanglement between the idler system and the reflected signal system is completely lost in the process. However, the residual quantum correlations between these two systems (idler-reflected signal) remain so strong that they could only be created by the presence of entanglement in the initial systems (idler-signal). Because the reflected signal is quantum-correlated with the retained idler system, it can be distinguished among all the uncorrelated background thermal photons that are also received by the detector. Because of this quantum labeling of the systems, the detection of quantum illumination is very efficient.

In 2015, an international collaboration coordinated by Stefano Pirandola [5][6] extended the protocol of quantum illumination to the microwave frequencies, thus providing the first theoretical prototype of quantum radar.

The original proposal from [3] was analyzed in the Bayesian setting of hypothesis testing, in which prior probabilities are assigned to the hypotheses that the target is absent or present. In 2017, a research paper[7] analyzed quantum illumination in the Neyman-Pearson or asymmetric setting of hypothesis testing, which is a setting of interest in quantum radar applications. It was found that the performance gains of quantum illumination are even greater than those from.[3]

In 2017, an optimum receiver design was proposed by Quntao Zhuang, Zheshen Zhang, and Jeffrey Shapiro.[8] Quantum illumination has also been extended to the scenario of target fading.[9]

In 2020, the ultimate limits for quantum illumination, allowing for an arbitrary number of optical modes entangled with a quantum memory were derived by Ranjith Nair and Mile Gu for all levels of background noise.[10] The results also showed that the 6 dB improvement cannot be surpassed - and is only achievable for very large background noise.

Related work on secure communication edit

In 2009, a secure communication scheme based on quantum illumination[11] was proposed. This scheme is a variant of the quantum cryptographic protocols based on continuous variables and two-way quantum communication introduced by Stefano Pirandola, Seth Lloyd and collaborators[12] in 2008.

Experiment edit

In 2013, Lopaeva et al. exploited photon number correlations, instead of entanglement, in a sub-optimal target detection experiment.[13] To illustrate the benefit of quantum entanglement, in 2013 Zhang et al. reported a secure communication experiment based on quantum illumination and demonstrated for the first time that entanglement can enable a substantial performance advantage in the presence of quantum decoherence.[14] In 2015, Zhang et al. applied quantum illumination in sensing and showed that employing entanglement can yield a higher signal-to-noise ratio than the optimal classical scheme can provide, even though the highly lossy and noisy environment completely destroys the initial entanglement.[15][16] This sensing experiment thus proved the original theoretical proposals of quantum illumination. The first experimental effort to perform microwave quantum illumination was based on using Josephson parametric amplifier and a digital receiver.[17][18] As applied to imaging, in 2019 England et al. demonstrated this principle by imaging through noise in a scanning configuration.[19] The first full-field imaging system based on quantum illumination that uses spatially-entangled photon pairs for imaging in the presence of noise and losses was reported in a two successive publications in 2019[20] and 2020[21] by two research groups from the University of Glasgow.

Applications edit

Potential applications of quantum illumination include target detection in high background noise environments, but also ultra-sensitive biological imaging and sensing, and secure communication.

Media reporting edit

Several news articles on quantum illumination have appeared in popular science media,[22][23] with the goal of elucidating the concept of quantum illumination in less technical terms.

References edit

  1. ^ Bennett, Charles H.; Brassard, Gilles; Crépeau, Claude; Jozsa, Richard; Peres, Asher; Wootters, William K. (1993-03-29). "Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels". Physical Review Letters. American Physical Society (APS). 70 (13): 1895–1899. Bibcode:1993PhRvL..70.1895B. CiteSeerX 10.1.1.46.9405. doi:10.1103/physrevlett.70.1895. ISSN 0031-9007. PMID 10053414.
  2. ^ Lloyd, Seth (2008-09-12). "Enhanced Sensitivity of Photodetection via Quantum Illumination". Science. American Association for the Advancement of Science (AAAS). 321 (5895): 1463–1465. Bibcode:2008Sci...321.1463L. doi:10.1126/science.1160627. ISSN 0036-8075. PMID 18787162. S2CID 30596567.
  3. ^ a b c d Tan, Si-Hui; Erkmen, Baris I.; Giovannetti, Vittorio; Guha, Saikat; Lloyd, Seth; Maccone, Lorenzo; Pirandola, Stefano; Shapiro, Jeffrey H. (2008-12-18). "Quantum Illumination with Gaussian States". Physical Review Letters. 101 (25): 253601. arXiv:0810.0534. Bibcode:2008PhRvL.101y3601T. doi:10.1103/physrevlett.101.253601. ISSN 0031-9007. PMID 19113706. S2CID 26890855.
  4. ^ Weedbrook, Christian; Pirandola, Stefano; García-Patrón, Raúl; Cerf, Nicolas J.; Ralph, Timothy C.; Shapiro, Jeffrey H.; Lloyd, Seth (2012-05-01). "Gaussian quantum information". Reviews of Modern Physics. 84 (2): 621–669. arXiv:1110.3234. Bibcode:2012RvMP...84..621W. doi:10.1103/revmodphys.84.621. ISSN 0034-6861. S2CID 119250535.
  5. ^ Barzanjeh, Shabir; Guha, Saikat; Weedbrook, Christian; Vitali, David; Shapiro, Jeffrey H.; Pirandola, Stefano (2015-02-27). "Microwave Quantum Illumination". Physical Review Letters. 114 (8): 080503. arXiv:1503.00189. Bibcode:2015PhRvL.114h0503B. doi:10.1103/physrevlett.114.080503. ISSN 0031-9007. PMID 25768743. S2CID 119189135.
  6. ^ Quantum Mechanics Could Improve Radar, Physics 8, 18 (2015)([1])
  7. ^ Wilde, Mark M.; Tomamichel, Marco; Berta, Mario; Lloyd, Seth (2017). "Gaussian hypothesis testing and quantum illumination". Physical Review Letters. American Physical Society (APS). 119 (12): 120501. arXiv:1608.06991. Bibcode:2017PhRvL.119l0501W. doi:10.1103/PhysRevLett.119.120501. PMID 29341649. S2CID 1949571.
  8. ^ Zhuang, Quntao; Zhang, Zheshen; Shapiro, Jeffrey H. (2017-01-27). "Optimum Mixed-State Discrimination for Noisy Entanglement-Enhanced Sensing". Physical Review Letters. 118 (4): 040801. arXiv:1609.01968. Bibcode:2017PhRvL.118d0801Z. doi:10.1103/PhysRevLett.118.040801. PMID 28186814. S2CID 206284828.
  9. ^ Zhuang, Quntao; Zhang, Zheshen; Shapiro, Jeffrey H. (2017-08-15). "Quantum illumination for enhanced detection of Rayleigh-fading targets". Physical Review A. 96 (2): 020302. arXiv:1706.05561. Bibcode:2017PhRvA..96b0302Z. doi:10.1103/PhysRevA.96.020302. S2CID 56098241.
  10. ^ Nair, Ranjith; Gu, Mile (2020-07-20). "Fundamental limits of quantum illumination". Optica. 7 (7): 771–774. arXiv:2002.12252. Bibcode:2020Optic...7..771N. doi:10.1364/OPTICA.391335. ISSN 2334-2536. S2CID 211532448.
  11. ^ Shapiro, Jeffrey H. (2009-08-17). "Defeating passive eavesdropping with quantum illumination". Physical Review A. American Physical Society (APS). 80 (2): 022320. arXiv:0904.2490. Bibcode:2009PhRvA..80b2320S. doi:10.1103/physreva.80.022320. ISSN 1050-2947. S2CID 56094608.
  12. ^ Pirandola, Stefano; Mancini, Stefano; Lloyd, Seth; Braunstein, Samuel L. (2008-07-11). "Continuous-variable quantum cryptography using two-way quantum communication". Nature Physics. Springer Science and Business Media LLC. 4 (9): 726–730. arXiv:quant-ph/0611167. Bibcode:2008NatPh...4..726P. doi:10.1038/nphys1018. ISSN 1745-2473. S2CID 12062818.
  13. ^ Lopaeva, E. D.; Ruo Berchera, I.; Degiovanni, I. P.; Olivares, S.; Brida, G.; Genovese, M. (2013-04-10). "Experimental Realization of Quantum Illumination". Physical Review Letters. 110 (15): 153603. arXiv:1303.4304. Bibcode:2013PhRvL.110o3603L. doi:10.1103/physrevlett.110.153603. ISSN 0031-9007. PMID 25167266. S2CID 636404.
  14. ^ Zhang, Zheshen; Tengner, Maria; Zhong, Tian; Wong, Franco N. C.; Shapiro, Jeffrey H. (2013-07-01). "Entanglement's Benefit Survives an Entanglement-Breaking Channel". Physical Review Letters. American Physical Society (APS). 111 (1): 010501. arXiv:1303.5343. Bibcode:2013PhRvL.111a0501Z. doi:10.1103/physrevlett.111.010501. ISSN 0031-9007. PMID 23862986. S2CID 6269724.
  15. ^ Zhang, Zheshen; Mouradian, Sara; Wong, Franco N. C.; Shapiro, Jeffrey H. (2015-03-20). "Entanglement-Enhanced Sensing in a Lossy and Noisy Environment". Physical Review Letters. 114 (11): 110506. arXiv:1411.5969. Bibcode:2015PhRvL.114k0506Z. doi:10.1103/physrevlett.114.110506. ISSN 0031-9007. PMID 25839252. S2CID 15101562.
  16. ^ Quantum sensor's advantages survive entanglement breakdown, MIT News, 9 March (2015), ([2])
  17. ^ Barzanjeh, S.; Pirandola, S.; Vitali, D.; Fink, J. M. (2020). "Microwave quantum illumination using a digital receiver". Science Advances. 6 (19): eabb0451. arXiv:1908.03058. Bibcode:2020SciA....6..451B. doi:10.1126/sciadv.abb0451. ISSN 2375-2548. PMC 7272231. PMID 32548249.
  18. ^ "Quantum radar has been demonstrated for the first time". MIT Technology Review. Retrieved 2020-06-15.
  19. ^ England, Duncan G.; Balaji, Bhashyam; Sussman, Benjamin J. (2019-02-19). "Quantum-enhanced standoff detection using correlated photon pairs". Physical Review A. 99 (2): 023828. arXiv:1811.04113. Bibcode:2019PhRvA..99b3828E. doi:10.1103/PhysRevA.99.023828. S2CID 53616393.
  20. ^ Defienne, H.; Reichert, M.; Fleischer, J.; Faccio, D. (2019). "Quantum image distillation". Science Advances. 5 (10): eaax0307. arXiv:1907.06526. Bibcode:2019SciA....5..307D. doi:10.1126/sciadv.aax0307. ISSN 2375-2548. PMC 6799981. PMID 31667343.
  21. ^ Gregory, T.; Moreau, P.-A.; Toninelli, E.; Padgett, M. J. (2020). "Imaging through noise with quantum illumination". Science Advances. 6 (6): eaay2652. arXiv:1907.09370. Bibcode:2020SciA....6.2652G. doi:10.1126/sciadv.aay2652. PMC 7007263. PMID 32083179.
  22. ^ "Broken quantum links still work". Nature. Springer Science and Business Media LLC. 499 (7457): 129. 2013. doi:10.1038/499129a. ISSN 0028-0836.
  23. ^ Lisa Grossman (July 17, 2013). "Fragility of entanglement no bar to quantum secrets". New Scientist. Retrieved 16 Nov 2019.

December 20, 2023
quantum, illumination, paradigm, target, detection, that, employs, quantum, entanglement, between, signal, electromagnetic, mode, idler, electromagnetic, mode, well, joint, measurement, these, modes, signal, mode, propagated, toward, region, space, either, los. Quantum illumination is a paradigm for target detection that employs quantum entanglement between a signal electromagnetic mode and an idler electromagnetic mode as well as joint measurement of these modes The signal mode is propagated toward a region of space and it is either lost or reflected depending on whether a target is absent or present respectively In principle quantum illumination can be beneficial even if the original entanglement is completely destroyed by a lossy and noisy environment Contents 1 Introduction 2 History 2 1 Theory 2 1 1 Related work on secure communication 2 2 Experiment 3 Applications 4 Media reporting 5 ReferencesIntroduction editMany quantum information applications such as quantum teleportation 1 quantum error correction and superdense coding rely on entanglement However entanglement is a fragile quantum property between particles and can be easily destroyed by loss and noise arising from interaction with the environment leading to quantum decoherence Lloyd Shapiro Sacchi and others showed that even though entanglement itself may not survive the residual correlation between the two initially entangled systems remains much higher than any initial classical states can provide This implies that the use of entanglement should not be dismissed in entanglement breaking scenarios Quantum illumination takes advantage of this stronger than classical residual correlations between two systems to achieve a performance enhancement over all schemes based on transmitting classical states with comparable power levels Quantum illumination has been proven to be particularly useful in very noisy environments History editTheory edit The concept of quantum illumination was introduced by Seth Lloyd and collaborators at MIT in 2008 This included a discrete variable version 2 and a continuous variable version developed in collaboration with Jeffrey Shapiro Stefano Pirandola Saikat Guha and others 3 the latter version being based on Gaussian states 4 The basic setup of quantum illumination is target detection Here the sender prepares two entangled systems called signal and idler The idler is retained while the signal is sent to probe the presence of a low reflectivity object in a region with bright background noise The reflection from the object is then combined with the retained idler system in a joint quantum measurement providing two possible outcomes object present or object absent More precisely the probing process is repeated many times so that many pairs of signal idler systems are collected at the receiver for the joint quantum detection The advantage of the scheme is evident at low energies where the mean number of photons in each signal system is very low of the order of one photon or less In this case at fixed low energy the probability of success in detecting a target has a remarkable improvement with respect to classical detection schemes where entanglement is not used and signal systems are prepared in coherent states technically there is a 6 dB improvement in the error exponent 3 A key feature of quantum illumination is that the entanglement between the idler system and the reflected signal system is completely lost in the process However the residual quantum correlations between these two systems idler reflected signal remain so strong that they could only be created by the presence of entanglement in the initial systems idler signal Because the reflected signal is quantum correlated with the retained idler system it can be distinguished among all the uncorrelated background thermal photons that are also received by the detector Because of this quantum labeling of the systems the detection of quantum illumination is very efficient In 2015 an international collaboration coordinated by Stefano Pirandola 5 6 extended the protocol of quantum illumination to the microwave frequencies thus providing the first theoretical prototype of quantum radar The original proposal from 3 was analyzed in the Bayesian setting of hypothesis testing in which prior probabilities are assigned to the hypotheses that the target is absent or present In 2017 a research paper 7 analyzed quantum illumination in the Neyman Pearson or asymmetric setting of hypothesis testing which is a setting of interest in quantum radar applications It was found that the performance gains of quantum illumination are even greater than those from 3 In 2017 an optimum receiver design was proposed by Quntao Zhuang Zheshen Zhang and Jeffrey Shapiro 8 Quantum illumination has also been extended to the scenario of target fading 9 In 2020 the ultimate limits for quantum illumination allowing for an arbitrary number of optical modes entangled with a quantum memory were derived by Ranjith Nair and Mile Gu for all levels of background noise 10 The results also showed that the 6 dB improvement cannot be surpassed and is only achievable for very large background noise Related work on secure communication edit In 2009 a secure communication scheme based on quantum illumination 11 was proposed This scheme is a variant of the quantum cryptographic protocols based on continuous variables and two way quantum communication introduced by Stefano Pirandola Seth Lloyd and collaborators 12 in 2008 Experiment edit In 2013 Lopaeva et al exploited photon number correlations instead of entanglement in a sub optimal target detection experiment 13 To illustrate the benefit of quantum entanglement in 2013 Zhang et al reported a secure communication experiment based on quantum illumination and demonstrated for the first time that entanglement can enable a substantial performance advantage in the presence of quantum decoherence 14 In 2015 Zhang et al applied quantum illumination in sensing and showed that employing entanglement can yield a higher signal to noise ratio than the optimal classical scheme can provide even though the highly lossy and noisy environment completely destroys the initial entanglement 15 16 This sensing experiment thus proved the original theoretical proposals of quantum illumination The first experimental effort to perform microwave quantum illumination was based on using Josephson parametric amplifier and a digital receiver 17 18 As applied to imaging in 2019 England et al demonstrated this principle by imaging through noise in a scanning configuration 19 The first full field imaging system based on quantum illumination that uses spatially entangled photon pairs for imaging in the presence of noise and losses was reported in a two successive publications in 2019 20 and 2020 21 by two research groups from the University of Glasgow Applications editPotential applications of quantum illumination include target detection in high background noise environments but also ultra sensitive biological imaging and sensing and secure communication Media reporting editSeveral news articles on quantum illumination have appeared in popular science media 22 23 with the goal of elucidating the concept of quantum illumination in less technical terms References edit Bennett Charles H Brassard Gilles Crepeau Claude Jozsa Richard Peres Asher Wootters William K 1993 03 29 Teleporting an unknown quantum state via dual classical and Einstein Podolsky Rosen channels Physical Review Letters American Physical Society APS 70 13 1895 1899 Bibcode 1993PhRvL 70 1895B CiteSeerX 10 1 1 46 9405 doi 10 1103 physrevlett 70 1895 ISSN 0031 9007 PMID 10053414 Lloyd Seth 2008 09 12 Enhanced Sensitivity of Photodetection via Quantum Illumination Science American Association for the Advancement of Science AAAS 321 5895 1463 1465 Bibcode 2008Sci 321 1463L doi 10 1126 science 1160627 ISSN 0036 8075 PMID 18787162 S2CID 30596567 a b c d Tan Si Hui Erkmen Baris I Giovannetti Vittorio Guha Saikat Lloyd Seth Maccone Lorenzo Pirandola Stefano Shapiro Jeffrey H 2008 12 18 Quantum Illumination with Gaussian States Physical Review Letters 101 25 253601 arXiv 0810 0534 Bibcode 2008PhRvL 101y3601T doi 10 1103 physrevlett 101 253601 ISSN 0031 9007 PMID 19113706 S2CID 26890855 Weedbrook Christian Pirandola Stefano Garcia Patron Raul Cerf Nicolas J Ralph Timothy C Shapiro Jeffrey H Lloyd Seth 2012 05 01 Gaussian quantum information Reviews of Modern Physics 84 2 621 669 arXiv 1110 3234 Bibcode 2012RvMP 84 621W doi 10 1103 revmodphys 84 621 ISSN 0034 6861 S2CID 119250535 Barzanjeh Shabir Guha Saikat Weedbrook Christian Vitali David Shapiro Jeffrey H Pirandola Stefano 2015 02 27 Microwave Quantum Illumination Physical Review Letters 114 8 080503 arXiv 1503 00189 Bibcode 2015PhRvL 114h0503B doi 10 1103 physrevlett 114 080503 ISSN 0031 9007 PMID 25768743 S2CID 119189135 Quantum Mechanics Could Improve Radar Physics 8 18 2015 1 Wilde Mark M Tomamichel Marco Berta Mario Lloyd Seth 2017 Gaussian hypothesis testing and quantum illumination Physical Review Letters American Physical Society APS 119 12 120501 arXiv 1608 06991 Bibcode 2017PhRvL 119l0501W doi 10 1103 PhysRevLett 119 120501 PMID 29341649 S2CID 1949571 Zhuang Quntao Zhang Zheshen Shapiro Jeffrey H 2017 01 27 Optimum Mixed State Discrimination for Noisy Entanglement Enhanced Sensing Physical Review Letters 118 4 040801 arXiv 1609 01968 Bibcode 2017PhRvL 118d0801Z doi 10 1103 PhysRevLett 118 040801 PMID 28186814 S2CID 206284828 Zhuang Quntao Zhang Zheshen Shapiro Jeffrey H 2017 08 15 Quantum illumination for enhanced detection of Rayleigh fading targets Physical Review A 96 2 020302 arXiv 1706 05561 Bibcode 2017PhRvA 96b0302Z doi 10 1103 PhysRevA 96 020302 S2CID 56098241 Nair Ranjith Gu Mile 2020 07 20 Fundamental limits of quantum illumination Optica 7 7 771 774 arXiv 2002 12252 Bibcode 2020Optic 7 771N doi 10 1364 OPTICA 391335 ISSN 2334 2536 S2CID 211532448 Shapiro Jeffrey H 2009 08 17 Defeating passive eavesdropping with quantum illumination Physical Review A American Physical Society APS 80 2 022320 arXiv 0904 2490 Bibcode 2009PhRvA 80b2320S doi 10 1103 physreva 80 022320 ISSN 1050 2947 S2CID 56094608 Pirandola Stefano Mancini Stefano Lloyd Seth Braunstein Samuel L 2008 07 11 Continuous variable quantum cryptography using two way quantum communication Nature Physics Springer Science and Business Media LLC 4 9 726 730 arXiv quant ph 0611167 Bibcode 2008NatPh 4 726P doi 10 1038 nphys1018 ISSN 1745 2473 S2CID 12062818 Lopaeva E D Ruo Berchera I Degiovanni I P Olivares S Brida G Genovese M 2013 04 10 Experimental Realization of Quantum Illumination Physical Review Letters 110 15 153603 arXiv 1303 4304 Bibcode 2013PhRvL 110o3603L doi 10 1103 physrevlett 110 153603 ISSN 0031 9007 PMID 25167266 S2CID 636404 Zhang Zheshen Tengner Maria Zhong Tian Wong Franco N C Shapiro Jeffrey H 2013 07 01 Entanglement s Benefit Survives an Entanglement Breaking Channel Physical Review Letters American Physical Society APS 111 1 010501 arXiv 1303 5343 Bibcode 2013PhRvL 111a0501Z doi 10 1103 physrevlett 111 010501 ISSN 0031 9007 PMID 23862986 S2CID 6269724 Zhang Zheshen Mouradian Sara Wong Franco N C Shapiro Jeffrey H 2015 03 20 Entanglement Enhanced Sensing in a Lossy and Noisy Environment Physical Review Letters 114 11 110506 arXiv 1411 5969 Bibcode 2015PhRvL 114k0506Z doi 10 1103 physrevlett 114 110506 ISSN 0031 9007 PMID 25839252 S2CID 15101562 Quantum sensor s advantages survive entanglement breakdown MIT News 9 March 2015 2 Barzanjeh S Pirandola S Vitali D Fink J M 2020 Microwave quantum illumination using a digital receiver Science Advances 6 19 eabb0451 arXiv 1908 03058 Bibcode 2020SciA 6 451B doi 10 1126 sciadv abb0451 ISSN 2375 2548 PMC 7272231 PMID 32548249 Quantum radar has been demonstrated for the first time MIT Technology Review Retrieved 2020 06 15 England Duncan G Balaji Bhashyam Sussman Benjamin J 2019 02 19 Quantum enhanced standoff detection using correlated photon pairs Physical Review A 99 2 023828 arXiv 1811 04113 Bibcode 2019PhRvA 99b3828E doi 10 1103 PhysRevA 99 023828 S2CID 53616393 Defienne H Reichert M Fleischer J Faccio D 2019 Quantum image distillation Science Advances 5 10 eaax0307 arXiv 1907 06526 Bibcode 2019SciA 5 307D doi 10 1126 sciadv aax0307 ISSN 2375 2548 PMC 6799981 PMID 31667343 Gregory T Moreau P A Toninelli E Padgett M J 2020 Imaging through noise with quantum illumination Science Advances 6 6 eaay2652 arXiv 1907 09370 Bibcode 2020SciA 6 2652G doi 10 1126 sciadv aay2652 PMC 7007263 PMID 32083179 Broken quantum links still work Nature Springer Science and Business Media LLC 499 7457 129 2013 doi 10 1038 499129a ISSN 0028 0836 Lisa Grossman July 17 2013 Fragility of entanglement no bar to quantum secrets New Scientist Retrieved 16 Nov 2019 Retrieved from https en wikipedia org w index php title Quantum illumination amp oldid 1188916266, wikipedia, wiki, book, books, library,

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