Classical capacities of quantum channels with environment assistance

Karumanchi, Siddharth; Mancini, Stefano; Winter, Andreas; Yang, Dong

doi:10.1134/s0032946016030029

Cited by 23 publications

(27 citation statements)

References 33 publications

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“…In [13] a simplification of this condition was delivered. See also [20] and [21] for a classical quantum channel model with a benevolent third channel user instead of with a jammer. These results are basis tools for secure communication over arbitrarily varying wiretap channels.…”

Section: Introductionmentioning

confidence: 99%

Message Transmission Over Classical Quantum Channels With a Jammer With Side Information: Message Transmission Capacity and Resources

Boche

Cai

2019

IEEE Trans. Inform. Theory

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In this paper we propose a new model for arbitrarily varying classical-quantum channels. In this model a jammer has side information. We consider two scenarios. In the first scenario the jammer knows the channel input, while in the second scenario the jammer knows both the channel input and the message. The transmitter and receiver share a secret random key with a vanishing key rate. We determine the capacity for both average and maximum error criteria for both scenarios. We also establish the strong converse. We show that all these corresponding capacities are equal, which means that additionally revealing the message to the jammer does not change the capacity.

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Section: Introductionmentioning

confidence: 99%

Message Transmission Over Classical Quantum Channels With a Jammer With Side Information: Message Transmission Capacity and Resources

Boche

Cai

2019

IEEE Trans. Inform. Theory

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“…It is due to their characterization which in most cases is given by a regularized formula [5][6][7][8][9][10][11][12][13][14][15]. Moreover, even nonregularized quantities are notoriously hard to compute.…”

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confidence: 99%

“…This gives rise to a host of environment-assisted classical capacities depending on whether we have active or passive environment assistance [13] or whether the sender and environment are allowed to share entanglement or interact by means of local operations and classical communication. In our work, we focus on the weakest variant of assistance for classical communication when the helper is in the product state with the sender [14]. The corresponding capacity is given by …”

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confidence: 99%

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Nonconvexity of private capacity and classical environment-assisted capacity of a quantum channel

Elkouss

Strelchuk

2016

Phys. Rev. A

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The capacity of classical channels is convex. This is not the case for the quantum capacity of a channel: The capacity of a mixture of different quantum channels exceeds the mixture of the individual capacities and thus is nonconvex. Here we show that this effect goes beyond the quantum capacity and holds for the private and classical environment-assisted capacities of quantum channels. DOI: 10.1103/PhysRevA.94.040301 Introduction. Classical information theory was laid down by Shannon in the 1940's to characterize the ultimate rate at which one could hope to transmit classical information over a classical communication channel: the channel capacity. Surprisingly, in retrospective, not only did it achieve its purpose, but the capacity of classical channels turned out to comply with all the properties that one could expect for in such a quantity: It can be efficiently computed [1,2] and it gauges the usefulness of the channel in the presence of any additional contextual channel. It is a natural consequence of additivity and convexity of the capacity in the set of channels.With quantum channels complemented by various auxiliary resources, a whole new range of communication tasks became feasible. Notably, they allow for the transmission of quantum and private classical communication, tasks beyond the reach of classical channels. For most of these tasks, the tools used to prove the capacity theorems in the classical case can be generalized. However, computability, additivity, and convexity-the three convenient properties of the classical capacity of classical channels-do not necessarily translate to the quantum case. In Table I we summarize what is known about these properties for a set of relevant quantum channel capacities.With the exception of the entanglement-assisted capacity [3,4], there is no known algorithm to compute any of these capacities. It is due to their characterization which in most cases is given by a regularized formula [5][6][7][8][9][10][11][12][13][14][15]. Moreover, even nonregularized quantities are notoriously hard to compute. For instance, the Holevo information is known to be NP-complete [16].A capacity is nonadditive as a function of a channel if, for a given pair of channels, the sum of their individual capacities is strictly smaller than the capacity of another channel which is constructed by using both channels in parallel. Hence, a nonadditive capacity is contextual: The usefulness of a channel for communication depends on which other channels are available. The private and quantum capacities are known to be nonadditive [17][18][19]. This observation motivated the authors in Ref.[15] to define a new quantity-the potential capacity-which characterizes the usefulness of a channel used in parallel with the best possible contextual channel.Another important property of the capacities of quantum channels is convexity. The capacity T of a quantum channel N is nonconvex if there exists a pair of channels N 1 and N 2 and p ∈ (0,1) such that

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Adversarial versus cooperative quantum estimation

Rexiti

Mancini

2019

Quantum Inf Process

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We address the estimation of a one-parameter family of isometries taking one input into two output systems. This primarily allows us to consider imperfect estimation by accessing only one output system, i.e. through a quantum channel. Then, on the one hand, we consider separate and adversarial control of the two output systems to introduce the concept of privacy of estimation. On the other hand we conceive the possibility of separate but cooperative control of the two output systems. Optimal estimation strategies are found according to the minimum mean square error. This also implies the generalization of Personik's theorem to the case of local measurements. Finally, applications to two-qubit unitaries (with one qubit in a fixed input state) are discussed.

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Classical capacities of quantum channels with environment assistance

Cited by 23 publications

References 33 publications

Message Transmission Over Classical Quantum Channels With a Jammer With Side Information: Message Transmission Capacity and Resources

Message Transmission Over Classical Quantum Channels With a Jammer With Side Information: Message Transmission Capacity and Resources

Nonconvexity of private capacity and classical environment-assisted capacity of a quantum channel

Adversarial versus cooperative quantum estimation

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