We approach two interconnected problems of quantum information processing in networks: Conference key agreement and entanglement distillation, both in the so-called source model where the given resource is a multipartite quantum state and the players interact over public classical channels to generate the desired correlation. The first problem is the distillation of a conference key when the source state is shared between a number of legal players and an eavesdropper; the eavesdropper, apart from starting off with this quantum side information, also observes the public communication between the players. The second is the distillation of Greenberger-Horne-Zeilinger (GHZ) states by means of local operations and classical communication (LOCC) from the given mixed state. These problem settings extend our previous paper [IEEE Trans. Inf. Theory 68(2):976-988, 2022], and we generalise its results: using a quantum version of the task of communication for omniscience, we derive novel lower bounds on the distillable conference key from any multipartite quantum state by means of non-interacting communication protocols. Secondly, we establish novel lower bounds on the yield of GHZ states from multipartite mixed states. Namely, we present two methods to produce bipartite entanglement between sufficiently many nodes so as to produce GHZ states. Next, we show that the conference key agreement protocol can be made coherent under certain conditions, enabling the direct generation of multipartite GHZ states.

We consider two related problems of extracting correlation from a given multipartite mixed quantum state: the first is the distillation of a conference key when the state is shared between a number of legal players and an eavesdropper; the eavesdropper, apart from starting off with this quantum side information, also observes the public communication between the players. The second is the distillation of Greenberger-Horne-Zeilinger (GHZ) states by means of LOCC from the given mixed state. These problem settings extend our previous paper [FS & AW, IEEE Trans. Inf. Theory 68(2):976-988, 2022], and we generalise its results: using a quantum version of the task of communication for omniscience, we derive a novel lower bound on the distillable secret key from any multipartite quantum state by means of a so-called non-interacting communication protocol. Secondly, by making the secret key distillation protocol coherent, we derive novel lower bounds on the distillation rate of GHZ states. Full details in the long version [1].

We present a broad investigation of asymptotic binary hypothesis testing, when each hypothesis represents asymptotically many independent instances of a quantum channel, and the tests are based on using the unknown channel multiple times and observing its output at the end. Unlike the familiar setting of quantum states as hypotheses, there is a fundamental distinction between adaptive and non-adaptive strategies with respect to the channel uses, and we introduce a number of further variants of the discrimination tasks by imposing different restrictions on the test strategies. Our main result is the first separation between adaptive and non-adaptive symmetric hypothesis testing exponents for quantum channels, which we derive from a general lower bound on the error probability for non-adaptive strategies; the concrete example we analyze is a pair of entanglement-breaking channels. Full details in [1].

The tasks of converting noisy multipartite quantum correlations into noiseless classical and quantum ones using local operations and classical communications (LOCC) are studied. For the former, known as common randomness (CR) distillation, two novel lower bounds on the "distillable common randomness", an operational measure of the total genuine (classical) correlations in a quantum state, are obtained. Our proof relies on a generalization of communication for omniscience (CO) [Csiszár and Narayan, IEEE Trans. Inf. Theory 50: 3047-3061, 2004]. For the latter, we derive two lower bounds on the rate at which Greenberger-Horne-Zeilinger (GHZ) states can be asymptotically distilled from any given pure state under LOCC. Our approach consists in "making coherent" the proposed CR distillation protocols and recycling of resources [Devetak, Harrow and Winter, IEEE Trans. Inf. Theory 54:4587-4618, 2008]. The first lower bound is identical to a recent result by Vrana and Christandl [IEEE Trans. Inf. Theory 65:5945-5958, 2019], which is based on a combinatorial approach to achieve the same rate. Our second lower bound generalises and improves upon this result, and unifies a number of other known lower bounds on GHZ distillation. Full details in the long version [1].

We study the communication capabilities of a quantum channel under the most general channel model known as the one-shot model. Unlike classical channels that can only be used to transmit classical information (bits), a quantum channel can be used for transmission of classical information, quantum information (qubits) and simultaneous transmission of classical and quantum information. In this work, we investigate the one-shot capabilities of a quantum channel for simultaneously transmitting bits and qubits. This problem was studied in the asymptotic regime for a memoryless channel where a regularized characterization of the capacity region was reported. It is known that the transmission of private classical information is closely related to the problem of quantum information transmission. We resort to this idea and find achievable and converse bounds on the simultaneous transmission of the public and private classical information. Then shifting the classical private rate to the quantum information rate leads to a rate region for simultaneous transmission of classical and quantum information. In the case of asymptotic i.i.d. setting, our one-shot result is evaluated to the known results in the literature. Our main tools used in the achievability proofs are position-based decoding and convex-split lemma.

The two-receiver broadcast channel with primary and third party receivers is studied. The sender wishes to reliably communicate a common (or public) message to both receivers as well as individualized and confidential messages to the primary receiver only. The third party receiver must be kept completely ignorant of the confidential message but there are no secrecy requirements associated to the individualized message. A trade-off arises between the rates of the three messages: when one of the rates is high, the other rates may need to back off to guarantee the reliable transmission of all three messages. In addition, the confidentiality requirement implies availability of local randomness at the transmitter in order to implement a stochastic encoding. This article studies the trade-off between the rates of the common, individualized and confidential messages as well as that of the local randomness in the one-shot regime of a quantum broadcast channel. We provide an achievability region, by proving a conditional version of the convex-split lemma combined with the position-based decoding, as well as a (weak) converse region. We study the asymptotic behaviour of our bounds and recover several well-known asymptotic results in the literature, including simultaneous transmission of classical and quantum information.

The 2-receiver broadcast channel with primary and third-party receivers is studied. The messages are classified into public, private and confidential. The messages in the public class are messages intended for both receivers. The private messages are intended for the primary receiver with no secrecy requirements imposed upon them. And the confidential messages are aimed exclusively to the primary receiver such that they must not be accessible to the other receiver. The encoder performs the necessary encryption by virtue of local randomness whose rate is assumed to be limited. We find an achievability region on the trade-off between the rates of the three messages and the source of randomness in the one-shot regime of a quantum broadcast channel.

We aim to study the optimal rates of transmission of public and private classical information over a quantum channel in the most general channel model. To this end, we discuss a scenario in which a quantum channel is being used only once, i.e., one-shot regime is considered. A quantum channel can be used to send classical information (bits) either publicly or privately and for either case, one-shot bounds have been reported in the literature. This paper investigates the one-shot capacity capabilities of a quantum channel for simultaneous transmission of public and private information. We derive an achievable rate region in the form of a tradeoff between public and private rates. We also provide converse bounds assessing the tightness of our achievable rates. Our main tools used in the achievability proofs are position-based decoding and convex-split lemma.

We propose a distributed opportunistic medium access control (MAC) scheme for maximizing the expected aggregate throughput in a multichannel wireless network such as a clustered orthogonal frequency-division multiple access (OFDMA) network. In our proposed scheme, each user attempts to send only on its best channel and transmits if the best-channel gain is higher than a given threshold, which is dynamically updated depending on previous idle and collision situations. In this way, with our proposed scheme, in a homogeneous system where the channel fading distribution is identical for all users, the best user for each channel is obtained in a distributed manner. We also obtain the optimal values of the thresholds so that the probability of successful transmission is maximized and a minimal number of transmission opportunities are wasted (e.g., due to collision or idle transmissions). In the asymptotic limit of a large number of users and sufficiently long transmission slot duration, we show that, in comparison with the optimal centralized scheme, the throughput loss for our proposed scheme goes to zero. Furthermore, we extend our distributed opportunistic MAC scheme for a homogeneous system to that for a heterogeneous system where the channel fading distribution is heterogeneous across users. Throughput performances and signaling overhead are analyzed for the proposed distributed MAC schemes and compared with those of the existing schemes. Simulation results show that our proposed schemes significantly improve the average aggregate throughput when compared with the existing schemes.