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arXiv:2407.07609 · Physical Review A

Continuous-variable dense coding under realistic nonideal scenarios

Mrinmoy Samanta, Ayan Patra, Rivu Gupta, Aditi Sen De

Published Aug 7, 2026• 1 citation

Abstract

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.

DOI: 10.1103/b2xp-5w9p

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Quantum dense coding of continuous variables via a two-mode squeezed vacuum state is considered for a noisy quantum channel. Classical information is encoded in the two quadrature components of one mode of a two-mode squeezed vacuum state and the encoded mode is sent through a noisy quantum channel which is assumed to be linearly dissipative. Decoding at the receiver side is performed by simultaneous measurement of two quadrature components of the two-mode state. By calculating the error probability of a binary communication system, we examine whether the dense coding is effective or not when a quantum channel is noisy.

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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.

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