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arXiv:1412.6247 · Physical Review A

Distributed quantum dense coding with two receivers in noisy environments

Tamoghna Das, R. Prabhu, Aditi Sen, Ujjwal Sen

Published Nov 24, 2015• 31 citations
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Abstract

We investigate the effect of noisy channels in a classical information transfer through a multipartite state which acts as a substrate for the distributed quantum dense coding protocol between several senders and two receivers. The situation is qualitatively different from the case with one or more senders and a single receiver. We obtain an upper bound on the multipartite capacity which is tightened in the case of the covariant noisy channel. We also establish a relation between the genuine multipartite entanglement of the shared state and the capacity of distributed dense coding using that state, both in the noiseless and the noisy scenarios. Specifically, we find that, in the case of multiple senders and two receivers, the corresponding generalized Greenberger-Horne-Zeilinger states possess higher dense coding capacities as compared to a significant fraction of pure states having the same multipartite entanglement.

DOI
10.1103/physreva.92.052330

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We investigate the effect of noisy channels in a classical information transfer through a multipartite state which acts as a substrate for the distributed quantum dense coding protocol between several senders and two receivers. The situation is qualitatively different from the case with one or more senders and a single receiver. We obtain an upper bound on the multipartite capacity which is tightened in the case of the covariant noisy channel. We also establish a relation between the genuine multipartite entanglement of the shared state and the capacity of distributed dense coding using that state, both in the noiseless and the noisy scenarios. Specifically, we find that, in the case of multiple senders and two receivers, the corresponding generalized Greenberger-Horne-Zeilinger states possess higher dense coding capacities as compared to a significant fraction of pure states having the same multipartite entanglement.
A highly entangled bipartite quantum state is more advantageous for the quantum dense coding protocol than states with low entanglement. Applications of quantum channels are most likely to be commercially important only in the multiparty regime, where such a correspondence does not exist even for pure quantum states. We establish a connection between the multiparty capacity of classical information transmission in quantum dense coding and several multipartite quantum correlation measures of the shared state, used in the dense coding protocol. In particular, we show that for the noiseless channel, if multipartite quantum correlations of an arbitrary multipartite state of arbitrary number of qubits are the same as those of the corresponding generalized Greenberger-Horne-Zeilinger state, then the multipartite dense coding capability of the former is the same as or better than that of the generalized Greenberger-Horne-Zeilinger state. Interestingly, in a noisy-channel scenario, where we consider both uncorrelated and correlated noise models, the relative abilities of the quantum channels to transfer classical information can get inverted by administration of a sufficient amount of noise. When the shared state is an arbitrary multipartite mixed state, we also establish a link between the classical capacity for the noiseless case and multipartite quantum correlation measures.
We investigate the distributed dense coding (DC) protocol, involving multiple senders and a single or two receivers under the influence of non-Markovian noise, acting on the encoded qubits transmitted from the senders to the receiver(s). We compare the effects of non-Markovianity on DC for both the dephasing and depolarizing channels. In the case of dephasing channels, we illustrate that for some classes of states, high non-Markovian strength can eradicate the negative influence of noisy channels which is not observed for depolarizing noise. Furthermore, we incorporate randomness into the noise models by replacing the Pauli matrices with random unitaries and demonstrate the constructive impact of stochastic noise models on the quenched averaged dense coding capacity. Interestingly, we report that the detrimental effect of non-Markovian depolarizing channels in the DC protocol can be eliminated when randomness is added to the channel.
Distributed computing, involving multiple servers collaborating on designated computations, faces a critical challenge in optimizing interserver communication---an issue central to the study of communication complexity. Quantum resources offer advantages over classical methods in addressing this challenge. In this work, we investigate a distributed computing scenario with multiple senders and a single receiver, establishing a scalable advantage of multipartite quantum entanglement in mitigating communication complexity. Specifically, we demonstrate that when the receiver and the senders share a multiqubit Greenberger-Horne-Zeilinger (GHZ) state---a quintessential form of genuine multipartite entanglement---certain global functions of the distributed inputs can be computed with only one bit of classical communication from each sender. In contrast, without entanglement, two bits of communication are required from all but one sender. Consequently, quantum entanglement reduces communication overhead by $n\ensuremath{-}1$ bits for nnn senders, allowing for arbitrary scaling with an increasing number of senders. We also show that the entanglement-based protocol exhibits significant robustness under white noise, thereby establishing the potential for experimental realization of this quantum advantage.
We establish a universal complementarity relation between the capacity of classical information transmission by employing a multiparty quantum state as a multiport quantum channel, and the corresponding genuine multipartite entanglement. The classical information transfer is from a sender to several receivers by using the quantum dense coding protocol with the multiparty quantum state shared between the sender and several receivers. The relation is derived when the multiparty entanglement is the relative entropy of entanglement as well as when it is the generalized geometric measure. The relation holds for arbitrary pure or mixed quantum states of an arbitrary number of parties in arbitrary dimensions.
The quantum dense-coding (DC) protocol, which has no security feature, deals with the transmission of classical information encoded in a quantum state by using shared entanglement between a single sender and a single receiver. Its appropriate variant has been established as a quantum key distribution (QKD) scheme for shared two-qubit maximally entangled states, with the security proof utilizing the uncertainty relation of complementary observables and the Shor-Preskill entanglement purification scheme. We present the DC-based QKD protocol for higher-dimensional systems and report the lower bounds on the secret key rate, when the shared state is a two-qudit maximally entangled state, and mixtures of maximally entangled states with different ranks. The analysis also includes the impact of noisy channels on the secure key rates, before and after encoding. In both the noiseless and the noisy scenarios, we demonstrate that the key rate as well as the robustness of the protocol against noise increases with the dimension. Further, we prove that the set of useless states in the DC-based QKD protocol is convex and compact.
We propose a distributed quantum dense coding protocol that uses a control system to superpose two dense coding processes, allowing us to simultaneously and coherently encode and non-classically route the sender's single-qubit system to two receiver labs. We find that dense coding with coherently controlled encoding and routing performs better than the standard dense coding protocol in both global and one-way local decoding strategies employed by receiver labs in weak entanglement regimes and with noisy mixed states. We extend the protocol to incorporate noisy channels and show that, there exists a certain noise strength below which our protocol outperforms the noiseless standard dense coding protocol in presence of quantum dephasing noise. We extend our protocol to an arbitrary number of receivers and analyse its performance under a global decoding strategy.