arXiv subjects

Gisbert Janßen

Publications and source records attributed to Gisbert Janßen.

10 recordsLinked to original sources

arXiv2020

Universal superposition codes: capacity regions of compound quantum broadcast channel with confidential messages

We derive universal codes for transmission of broadcast and confidential messages over classical-quantum-quantum and fully quantum channels. These codes are robust to channel uncertainties considered in the compound model. To construct these codes we generalize random codes for transmission of public messages, to derive a universal superposition coding for the compound quantum broadcast channel. As an application, we give a multi-letter characterization of regions corresponding to the capacity of the compound quantum broadcast channel for transmitting broadcast and confidential messages simultaneously. This is done for two types of broadcast messages, one called public and the other common.

quant-ph↗

arXiv2019

Universal random codes: Capacity regions of the compound quantum multiple-access channel with one classical and one quantum sender

We consider the compound memoryless quantum multiple-access channel (QMAC) with two sending terminals. In this model, the transmission is governed by the memoryless extensions of a completely positive and trace preserving map which can be any element of a prescribed set of possible maps. We study a communication scenario, where one of the senders aims for transmission of classical messages while the other sender sends quantum information. Combining powerful universal random coding results for classical and quantum information transmission over point-to-point channels, we establish universal codes for the mentioned two-sender task. Conversely, we prove that the two-dimensional rate region achievable with these codes is optimal. In consequence, we obtain a multi-letter characterization of the capacity region of each compound QMAC for the considered transmission task.

quant-ph↗

arXiv2018

Simultaneous transmission of classical and quantum information under channel uncertainty and jamming attacks

We derive universal codes for simultaneous transmission of classical messages and entanglement through quantum channels, possibly under attack of a malignant third party. These codes are robust to different kinds of channel uncertainty. To construct such universal codes, we invoke and generalize properties of random codes for classical and quantum message transmission through quantum channels. We show these codes to be optimal by giving a multi-letter characterization of regions corresponding to the capacity of compound quantum channels for simultaneously transmitting and generating entanglement with classical messages. Also, we give dichotomy statements in which we characterize the capacity of arbitrarily varying quantum channels for simultaneous transmission of classical messages and entanglement. These include cases where the malignant jammer present in the arbitrarily varying channel model is classical (chooses channel states of product form) and fully quantum (is capable of general attacks not necessarily of product form).

math-ph↗

arXiv2017

Randomness cost of symmetric twirling

We study random unitary channels which reproduce the action of the twirling channel corresponding to the representation of the symmetric groupon an n-fold tensor product. We derive upper andlower bounds on the randomness cost of implementing such a map which depend exponentially on the number of systems. Consequently, symmetrictwirling can be regarded as a reasonable Shannon theoretic protocol. On the other hand, such protocols are disqualified by their resource-inefficiency in situations where randomness is a costly resource.

quant-ph↗

arXiv2017

Entanglement-assisted classical capacities of compound and arbitrarily varying quantum channels

We consider classical message transmission under entanglement assistance for compound memoryless and arbitrarily varying quantum channels. In both cases, we prove general coding theorems together with corresponding weak converse bounds. In this way, we obtain single-letter characterizations of the entanglement-assisted classical capacities for both channel models. Moreover, we show that the entanglement-assisted classical capacity does exhibit no strong converse property for some compound quantum channels for the average as well as the maximal error criterion. A strong converse to the entanglement-assisted classical capacities does hold for each arbitrarily varying quantum channel.

quant-ph↗

arXiv2016

Distillation of secret key from a class of compound memoryless quantum sources

We consider secret-key distillation from tripartite compound classical-quantum-quantum (cqq) sources with free forward public communication under strong security criterion. We design protocols which are universally reliable and secure in this scenario. These are shown to achieve asymptotically optimal rates as long as a certain regularity condition is fulfilled by the the set of its generating density matrices. We derive a multi-letter formula which describes the optimal forward secret-key capacity for all compound cqq sources being regular in this sense. We also determine the forward secret-key distillation capacity for situations, where the legitimate sending party has perfect knowledge of his/her marginal state deriving from the source statistics. In this case regularity conditions can be dropped. Our results show that the capacities with and without the mentioned kind of state knowledge are equal as long as the source is generated by a regular set of density matrices. We demonstrate that regularity of cqq sources is not only a technical but also an operational issue. For this reason, we give an example of a source which has zero secret-key distillation capacity without sender knowledge, while achieving positive rates is possible if sender marginal knowledge is provided.

quant-ph↗

arXiv2014

Resource cost results for one-way entanglement distillation and state merging of compound and arbitrarily varying quantum sources

We consider one-way quantum state merging and entanglement distillation under compound and arbitrarily varying source models. Regarding quantum compound sources, where the source is memoryless, but the source state an unknown member of a certain set of density matrices, we continue investigations begun in the work of Bjelaković et. al. [Universal quantum state merging, J. Math. Phys. 54, 032204 (2013)] and determine the classical as well as entanglement cost of state merging. We further investigate quantum state merging and entanglement distillation protocols for arbitrarily varying quantum sources (AVQS). In the AVQS model, the source state is assumed to vary in an arbitrary manner for each source output due to environmental fluctuations or adversarial manipulation. We determine the one-way entanglement distillation capacity for AVQS, where we invoke the famous robustification and elimination techniques introduced by R. Ahlswede. Regarding quantum state merging for AVQS we show by example, that the robustification and elimination based approach generally leads to suboptimal entanglement as well as classical communication rates.

quant-ph↗

arXiv2014

Resource Cost Results for Entanglement Distillation and State Merging under Source Uncertainties

We introduce one-way LOCC protocols for quantum state merging for compound sources, which have asymptotically optimal entanglement as well as classical communication resource costs. For the arbitrarily varying quantum source (AVQS) model, we determine the one-way entanglement distillation capacity, where we utilize the robustification and elimination techniques, well-known from classical as well as quantum channel coding under assumption of arbitrarily varying noise. Investigating quantum state merging for AVQS, we demonstrate by example, that the usual robustification procedure leads to suboptimal resource costs in this case.

quant-ph↗

arXiv2013

Universal quantum state merging

We determine the optimal entanglement rate of quantum state merging when assuming that the state is unknown except for its membership in a certain set of states. We find that merging is possible at the lowest rate allowed by the individual states. Additionally, we establish a lower bound for the classical cost of state merging under state uncertainty. To this end we give an elementary proof for the cost in case of a perfectly known state which makes no use of the "resource framework". As applications of our main result, we determine the capacity for one-way entanglement distillation if the source is not perfectly known. Moreover, we give another achievability proof for the entanglement generation capacity over compound quantum channels.

quant-ph↗

arXiv2012

Arbitrarily varying and compound classical-quantum channels and a note on quantum zero-error capacities

We consider compound as well as arbitrarily varying classical-quantum channel models. For classical-quantum compound channels, we give an elementary proof of the direct part of the coding theorem. A weak converse under average error criterion to this statement is also established. We use this result together with the robustification and elimination technique developed by Ahlswede in order to give an alternative proof of the direct part of the coding theorem for a finite classical-quantum arbitrarily varying channels with the criterion of success being average error probability. Moreover we provide a proof of the strong converse to the random coding capacity in this setting.The notion of symmetrizability for the maximal error probability is defined and it is shown to be both necessary and sufficient for the capacity for message transmission with maximal error probability criterion to equal zero. Finally, it is shown that the connection between zero-error capacity and certain arbitrarily varying channels is, just like in the case of quantum channels, only partially valid for classical-quantum channels.

quant-ph↗