Fetching the paper…
Reading the bibliography…
We consider a variant of the phase retrieval problem, where vectors are replaced by unitary matrices, i.e., the unknown signal is a unitary matrix U, and the measurements consist of squared inner products |Tr(C*U)|^2 with unitary matrices C that are chosen by the observer.
R. P. Millane, “Phase retrieval in crystallography and optics,” J. Optical Society of America A
1990
Earlier work this paper cites.
Stabilizer codes and quantum error correction
D. Gottesman · 1997
Earlier work this paper cites.
Quantum data hiding
D. P. DiVincenzo, D. W. Leung, and B. M. Terhal · 2002
Earlier work this paper cites.
Lectures on Discrete Geometry
J. Matousek · 2002
Earlier work this paper cites.
Moments and cumulants of polynomial random variables on unitary groups, the itzykson-zuber integral and free probability
B. Collins · 2003
Earlier work this paper cites.
A. Ambainis and A. D. Smith, “Small Pseudo-random Families of Matrices: Derandomizing Approximate Quantum Encryption,” Proc. APPROX-RANDOM 2004
2004
Earlier work this paper cites.
Integration with respect to the haar measure on unitary, orthogonal and symplectic group
B. Collins and P. Sniady · 2006
Earlier work this paper cites.
Entanglement and the foundations of statistical mechanics
S. Popescu, A. J. Short, and A. Winter · 2006
Earlier work this paper cites.
J. Emerson et al, “Symmetrised Characterisation of Noisy Quantum Processes,” Science
2007
Earlier work this paper cites.
A. Ambainis and J. Emerson, “Quantum t-designs: t-wise independence in the quantum world,” Twenty-Second Annual IEEE Conference on Computational Complexity (CCC’07)
2007
Earlier work this paper cites.
D. Gross, K. Audenaert and J. Eisert, “Evenly distributed unitaries: on the structure of unitary designs,” J. Math. Phys
2007
Earlier work this paper cites.
Optimizing quantum process tomography with unitary 2-designs
A. J. Scott · 2008
Earlier work this paper cites.
Randomized benchmarking of quantum gates
E. Knill, et al · 2008
Earlier work this paper cites.
R. Balan, B. G. Bodmann, P. G. Casazza, and D. Edidin. Painless reconstruction from magnitudes of frame coefficients. J. Fourier Anal. Appl
2009
Earlier work this paper cites.
C.B. Mendl and M.M. Wolf, “Unital Quantum Channels - Convex Structure and Revivals of Birkhoff’s Theorem,” Commun. Math. Phys
2009
Earlier work this paper cites.
Exact and approximate unitary 2-designs and their application to fidelity estimation
C. Dankert, R. Cleve, J. Emerson, and E. Livine · 2009
Earlier work this paper cites.
Exact matrix completion via convex optimization
E. J. Candes and B. Recht · 2009
Earlier work this paper cites.
Large deviation bounds for k-designs
R. A. Low · 2009
Earlier work this paper cites.
Quantum state tomography via compressed sensing
D. Gross, Y.-K. Liu, S. T. Flammia, S. Becker, and J. Eisert · 2010
Cited alongside, same era.
R. A. Low, Pseudo-randomness and Learning in Quantum Computation
2010
Cited alongside, same era.
Efficient quantum state tomography
M. Cramer et al · 2010
Cited alongside, same era.
Universal low-rank matrix recovery from pauli measurements
Y.-K. Liu · 2011
Cited alongside, same era.
Recovering low-rank matrices from few coefficients in any basis
D. Gross · 2011
Cited alongside, same era.
Efficient measurement of quantum dynamics via compressive sensing
A. Shabani, et al · 2011
Cited alongside, same era.
Self-consistent tomography of the state-measurement gram matrix
C. Stark · 2014
Later among the works it cites.
Quantum process tomography of unitary and near-unitary maps
Charles H. Baldwin, Amir Kalev, and Ivan H. Deutsch · 2014
Later among the works it cites.
Robust extraction of tomographic information via randomized benchmarking
S. Kimmel, M. P. da Silva, C. A. Ryan, B. R. Johnson, and T. Ohki · 2014
Later among the works it cites.
Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao and M. Segev, “Phase Retrieval with Application to Optical Imaging: A contemporary overview,” IEEE Signal Processing Magazine
2015
Closest in time.
A partial derandomization of phaselift using spherical designs
D. Gross, F. Krahmer, and R. Kueng · 2015
Closest in time.
Near-linear constructions of exact unitary 2-designs
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
A. Shabani, M. Mohseni, S. Lloyd, R. L. Kosut, and H. Rabitz · 2011
Cited alongside, same era.
Scalable and robust randomized benchmarking of quantum processes
E. Magesan, J. M. Gambetta, and J. Emerson · 2011
Cited alongside, same era.
Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators
S. T Flammia, D. Gross, Y.-K. Liu, and J. Eisert · 2012
Cited alongside, same era.
Restricted strong convexity and weighted matrix completion: Optimal bounds with noise
S. Negahban and M. J. Wainwright · 2012
Cited alongside, same era.
Efficient measurement of quantum gate error by interleaved randomized benchmarking
Easwar Magesan, et al · 2012
Cited alongside, same era.
Compressed sensing: theory and applications
R. Vershynin · 2012
Cited alongside, same era.
R. Cleve, D. Leung, L. Liu, and C. Wang · 2015
Closest in time.
Qubit stabilizer states are complex projective 3-designs
R. Kueng and D. Gross · 2015
Closest in time.
The clifford group forms a unitary 3-design
Z. Webb · 2015
Closest in time.
Multiqubit clifford groups are unitary 3-designs
H. Zhu · 2015
Closest in time.
Bounding the Smallest Singular Value of a Random Matrix Without Concentration
V. Koltchinskii and S. Mendelson · 2015
Closest in time.
Learning without Concentration
S. Mendelson · 2015
Closest in time.
Convex recovery of a structured signal from independent random linear measurements
J. A. Tropp · 2015
Closest in time.
Introduction to quantum gate set tomography
D. Greenbaum · 2015
Closest in time.
Informationally complete measurements from compressed sensing methodology
A. Kalev, R. L. Kosut, and I. H. Deutsch · 2015
Closest in time.
Demonstration of robust quantum gate tomography via randomized benchmarking
Blake R Johnson, et al · 2015
Closest in time.
E. Candes, X. Li and M. Soltanolkotabi, “Phase Retrieval via Wirtinger Flow: Theory and Algorithms,” IEEE Trans. Info. Theory
2015
Closest in time.
Low rank matrix recovery from rank one measurements. Applied and Comput. Harmonic Analysis
R. Kueng, H. Rauhut, and U. Terstiege · 2017
Closest in time.