Built on

Scott Aaronson and Guy N Rothblum, Gentle measurement of quantum states and differential privacy , Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, pp. 322–333, 2019, 1904.08747
Original
1904
Earlier work this paper cites.
C Greganti, TF Demarie, M Ringbauer, JA Jones, V Saggio, I Alonso Calafell, LA Rozema, A Erhard, M Meth, L Postler, et al., Cross-verification of independent quantum devices , Physical Review X 11
Original
1905
Earlier work this paper cites.
Andreas Elben, Benoît Vermersch, Rick van Bijnen, Christian Kokail, Tiff Brydges, Christine Maier, Manoj K Joshi, Rainer Blatt, Christian F Roos, and Peter Zoller, Cross-platform verification of intermediate scale quantum devices , Physical Review Letters 124
Original
1909
Earlier work this paper cites.
Jens Eisert, Dominik Hangleiter, Nathan Walk, Ingo Roth, Damian Markham, Rhea Parekh, Ulysse Chabaud, and Elham Kashefi, Quantum certification and benchmarking , Nature Reviews Physics 2
Original
1910
Earlier work this paper cites.
Carl W Helstrom, Quantum detection and estimation theory , Journal of Statistical Physics 1
1969
Earlier work this paper cites.
Zdenek Hradil, Quantum state estimation , Physical Review A 55
1997
Earlier work this paper cites.
Bin Yu, Assouad, fano, and le cam , Festschrift for Lucien Le Cam: research papers in probability and statistics (1997)
1997
Earlier work this paper cites.
Charles H Bennett, David P DiVincenzo, Christopher A Fuchs, Tal Mor, Eric Rains, Peter W Shor, John A Smolin, and William K Wootters, Quantum nonlocality without entanglement , Physical Review A 59
1999
Earlier work this paper cites.
Hartmut Klauck, Ashwin Nayak, Amnon Ta-Shma, and David Zuckerman, Interaction in quantum communication and the complexity of set disjointness , Proceedings of the thirty-third annual ACM symposium on Theory of computing, pp. 124–133, 2001
2001
Earlier work this paper cites.
Artur K. Ekert, Carolina Moura Alves, Daniel K. L. Oi, Michał Horodecki, Paweł Horodecki, and L. C. Kwek, Direct estimations of linear and nonlinear functionals of a quantum state , Phys. Rev. Lett. 88
2002
Earlier work this paper cites.
Hsin-Yuan Huang, Richard Kueng, and John Preskill, Predicting many properties of a quantum system from very few measurements , Nature Physics 16
Original
2002
Earlier work this paper cites.
Sebastien Bubeck, Sitan Chen, and Jerry Li, Entanglement is necessary for optimal quantum property testing , 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS), pp. 692–703, IEEE, 2020, 2004.07869
Original
2004
Earlier work this paper cites.
Hartmut Klauck, Quantum and classical communication-space tradeoffs from rectangle bounds , FSTTCS 2004: Foundations of Software Technology and Theoretical Computer Science: 24th International Conference, Chennai, India, December 16-18, 2004. Proceedings 24, pp. 384–395, Springer, 2005, quant-ph/0412088
2005
Earlier work this paper cites.
Patrick Hayden, Debbie W Leung, and Andreas Winter, Aspects of generic entanglement , Communications in mathematical physics 265
2006
Earlier work this paper cites.
Paul Magnard, Simon Storz, Philipp Kurpiers, Josua Schär, Fabian Marxer, Janis Lütolf, Theo Walter, J-C Besse, Mihai Gabureac, Kevin Reuer, et al., Microwave quantum link between superconducting circuits housed in spatially separated cryogenic systems , Physical Review Letters 125
Original
2008
Earlier work this paper cites.
Eric Chitambar and Runyao Duan, Nonlocal entanglement transformations achievable by separable operations , Physical Review Letters 103
Original
2009
Earlier work this paper cites.
Robin Blume-Kohout, Optimal, reliable estimation of quantum states , New Journal of Physics 12
2010
Earlier work this paper cites.
Giulio Chiribella, On quantum estimation, quantum cloning and finite quantum de finetti theorems , Conference on Quantum Computation, Communication, and Cryptography, pp. 9–25, Springer, 2010, 1010.1875
Original
2010
Earlier work this paper cites.
David Gross, Yi-Kai Liu, Steven T Flammia, Stephen Becker, and Jens Eisert, Quantum state tomography via compressed sensing , Physical Review Letters 105
Original
2010
Earlier work this paper cites.
Costin B 𝐮 \mathbf{u} adescu and Ryan O’Donnell, Improved quantum data analysis , Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing, pp. 1398–1411, 2021, 2011.10908
Original
2011
Earlier work this paper cites.
Marcus P da Silva, Olivier Landon-Cardinal, and David Poulin, Practical characterization of quantum devices without tomography , Physical Review Letters 107
Original
2011
Earlier work this paper cites.
Steven T Flammia and Yi-Kai Liu, Direct fidelity estimation from few pauli measurements , Physical Review Letters 106
Original
2011
Earlier work this paper cites.
Guillaume Aubrun, Partial transposition of random states and non-centered semicircular distributions , Random Matrices: Theory and Applications 1
2012
Earlier work this paper cites.

Similar

Konrad Banaszek, Marcus Cramer, and David Gross, Focus on quantum tomography , New Journal of Physics 15
2013
Cited alongside, same era.
Aram Harrow, The church of the symmetric subspace , arXiv:1308.6595 (2013), 1308.06595
Original
2013
Cited alongside, same era.
Guillaume Aubrun, Stanislaw J Szarek, and Deping Ye, Entanglement thresholds for random induced states , Communications on Pure and Applied Mathematics 67
2014
Cited alongside, same era.
Jeongwan Haah, Aram W Harrow, Zhengfeng Ji, Xiaodi Wu, and Nengkun Yu, Sample-optimal tomography of quantum states , Proceedings of the Forty-eighth Annual ACM Symposium on Theory of Computing, pp. 913–925, 2016, 1508.01797
Original
2016
Cited alongside, same era.
Ryan O’Donnell and John Wright, Efficient quantum tomography , Proceedings of the forty-eighth annual ACM symposium on Theory of Computing, pp. 899–912, 2016, 1508.01907

Then

Hsin-Yuan Huang, Richard Kueng, Giacomo Torlai, Victor V Albert, and John Preskill, Provably efficient machine learning for quantum many-body problems , Science 377
Original
2022
Later among the works it cites.
Daiwei Zhu, Ze-Pei Cian, Crystal Noel, Andrew Risinger, Debopriyo Biswas, Laird Egan, Yingyue Zhu, Alaina M Green, C Huerta Alderete, Nhung H Nguyen, et al., Cross-platform comparison of arbitrary quantum states , Nature communications 13
Original
2022
Later among the works it cites.
Anurag Anshu and Srinivasan Arunachalam, A survey on the complexity of learning quantum states , Nature Reviews Physics (2023), 2305.20069
Original
2023
Later among the works it cites.
Sitan Chen and Weiyuan Gong, Efficient Pauli channel estimation with logarithmic quantum memory , arXiv:2309.14326 (2023), 2309.14326
Original
2023
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

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Reading the bibliography…

2024

On the sample complexity of purity and inner product estimation

Gong, Weiyuan, Haferkamp, Jonas, Ye, Qi et al.

Understand

We study the sample complexity of the prototypical tasks quantum purity estimation and quantum inner product estimation.

In purity estimation, we are to estimate $tr(\rho^2)$ of an unknown quantum state $\rho$ to additive error $\epsilon$.
Meanwhile, for quantum inner product estimation, Alice and Bob are to estimate $tr(\rho\sigma)$ to additive error $\epsilon$ given copies of unknown quantum state $\rho$ and $\sigma$ using classical communication and restricted quantum communication.
In this paper, we show a strong connection between the sample complexity of purity estimation with bounded quantum memory and inner product estimation with bounded quantum communication and unentangled measurements.

Built on

Scott Aaronson and Guy N Rothblum, Gentle measurement of quantum states and differential privacy , Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, pp. 322–333, 2019, 1904.08747
Original
1904
Earlier work this paper cites.
C Greganti, TF Demarie, M Ringbauer, JA Jones, V Saggio, I Alonso Calafell, LA Rozema, A Erhard, M Meth, L Postler, et al., Cross-verification of independent quantum devices , Physical Review X 11
Original
1905
Earlier work this paper cites.
Andreas Elben, Benoît Vermersch, Rick van Bijnen, Christian Kokail, Tiff Brydges, Christine Maier, Manoj K Joshi, Rainer Blatt, Christian F Roos, and Peter Zoller, Cross-platform verification of intermediate scale quantum devices , Physical Review Letters 124
Original
1909
Earlier work this paper cites.
Jens Eisert, Dominik Hangleiter, Nathan Walk, Ingo Roth, Damian Markham, Rhea Parekh, Ulysse Chabaud, and Elham Kashefi, Quantum certification and benchmarking , Nature Reviews Physics 2
Original
1910
Earlier work this paper cites.
Carl W Helstrom, Quantum detection and estimation theory , Journal of Statistical Physics 1
1969
Earlier work this paper cites.
Zdenek Hradil, Quantum state estimation , Physical Review A 55
1997
Earlier work this paper cites.
Bin Yu, Assouad, fano, and le cam , Festschrift for Lucien Le Cam: research papers in probability and statistics (1997)
1997
Earlier work this paper cites.
Charles H Bennett, David P DiVincenzo, Christopher A Fuchs, Tal Mor, Eric Rains, Peter W Shor, John A Smolin, and William K Wootters, Quantum nonlocality without entanglement , Physical Review A 59
1999
Earlier work this paper cites.
Hartmut Klauck, Ashwin Nayak, Amnon Ta-Shma, and David Zuckerman, Interaction in quantum communication and the complexity of set disjointness , Proceedings of the thirty-third annual ACM symposium on Theory of computing, pp. 124–133, 2001
2001
Earlier work this paper cites.
Artur K. Ekert, Carolina Moura Alves, Daniel K. L. Oi, Michał Horodecki, Paweł Horodecki, and L. C. Kwek, Direct estimations of linear and nonlinear functionals of a quantum state , Phys. Rev. Lett. 88
2002
Earlier work this paper cites.
Hsin-Yuan Huang, Richard Kueng, and John Preskill, Predicting many properties of a quantum system from very few measurements , Nature Physics 16
Original
2002
Earlier work this paper cites.
Sebastien Bubeck, Sitan Chen, and Jerry Li, Entanglement is necessary for optimal quantum property testing , 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS), pp. 692–703, IEEE, 2020, 2004.07869
Original
2004
Earlier work this paper cites.
Hartmut Klauck, Quantum and classical communication-space tradeoffs from rectangle bounds , FSTTCS 2004: Foundations of Software Technology and Theoretical Computer Science: 24th International Conference, Chennai, India, December 16-18, 2004. Proceedings 24, pp. 384–395, Springer, 2005, quant-ph/0412088
2005
Earlier work this paper cites.
Patrick Hayden, Debbie W Leung, and Andreas Winter, Aspects of generic entanglement , Communications in mathematical physics 265
2006
Earlier work this paper cites.
Paul Magnard, Simon Storz, Philipp Kurpiers, Josua Schär, Fabian Marxer, Janis Lütolf, Theo Walter, J-C Besse, Mihai Gabureac, Kevin Reuer, et al., Microwave quantum link between superconducting circuits housed in spatially separated cryogenic systems , Physical Review Letters 125
Original
2008
Earlier work this paper cites.
Eric Chitambar and Runyao Duan, Nonlocal entanglement transformations achievable by separable operations , Physical Review Letters 103
Original
2009
Earlier work this paper cites.
Robin Blume-Kohout, Optimal, reliable estimation of quantum states , New Journal of Physics 12
2010
Earlier work this paper cites.
Giulio Chiribella, On quantum estimation, quantum cloning and finite quantum de finetti theorems , Conference on Quantum Computation, Communication, and Cryptography, pp. 9–25, Springer, 2010, 1010.1875
Original
2010
Earlier work this paper cites.
David Gross, Yi-Kai Liu, Steven T Flammia, Stephen Becker, and Jens Eisert, Quantum state tomography via compressed sensing , Physical Review Letters 105
Original
2010
Earlier work this paper cites.
Costin B 𝐮 \mathbf{u} adescu and Ryan O’Donnell, Improved quantum data analysis , Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing, pp. 1398–1411, 2021, 2011.10908
Original
2011
Earlier work this paper cites.
Marcus P da Silva, Olivier Landon-Cardinal, and David Poulin, Practical characterization of quantum devices without tomography , Physical Review Letters 107
Original
2011
Earlier work this paper cites.
Steven T Flammia and Yi-Kai Liu, Direct fidelity estimation from few pauli measurements , Physical Review Letters 106
Original
2011
Earlier work this paper cites.
Guillaume Aubrun, Partial transposition of random states and non-centered semicircular distributions , Random Matrices: Theory and Applications 1
2012
Earlier work this paper cites.

Similar

Konrad Banaszek, Marcus Cramer, and David Gross, Focus on quantum tomography , New Journal of Physics 15
2013
Cited alongside, same era.
Aram Harrow, The church of the symmetric subspace , arXiv:1308.6595 (2013), 1308.06595
Original
2013
Cited alongside, same era.
Guillaume Aubrun, Stanislaw J Szarek, and Deping Ye, Entanglement thresholds for random induced states , Communications on Pure and Applied Mathematics 67
2014
Cited alongside, same era.
Jeongwan Haah, Aram W Harrow, Zhengfeng Ji, Xiaodi Wu, and Nengkun Yu, Sample-optimal tomography of quantum states , Proceedings of the Forty-eighth Annual ACM Symposium on Theory of Computing, pp. 913–925, 2016, 1508.01797
Original
2016
Cited alongside, same era.
Ryan O’Donnell and John Wright, Efficient quantum tomography , Proceedings of the forty-eighth annual ACM symposium on Theory of Computing, pp. 899–912, 2016, 1508.01907

Then

Hsin-Yuan Huang, Richard Kueng, Giacomo Torlai, Victor V Albert, and John Preskill, Provably efficient machine learning for quantum many-body problems , Science 377
Original
2022
Later among the works it cites.
Daiwei Zhu, Ze-Pei Cian, Crystal Noel, Andrew Risinger, Debopriyo Biswas, Laird Egan, Yingyue Zhu, Alaina M Green, C Huerta Alderete, Nhung H Nguyen, et al., Cross-platform comparison of arbitrary quantum states , Nature communications 13
Original
2022
Later among the works it cites.
Anurag Anshu and Srinivasan Arunachalam, A survey on the complexity of learning quantum states , Nature Reviews Physics (2023), 2305.20069
Original
2023
Later among the works it cites.
Sitan Chen and Weiyuan Gong, Efficient Pauli channel estimation with logarithmic quantum memory , arXiv:2309.14326 (2023), 2309.14326
Original
2023
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Original

2016

Cited alongside, same era.

Ingemar Bengtsson and Karol Życzkowski, Geometry of quantum states: an introduction to quantum entanglement , Cambridge university press, 2017

2017

Cited alongside, same era.

Ronald Lewis Graham, Donald Ervin Knuth, and Oren Patashnik, Concrete mathematics: A foundation for computer science , 2. ed., 31. print ed., Addison-Wesley, 2017

2017

Cited alongside, same era.

Scott Aaronson, Shadow tomography of quantum states , Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, pp. 325–338, 2018, 1711.01053

Original

2018

Cited alongside, same era.

Scott Aaronson, Xinyi Chen, Elad Hazan, Satyen Kale, and Ashwin Nayak, Online learning of quantum states , Advances in neural information processing systems, vol. 31, 2018, 1802.09025

Original

2018

Cited alongside, same era.

Philipp Kurpiers, Paul Magnard, Theo Walter, Baptiste Royer, Marek Pechal, Johannes Heinsoo, Yves Salathé, Abdulkadir Akin, Simon Storz, J-C Besse, et al., Deterministic quantum state transfer and remote entanglement using microwave photons , Nature 558

Original