Fetching the paper…
Reading the bibliography…
We describe a graphical calculus for completely positive maps and in doing so review the theory of open quantum systems and other fundamental primitives of quantum information theory using the language of tensor networks.
Positive functions on C*-algebras
W. F. Stinespring · 1955
Earlier work this paper cites.
Dynamical Mappings of Density Operators in Quantum Mechanics
T. F. Jordan and E. C. G. Sudarshan · 1961
Earlier work this paper cites.
Applications of negative dimensional tensors
R. Penrose · 1971
Earlier work this paper cites.
Linear transformations which preserve trace and positive semidefiniteness of operators
A. Jamiołkowski · 1972
Earlier work this paper cites.
Completely Positive Linear Maps on Complex Matrices
M. D. Choi · 1975
Earlier work this paper cites.
Coherence for compact closed categories
G. M. Kelly and M. L. Laplaza · 1980
Earlier work this paper cites.
States, Effects and Operations: Fundamental Notions of Quantum Theory
K. Kraus · 1983
Earlier work this paper cites.
Matrix Analysis
R. A. Horn and C. R. Johnson · 1985
Earlier work this paper cites.
The geometry of tensor calculus i
R. Joyal and A. Street · 1991
Earlier work this paper cites.
Sending entanglement through noisy quantum channels
B. Schumacher · 1996
Earlier work this paper cites.
General teleportation channel, singlet fraction, and quasidistillation
M. Horodecki, P. Horodecki, and R. Horodecki · 1999
Earlier work this paper cites.
Quantum Computation and Quantum Information
M. A. Nielsen and I. L. Chuang · 2000
Earlier work this paper cites.
Quantum tomography for measuring experimentally the matrix elements of an arbitrary quantum operation
G. M. D’Ariano and P. Lo Presti · 2001
Earlier work this paper cites.
A simple formula for the average gate fidelity of a quantum dynamical operation
M. A. Nielsen · 2002
Earlier work this paper cites.
Ancilla-assisted quantum process tomography
J. B. Altepeter, D. Branning, E. Jeffrey, T. C. Wei, P. G. Kwiat, R.T. Thew, J. L. O’Brien, M. A. Nielsen, and A. G. White · 2003
Cited alongside, same era.
Imprinting complete information about a quantum channel on its output state
G. M. D’Ariano and P. Lo Presti · 2003
Cited alongside, same era.
A categorical semantics of quantum protocols
S. Abramsky and B. Coecke · 2004
Cited alongside, same era.
Quantum process tomography of the quantum Fourier transform
Y. S. Weinstein, T. F. Havel, J. Emerson, N. Boulant, M. Saraceno, S. Lloyd, and D. G. Cory · 2004
Cited alongside, same era.
Scalable noise estimation with random unitary operators
J. Emerson, R. Alicki, and K. Życzkowski · 2005
Cited alongside, same era.
Geometry of Quantum States
I. Bengtsson and K. Życzkowski · 2006
Cited alongside, same era.
B. Collins and I. Nechita · 2009
Later among the works it cites.
Vectorization of quantum operations and its use
A. Gilchrist, D. R. Terno, and C. J. Wood · 2009
Later among the works it cites.
Categorical Tensor Network States
J. D. Biamonte, S. R. Clark, and D. Jaksch · 2010
Later among the works it cites.
Random Quantum Channels I: Graphical Calculus and the Bell State Phenomenon
B. Collins and I. Nechita · 2010
Later among the works it cites.
Categorical Quantum Circuits
V. Bergholm and J. D. Biamonte · 2011
Closest in time.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Dagger Compact Closed Categories and Completely Positive Maps::(Extended Abstract)
P. Selinger · 2007
Cited alongside, same era.
Optimum quantum error recovery using semidefinite programming
A. S. Fletcher, P. W. Shor, and M. Z. Win · 2007
Cited alongside, same era.
Class of quantum many-body states that can be efficiently simulated
G. Vidal · 2008
Cited alongside, same era.
Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems
F. Verstraete, V. Murg, and J. I. Cirac · 2008
Cited alongside, same era.
Dynamics beyond completely positive maps: Some properties and applications
H. A. Carteret, D. R. Terno, and K. Życzkowski · 2008
Cited alongside, same era.
A Prehistory of n-Categorical Physics
J. C. Baez and A. Lauda · 2009
Cited alongside, same era.
Finite Dimensional Hilbert Spaces are Complete for Dagger Compact Closed Categories (Extended Abstract)
P. Selinger · 2011
Closest in time.
Picturing classical and quantum Bayesian inference
B. Coecke and R. W. Spekkens · 2011
Closest in time.
Pictures of complete positivity in arbitrary dimension
B. Coecke and C. Heunen · 2011
Closest in time.
A survey of graphical languages for monoidal categories
P. Selinger · 2011
Closest in time.
Informational derivation of quantum theory
G. Chiribella, Giacomo M. D’Ariano, G. M., and P. Perinotti · 2011
Closest in time.
Reformulating and Reconstructing Quantum Theory
L. Hardy · 2011
Closest in time.
Quantum gate fidelity in terms of choi matrices
N. Johnston and D. W. Kribs · 2011
Closest in time.
Gate fidelity fluctuations and quantum process invariants
E. Magesan, R. Blume-Kohout, and J. Emerson · 2011
Closest in time.
Entangled and sequential quantum protocols with dephasing
S. Boixo and C. Heunen · 2012
Closest in time.