In this work, we prove a novel one-shot multi-sender decoupling theorem generalising Dupuis result. We start off with a multipartite quantum state, say on A1 A2 R, where A1, A2 are treated as the two sender systems and R is the reference system. We apply independent Haar random unitaries in tensor product on A1 and A2 and then send the resulting systems through a quantum channel. We want the channel output B to be almost in tensor with the untouched reference R. Our main result shows that this is indeed the case if suitable entropic conditions are met. An immediate application of our main result is to obtain a one-shot simultaneous decoder for sending quantum information over a k-sender entanglement unassisted quantum multiple access channel (QMAC). The rate region achieved by this decoder is the natural one-shot quantum analogue of the pentagonal classical rate region. Assuming a simultaneous smoothing conjecture, this one-shot rate region approaches the optimal rate region of Yard, Dein the asymptotic iid limit. Our work is the first one to obtain a non-trivial simultaneous decoder for the QMAC with limited entanglement assistance in both one-shot and asymptotic iid settings; previous works used unlimited entanglement assistance.
In this work, we prove a novel one-shot multi-sender decoupling theorem generalising Dupuis result. We start off with a multipartite quantum state, say on A1 A2 R, where A1, A2 are treated as the two sender systems and R is the reference system. We apply independent Haar random unitaries in tensor product on A1 and A2 and then send the resulting systems through a quantum channel. We want the channel output B to be almost in tensor with the untouched reference R. Our main result shows that this is indeed the case if suitable entropic conditions are met. An immediate application of our main result is to obtain a one-shot simultaneous decoder for sending quantum information over a k-sender entanglement unassisted quantum multiple access channel (QMAC). The rate region achieved by this decoder is the natural one-shot quantum analogue of the pentagonal classical rate region. Assuming a simultaneous smoothing conjecture, this one-shot rate region approaches the optimal rate region of Yard, Dein the asymptotic iid limit. Our work is the first one to obtain a non-trivial simultaneous decoder for the QMAC with limited entanglement assistance in both one-shot and asymptotic iid settings; previous works used unlimited entanglement assistance.
In this work, we prove a novel one-shot ‘multi-sender’ decoupling theorem generalising Dupuis' seminal single sender decoupling theorem. We start off with a multipartite quantum state, say onA1A2R, whereA1,A2are treated as the two ‘sender’ systems andRis the reference system. We apply independent Haar random unitaries in tensor product onA1andA2and then send the resulting systems through a quantum channel. We want the channel outputBto be almost in tensor with the untouched referenceR. Our main result shows that this is indeed the case if suitable entropic conditions are met. An immediate application of our main result is to obtain a one-shot simultaneous decoder for sending quantum information over ak-sender entanglement unassisted quantum multiple access channel (QMAC). The rate region achieved by this decoder is the natural one-shot quantum analogue of the pentagonal classical rate region. Assuming a simultaneous smoothing conjecture, this one-shot rate region approaches the optimal rate region of Yard et al. [20] in the asymptotic iid limit. Our work is the first one to obtain a non-trivial simultaneous decoder for the QMAC with limited entanglement assistance in both one-shot and asymptotic iid settings; previous works used unlimited entanglement assistance.
We prove the first non-trivial one-shot inner bounds for sending quantum information over an entanglement unassisted two-sender quantum multiple access channel (QMAC) and an unassisted two-sender two-receiver quantum interference channel (QIC). Previous works only studied the unassisted QMAC in the limit of many independent and identical uses of the channel also known as the asymptotic iid limit, and did not study the unassisted QIC at all. We employ two techniques, rate splitting and successive cancellation, in order to obtain our inner bound. Rate splitting was earlier used to obtain inner bounds, avoiding time sharing, for classical channels in the asymptotic iid setting. Our main technical contribution is to extend rate splitting from the classical asymptotic iid setting to the quantum one-shot setting. In the asymptotic iid limit our one-shot inner bound for QMAC approaches the rate region of Yard et al. [22]. For the QIC we get novel non-trivial rate regions in the asymptotic iid setting. All our results also extend to the case where limited entanglement assistance is provided, in both one-shot and asymptotic iid settings. The limited entanglement results for one-shot setting for both QMAC and QIC are new. For the QIC the limited entanglement results are new even in the asymptotic iid setting.
We provide the first inner bounds for sending private classical information over a quantum multiple access channel. We do so by using three powerful information theoretic techniques: rate splitting, quantum simultaneous decoding for multiple access channels, and a novel smoothed distributed covering lemma for classical quantum channels. Our inner bounds are given in the one shot setting and accordingly the three techniques used are all very recent ones specifically designed to work in this setting. The last technique is new to this work and is our main technical advancement. For the asymptotic iid setting, our one shot inner bounds lead to the natural quantum analogue of the best classical inner bounds for this problem. A full version of this paper is accessible at [5].
We consider the problem of simulating a two-sender multiple access channel (MAC) for fixed product inputs, where each sender transmits a message to the decoder over a rate-limited noiseless link based on its input and unlimited randomness shared with the decoder. As our main contribution, we characterize the one-shot communication cost region via almost-matching inner and outer bounds phrased in terms of the smooth max-information of the channel. The achievability relies on a rejection-sampling algorithm to simulate a quantization channel between each sender and decoder, and producing the final output based on the output of these intermediate channels. The converse follows via information-spectrum based arguments relating operational quantities to information measures. Our one-shot results recover the single-letter asymptotic rate region for MAC simulation with fixed, independent and identically distributed product inputs, that was obtained in [Kurri et al., IEEE Transactions on Information Theory 68, 7575 (2022)]. We extend our result to quantum-to-classical channels with a separable decomposition [Atif et al., IEEE Transactions on Information Theory 68, 1085 (2022)], for which we obtain a similar characterization.
Abstract We show that a simple telescoping sum trick, together with the triangle inequality and a tensorisation property of expected-contractive coefficients of random channels, allow us to achieve general simultaneous decoupling for multiple users via local actions. Employing both old (Dupuis et al. in Commun Math Phys 328:251–284, 2014) and new methods (Dupuis in IEEE Trans Inf Theory 69:7784–7792, 2023), we obtain bounds on the expected deviation from ideal decoupling either in the one-shot setting in terms of smooth min-entropies, or the finite block length setting in terms of Rényi entropies. These bounds are essentially optimal without the need to address the simultaneous smoothing conjecture, which remains unresolved. This leads to one-shot, finite block length, and asymptotic achievability results for several tasks in quantum Shannon theory, including local randomness extraction of multiple parties, multi-party assisted entanglement concentration, multi-party quantum state merging, and quantum coding for the quantum multiple access channel. Because of the one-shot nature of our protocols, we obtain achievability results without the need for time-sharing, which at the same time leads to easy proofs of the asymptotic coding theorems. We show that our one-shot decoupling bounds furthermore yield achievable rates (so far only conjectured) for all four tasks in compound settings, which are additionally optimal for entanglement of assistance and state merging.
We prove the first non-trivial one-shot inner bounds for sending quantum information over an entanglement unassisted two-sender quantum multiple access channel (QMAC) and an unassisted two-sender two-receiver quantum interference channel (QIC). Previous works only studied the unassisted QMAC in the limit of many independent and identical uses of the channel also known as the asymptotic iid limit, and did not study the unassisted QIC at all. We employ two techniques, rate splitting and successive cancellation}, in order to obtain our inner bound. Rate splitting was earlier used to obtain inner bounds, avoiding time sharing, for classical channels in the asymptotic iid setting. Our main technical contribution is to extend rate splitting from the classical asymptotic iid setting to the quantum one-shot setting. In the asymptotic iid limit our one-shot inner bound for QMAC approaches the rate region of Yard, Devetak and Hayden. For the QIC we get novel non-trivial rate regions in the asymptotic iid setting. All our results also extend to the case where limited entanglement assistance is provided, in both one-shot and asymptotic iid settings. The limited entanglement results for one-setting for both QMAC and QIC are new. For the QIC the limited entanglement results are new even in the asymptotic iid setting.