When does noise increase the quantum capacity?

@article{Brando2012WhenDN,
  title={When does noise increase the quantum capacity?},
  author={Fernando G. S. L. Brand{\~a}o and Jonathan Oppenheim and Sergii Strelchuk},
  journal={Physical review letters},
  year={2012},
  volume={108 4},
  pages={
          040501
        }
}
Superactivation is the property that two channels with zero quantum capacity can be used together to yield a positive capacity. Here we demonstrate that this effect exists for a wide class of inequivalent channels, none of which can simulate each other. We also consider the case where one of two zero-capacity channels is applied, but the sender is ignorant of which one is applied. We find examples where the greater the entropy of mixing of the channels, the greater the lower bound for the… 
View on PubMed
authors.library.caltech.edu
28 Citations
Background Citations
9

Figures and Tables from this paper

28 Citations

Quasi-superactivation of classical capacity of zero-capacity quantum channels
TLDR
It is shown that a nonzero classical capacity can be achieved for all zero-capacity quantum channels and it only requires the assistance of an elementary photon–atom interaction process – stimulated emission.
Superactivation of quantum channels is limited by the quantum relative entropy function
TLDR
It is proved that the possibility of superactivation of quantum channel capacities is determined by the mathematical properties of the quantum relative entropy function, and the proposed theorems and connections hold for all other channel capacities of quantum channels for which the superactivation is possible.
Parrondo's paradox and superactivation of classical and quantum capacity of communication channels with memory
TLDR
This construction uses a single family of erasure channels with classical memory to achieve the same superactivation-like effect for quantum capacity without any of the ingredients above.
Unbounded number of channel uses may be required to detect quantum capacity.
TLDR
It is shown that for any number of uses, there are channels for which the coherent information is zero, but which nonetheless have capacity, and that only a finite number of channel uses is always sufficient.
Algorithmic superactivation of asymptotic quantum capacity of zero-capacity quantum channels
Hybrid zero-capacity channels
TLDR
Hybrid channels provide the first example of highly cloneable binding entanglement channels, for which known superactivation protocols must fail - superactivation is the effect where two channels each with zero quantum capacity having positive capacity when used together.
Secure Communication over Zero-Private Capacity Quantum Channels
TLDR
It is proved that the polaractivation works for arbitrary zero private-capacity quantum channels and it is demonstrated, that the symmetric private classical capacity of arbitrary zeroPrivate quantum channels is polaractive.
Information Geometric Superactivation of Asymptotic Quantum Capacity and Classical Zero-Error Capacity of Zero-Capacity Quantum Channels
TLDR
This PhD Thesis provides an algorithmic solution to the problem of superactivation and proves that superactivation effect is rooted in information geometric issues.
Entropic singularities give rise to quantum transmission
TLDR
This work shows non-additivity in a simple low-noise channel and proves a general theorem concerning positivity of a channel’s coherent information, and shows a wide class of zero quantum capacity qubit channels can assist an incomplete erasure channel in sending quantum information.
How Deep the Theory of Quantum Communications Goes: Superadditivity, Superactivation and Causal Activation
TLDR
The aim of this treatise is to shed light on phenomena of superadditivity, superactivation and causal activation by providing the reader with an easy access and guide towards the relevant literature and the prominent results from a communication engineering perspective.
...
...

References

SHOWING 1-10 OF 36 REFERENCES
Private capacity of quantum channels is not additive.
TLDR
It is concluded for the first time that the classical private capacity is nonadditive: in this construction even the quantum capacity of the tensor product of two channels can be greater than the sum of their individual classical private capacities.
Quantum Communication with Zero-Capacity Channels
TLDR
It is shown theoretically that two quantum channels, each with a transmission capacity of zero, can have a nonzero capacity when used together, implying that the quantum capacity does not completely specify a channel's ability to transmit quantum information.
Extensive nonadditivity of privacy.
TLDR
This work studies the power of quantum channels with limited private capacity, focusing on channels that dephase in random bases, providing a natural setting manifesting nonadditivity of privacy of the strongest possible sort.
The structure of degradable quantum channels
TLDR
A comprehensive review of what is currently known about the structure of degradable quantum channels is given, including a number of new results as well as alternate proofs of some known results.
A single quantum cannot be cloned
If a photon of definite polarization encounters an excited atom, there is typically some nonvanishing probability that the atom will emit a second photon by stimulated emission. Such a photon is…
Capacity of the noisy quantum channel
An upper limit is given to the amount of quantum information that can be transmitted reliably down a noisy, decoherent quantum channel. A class of quantum error-correcting codes is presented that…
General Paradigm for Distilling Classical Key From Quantum States
TLDR
It is demonstrated that all quantum cryptographic protocols can be recast in a way which looks like entanglement theory, with the only change being that instead of distilling Einstein-Podolsky-Rosen (EPR) pairs, the parties distill private states.
Mixed-State Entanglement and Distillation: Is there a “Bound” Entanglement in Nature?
It is shown that if a mixed state can be distilled to the singlet form it must violate partial transposition criterion [A. Peres, Phys. Rev. Lett. 76, 1413 (1996)]. It implies that there are two…
Binding entanglement channels
TLDR
It is shown that any bound entangled state can be used for the construction of a map corresponding to the binding entanglement channel, and this class of channels is provided.
Secure key from bound entanglement.
TLDR
The set of shared quantum states which contain a cryptographically private key is characterized and the theory of privacy is recast as a paradigm closely related to that used in entanglement manipulation.
...
...