Fetching the paper…
Reading the bibliography…
We consider the problem of quantum state certification, where one is given $n$ copies of an unknown $d$-dimensional quantum mixed state $\rho$, and one wants to test whether $\rho$ is equal to some known mixed state $\sigma$ or else is $\epsilon$-far from $\sigma$.
Some characters of the symmetric group
Richard Ingram · 1950
Earlier work this paper cites.
A generalized Schwarz inequality and algebraic invariants for operator algebras
Richard Kadison · 1952
Earlier work this paper cites.
Quantum Detection and Estimation Theory
Carl Helstrom · 1976
Earlier work this paper cites.
The “transition probability” in the state space of a ∗ * -algebra
Armin Uhlmann · 1976
Earlier work this paper cites.
Symmetry properties of product states for the system of N N n n -level atoms
Robert Alicki, Sławomir Rudnicki, and Sławomir Sadowski · 1988
Earlier work this paper cites.
Statistical distance and the geometry of quantum states
Samuel Braunstein and Carlton Caves · 1994
Earlier work this paper cites.
On the complexity of computing characters of finite groups
Charles Hepler · 1994
Earlier work this paper cites.
Mathematical techniques for quantum communication theory
Christopher Fuchs and Carlton Caves · 1995
Earlier work this paper cites.
Monotone metrics on matrix spaces
Dénes Petz · 1996
Earlier work this paper cites.
Shifted Schur functions
Andrei Okounkov and Grigori Olshanski · 1998
Earlier work this paper cites.
On testing expansion in bounded-degree graphs
Oded Goldreich and Dana Ron · 2000
Earlier work this paper cites.
Testing random variables for independence and identity
Tuğkan Batu, Eldar Fischer, Lance Fortnow, Ravi Kumar, Ronitt Rubinfeld, and Patrick White · 2001
Earlier work this paper cites.
The algebra of conjugacy classes in symmetric groups and partial permutations
Vladimir Ivanov and Sergei Kerov · 2001
Earlier work this paper cites.
Estimating the spectrum of a density operator
Michael Keyl and Reinhard Werner · 2001
Earlier work this paper cites.
On choosing and bounding probability metrics
Alison Gibbs and Francis Su · 2002
Earlier work this paper cites.
Quantum universal variable-length source coding
Masahito Hayashi and Keiji Matsumoto · 2002
Earlier work this paper cites.
Kerov’s central limit theorem for the Plancherel measure on Young diagrams
Vladimir Ivanov and Grigori Olshanski · 2002
Earlier work this paper cites.
The quantum Schur transform: I. efficient qudit circuits
Dave Bacon, Isaac Chuang, and Aram Harrow · 2005
Earlier work this paper cites.
Distance measures to compare real and ideal quantum processes
Alexei Gilchrist, Nathan Langford, and Michael Nielsen · 2005
Cited alongside, same era.
Applications of coherent classical communication and the Schur transform to quantum information theory
Aram Harrow · 2005
Cited alongside, same era.
Scalable multiparticle entanglement of trapped ions
Hartmut Häffner, Wolfgang Hänsel, Christian Roos, Jan Benhelm, Michael Chwalla, Timo Körber, Umakant Rapol, Mark Riebe, Piet Schmidt, Christoph Becher, Otfried Günhe, Wolfgang Dür, and Rainer Blatt · 2005
Cited alongside, same era.
The spectra of quantum states and the Kronecker coefficients of the symmetric group
Matthias Christandl and Graeme Mitchison · 2006
Cited alongside, same era.
Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
Benoît Collins and Piotr Śniady · 2006
Cited alongside, same era.
Reliable quantum certification of photonic state preparations
Leandro Aolita, Christian Gogolin, Martin Kliesch, and Jens Eisert · 2015
Later among the works it cites.
A survey on distribution testing: Your data is big. But is it blue?
Clément Canonne · 2015
Later among the works it cites.
On learning distributions from their samples
Sudeep Kamath, Alon Orlitsky, Dheeraj Pichapati, and Ananda Theertha Suresh · 2015
Later among the works it cites.
Quantum spectrum testing
Ryan O’Donnell and John Wright · 2015
Later among the works it cites.
Quantum chi-squared and goodness of fit testing
Kristan Temme and Frank Verstraete · 2015
Later among the works it cites.
Collision-based testers are optimal for uniformity and closeness
Ilias Diakonikolas, Themis Gouleakis, John Peebles, and Eric Price · 2016
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Ingemar Bengtsson and Karol Życzkowski · 2007
Cited alongside, same era.
Weak Fourier-Schur sampling, the hidden subgroup problem, and the quantum collision problem
Andrew Childs, Aram Harrow, and Paweł Wocjan · 2007
Cited alongside, same era.
Asymptotic error rates in quantum hypothesis testing
Koenraad Audenaert, Michael Nussbaum, Arleta Szkoła, and Frank Verstraete · 2008
Cited alongside, same era.
A coincidence-based test for uniformity given very sparsely sampled discrete data
Liam Paninski · 2008
Cited alongside, same era.
Sublinear estimation of entropy and information distances
Sudipto Guha, Andrew McGregor, and Suresh Venkatasubramanian · 2009
Cited alongside, same era.
Symmetry, representations, and invariants
Roe Goodman and Nolan Wallach · 2009
Cited alongside, same era.
The χ 2 \chi^{2} -divergence and mixing times of quantum Markov processes
Kristan Temme, Michael Kastoryano, Mary Ruskai, Michael Wolf, and Frank Verstraete · 2010
Cited alongside, same era.
A new approach for testing properties of discrete distributions
Ilias Diakonikolas and Daniel Kane · 2016
Later among the works it cites.
Sample-optimal tomography of quantum states
Jeongwan Haah, Aram Harrow, Zhengfeng Ji, Xiaodi Wu, and Nengkun Yu · 2016
Later among the works it cites.
A Survey of Quantum Property Testing
Ashley Montanaro and Ronald de Wolf · 2016
Later among the works it cites.
Efficient quantum tomography
Ryan O’Donnell and John Wright · 2016
Later among the works it cites.
Distribution testing lower bounds via reductions from communication complexity
Eric Blais, Clément Canonne, and Tom Gur · 2017
Closest in time.
On measures of entropy and information
Gavin Crooks · 2017
Closest in time.
Which distribution distances are sublinearly testable?
Constantinos Daskalakis, Gautam Kamath, and John Wright · 2017
Closest in time.
Different quantum f f -divergences and the reversibility of quantum operations
Fumio Hiai and Milán Mosonyi · 2017
Closest in time.
Efficient quantum tomography II
Ryan O’Donnell and John Wright · 2017
Closest in time.
On the complexity of computing Kronecker coefficients
Igor Pak and Greta Panova · 2017
Closest in time.
An automatic inequality prover and instance optimal identity testing
Gregory Valiant and Paul Valiant · 2017
Closest in time.
Lecture notes for ECE598YW: Information-theoretic methods for high-dimensional statistics, 2017
Yihong Wu · 2017
Closest in time.