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arXiv:2204.14147 · Physical Review A

Quantum dense coding network using multimode squeezed states of light

Ayan Patra, Rivu Gupta, Saptarshi Roy, Tamoghna Das, Aditi Sen

Published Nov 14, 2022• 11 citations
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Abstract

We present a framework of a multimode dense coding network with multiple senders and a single receiver using continuous variable systems. The protocol is scalable to arbitrary numbers of modes with the encoding being displacements while the decoding involves homodyne measurements of the modes after they are combined in a pairwise manner by a sequence of beam splitters, thereby exhibiting its potentiality to implement in laboratories with currently available resources. We compute the closed form expression of the dense coding capacity for the cases of two and three senders that involve sharing of three- and four-mode states, respectively. The dense coding capacity is computed with the constraint of fixed average energy transmission when the modes of the sender are transferred to the receiver after the encoding operation. In both the cases, we demonstrate the quantum advantage of the protocol using paradigmatic classes of three- and four-mode states. The quantum advantage increases with the increase in the amount of energy that is allowed to be transmitted from the senders to the receiver.

DOI
10.1103/physreva.106.052607

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We present a framework of a multimode dense coding network with multiple senders and a single receiver using continuous variable systems. The protocol is scalable to arbitrary numbers of modes with the encoding being displacements while the decoding involves homodyne measurements of the modes after they are combined in a pairwise manner by a sequence of beam splitters, thereby exhibiting its potentiality to implement in laboratories with currently available resources. We compute the closed form expression of the dense coding capacity for the cases of two and three senders that involve sharing of three- and four-mode states, respectively. The dense coding capacity is computed with the constraint of fixed average energy transmission when the modes of the sender are transferred to the receiver after the encoding operation. In both the cases, we demonstrate the quantum advantage of the protocol using paradigmatic classes of three- and four-mode states. The quantum advantage increases with the increase in the amount of energy that is allowed to be transmitted from the senders to the receiver.
We analyze the continuous variable (CV) dense coding protocol between a single sender and a single receiver when affected by noise in the shared and encoded states, as well as when the decoding is imperfect. We present a formalism to derive the dense coding capacity (DCC) of generic two-mode Gaussian states when affected by Gaussian noise models. When the constituent modes are affected by quantum-limited amplifiers, pure-loss channels, and environmental interactions, together with an inefficient decoding mechanism comprising imperfect double-homodyne detection, we specifically investigate the performance of the two-mode squeezed vacuum state (TMSV) by varying the strength of the noise. Through numerical simulations, we further show that the negative conditional entropy may be used to assess the quantum advantage of CV dense coding in Gaussian setups. While comparing the TMSV with other Gaussian states, we identify a class of pure Gaussian states capable of furnishing a capacity equal to that of the TMSV, under equal energy constraints in the ideal regime. Further, we demonstrate that, while the TMSV state is more susceptible to noise, it still provides the maximum quantum advantage in the DC protocol under practical conditions.
We consider generalizations of the dense coding protocol with an arbitrary number of senders and either one or two receivers, sharing a multiparty quantum state, and using a noiseless channel. For the case of a single receiver, the capacity of such information transfer is found exactly. It is shown that the capacity is not enhanced by allowing the senders to perform joint operations. We provide a nontrivial upper bound on the capacity in the case of two receivers. We also give a classification of the set of all multiparty states in terms of their usefulness for dense coding. We provide examples for each of these classes, and discuss some of their properties.
We study a continuous-variable dense coding protocol, originally proposed to employ a two-mode squeezed state, using a general two-mode Gaussian state as a quantum channel. We particularly obtain conditions to manifest quantum advantage by beating two well-known single-mode schemes, namely, the squeezed-state scheme (best Gaussian scheme) and the number-state scheme (optimal scheme achieving the Holevo bound). We then extend our study to a multipartite Gaussian state and investigate the monogamy of operational entanglement measured by the communication capacity under the dense coding protocol. We show that this operational entanglement represents a strict monogamy relation, by means of Heisenberg's uncertainty principle among different parties; i.e., the quantum advantage for communication can be possible for only one pair of two-mode systems among many parties.
We introduce a probabilistic version of the one-shot quantum dense coding protocol in both two- and multiport scenarios in which the sender(s) transmit(s) only complete messages unambiguously, to a single receiver, and we refer to it as conclusive quantum dense coding. We derive the relevant form of the mutual information between encoded information and measurement results in the scenario considered. We analyze the corresponding capacities of shared states between two, three, and more qubits, and two qutrits. We identify cases where Pauli and generalized Pauli operators are not sufficient as encoders to attain the optimal one-shot conclusive quantum dense coding capacities. We find that there is a rich connection between the capacities and the bipartite as well as multipartite entanglements of the shared state.
We introduce the notion of distributed quantum dense coding, i.e., the generalization of quantum dense coding to more than one sender and more than one receiver. We show that global operations (as compared to local operations) of the senders do not increase the information transfer capacity, in the case of a single receiver. For the case of two receivers, using local operations and classical communication, a nontrivial upper bound for the capacity is derived. We propose a general classification scheme of quantum states according to their usefulness for dense coding. In the bipartite case (for any dimensions), bound entanglement is not useful for this task.