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For all 1 < p < 2, we demonstrate the existence of quantum channels with non-multiplicative maximal p-norms.
Noise at optical frequencies; information theory
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The early days of information theory
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Information theoretical aspects of quantum measurements
A. S. Holevo · 1973
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E. Lubkin · 1978
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Completely bounded maps and dilations
V. I. Paulsen · 1986
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A new proof of the quantum noiseless coding theorem
R. Jozsa and B. Schumacher · 1994
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Quantum coding
B. Schumacher · 1995
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Classical information capacity of a quantum channel
P. Hausladen, R. Jozsa, B. Schumacher, M. Westmoreland, and W. K. Wootters · 1996
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Mixed-state entanglement and quantum error correction
C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters · 1996
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Sending classical information via noisy quantum channels
B. Schumacher and M. D. Westmoreland · 1997
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The capacity of the quantum channel with general signal states
A. S. Holevo · 1998
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Quantum coding theorems
A. S. Holevo · 1998
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On some additivity problems of quantum information theory
G. G. Amosov, A. S. Holevo, and R. F. Werner · 2000
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The asymptotic entanglement cost of preparing a quantum state
P. M. Hayden, M. Horodecki, and B. M. Terhal · 2001
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Entanglement measures under symmetry
K. G. H. Vollbrecht and R. F. Werner · 2001
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Minimal entropy of states emerging from noisy quantum channels
C. King and M. B. Ruskai · 2001
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Numerical experiments on the capacity of quantum channel with entangled input states
S. Osawa and H. Nagaoka · 2001
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On the multiplicativity conjecture for quantum channels
G. G. Amosov and A. S. Holevo · 2001
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Maximization of capacity and p-norms for some product channels
C. King · 2001
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Additivity of the classical capacity of entanglement-breaking quantum channels
P. W. Shor · 2002
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Entanglement cost of bipartite mixed states
G. Vidal, W. Dür, and J. I. Cirac · 2002
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Additivity for unital qubit channels
C. King · 2002
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Additivity of the capacity of depolarizing channels
A. Fujiwara and T. Hashizumé · 2002
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Comments on multiplicativity of maximal p-norms when p= 2
C. King and M. B. Ruskai · 2004
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Multiplicativity of maximal p-norms in Werner-Holevo channels for 1 < p < 2 1<p<2
N. Datta · 2004
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Invariant and group theoretical integrations over the U(n) group
S. Aubert and C. S. Lam · 2004
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The capacity of a quantum channel for simultaneous transmission of classical and quantum information
I. Devetak and P. W. Shor · 2005
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Properties of conjugate channels with applications to additivity and multiplicativity
C. King, K. Matsumoto, M. Nathanson, and M. B. Ruskai · 2005
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Extending additivity from symmetric to asymmetric channels
M. Fukuda · 2005
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R. F. Werner and A. S. Holevo · 2002
Cited alongside, same era.
Strong superadditivity of the entanglement of formation follows from its additivity
A. A. Pomeransky · 2003
Cited alongside, same era.
The capacity of the quantum depolarizing channel
C. King · 2003
Cited alongside, same era.
Maximal p p -norms of entanglement breaking channels
C. King · 2003
Cited alongside, same era.
Invariant integration over the unitary group
S. Aubert and C. S. Lam · 2003
Cited alongside, same era.
On strong superadditivity of the entanglement of formation
K. M. R. Audenaert and S. L. Braunstein · 2004
Cited alongside, same era.
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Multiplicativity properties of entrywise positive maps
C. King and M. B. Ruskai · 2005
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Multiplicativity of maximal output purities of gaussian channels under gaussian inputs
A. Serafini, J. Eisert, and M. M. Wolf · 2005
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Classical information capacity of a class of quantum channels
M. M. Wolf and J. Eisert · 2005
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Multiplicativity of completely bounded p-norms implies a new additivity result
I. Devetak, M. Junge, C. King, and M. B. Ruskai · 2006
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Aspects of generic entanglement
P. Hayden, D. W. Leung, and A. Winter · 2006
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Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
B. Collins and P. Śniady · 2006
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The additivity problem in quantum information theory
A. S. Holevo · 2007
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Multiplicativity of the maximal output 2-norm for depolarized werner-holevo channels
S. Michalakis · 2007
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The maximum output p p -norm of quantum channels is not multiplicative for any p > 2 p{>}2
A. Winter · 2007
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The maximal p p -norm multiplicativity conjecture is really, really false
F. Dupuis, P. Hayden, D. Leung, and A. Winter · 2007
Closest in time.