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Journal of Optics B Quantum and Semiclassical Optics

Quantum dense coding via a two-mode squeezed-vacuum state

Masashi Ban

Published Oct 18, 1999• 138 citations
Publisher

Abstract

Quantum dense coding via a two-mode squeezed-vacuum state is proposed, where classical information is encoded in two quadrature components of one mode of a two-mode squeezed-vacuum state. Decoding at a receiver side is performed by simultaneous measurement of two quadrature components of the two-mode state. Since a two-mode squeezed-vacuum state is partially entangled, the information can only be transmitted without error in the strong-squeezing limit.

DOI
10.1088/1464-4266/1/6/101

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Quantum dense coding via a two-mode squeezed-vacuum state is proposed, where classical information is encoded in two quadrature components of one mode of a two-mode squeezed-vacuum state. Decoding at a receiver side is performed by simultaneous measurement of two quadrature components of the two-mode state. Since a two-mode squeezed-vacuum state is partially entangled, the information can only be transmitted without error in the strong-squeezing limit.
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.
We have experimentally realized the scheme initially proposed as quantum dense coding with continuous variables [Ban, J. Opt. B: Quantum Semiclassical Opt. 1, L9 (1999); Braunstein and Kimble, Phys. Rev. A 61, 042302 (2000)]. In our experiment, a pair of EPR (Einstein-Podolsky-Rosen) beams is generated from two independent squeezed vacua. After adding a two-quadrature signal to one of the EPR beams, two squeezed beams that contain the signal were recovered. Although our squeezing level is not sufficient to demonstrate the channel capacity gain over the Holevo limit of a single-mode channel without entanglement, our channel is superior to conventional channels such as coherent and squeezing channels. In addition, the optical addition and subtraction processes demonstrated are elementary operations of universal quantum information processing on continuous variables.
The possibility is explicitly shown that the average probability of error is reduced and the transmission rate of information is enhanced by means of entangled input states to a communication channel. When two senders transmit some information to a receiver, they encode the information in the quadrature amplitudes of both modes of a two-mode squeezed vacuum state. The receiver performs a simultaneous measurement of the two quadrature amplitudes of the received two-mode state. In this case, if the average value of the photon number supplied to the communication system is not so small, the average probability of error becomes smaller than that of the communication system without entanglement. Furthermore, the transmission rate of information becomes larger than the quantum capacity of classical information of the communication system without entanglement.
We study the measurement-induced non-Gaussian operation on the single- and two-mode Gaussian squeezed vacuum states with beam splitters and on-off type photon detectors, with which mixed non-Gaussian states are generally obtained in the conditional process. It is known that the entanglement can be enhanced via this non-Gaussian operation on the two-mode squeezed vacuum state. We show that, in the range of practical squeezing parameters, the conditional outputs are still close to Gaussian states, but their second order variances of quantum fluctuations and correlations are effectively suppressed and enhanced, respectively. To investigate an operational meaning of these states, especially entangled states, we also evaluate the quantum dense coding scheme from the viewpoint of the mutual information, and we show that non-Gaussian entangled state can be advantageous compared with the original two-mode squeezed state.
The photon subtraction operation is an effective method to enhance an entanglement of the two-mode squeezed vacuum state. We show that it can be well approximated to the two-mode squeezed state with an enhanced squeezing although it is basically a mixed and non-Gaussian state. Such property can be directly observed by the current technology. We also study the continuous variable quantum dense coding with the photon subtracted two-mode squeezed state. It is shown that, in particular squeezing region, its error probability performance can be greatly improved from the original two-mode squeezed state. Since quantum dense coding is the protocol to transmit classical information, our analysis provides an alternative operational meaning of the entanglement involved in the on-off photon subtracted state, compared to the previous results, such as teleportation or the nonlocality, that could help to quantify the entanglement of mixed and non-Gaussian states.
Highly efficient quantum dense coding for continuous variables has been experimentally accomplished by means of exploiting a bright Einstein-Podolsky-Rosen (EPR) beam with anticorrelation of amplitude quadratures and correlation of phase quadratures. Two bits of classical information are encoded on two quadratures of a half of a bright EPR beam, then are simultaneously decoded by the other half of the EPR beam with the sensitivities beyond that of the shot noise limit. A high degree of immunity to unauthorized eavesdropping has been experimentally demonstrated.