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Physical Review A

Dense coding in photonic quantum communication with enhanced information capacity

Kaoru Shimizu, Nobuyuki Imoto, Takaaki Mukai

Published Feb 1, 1999• 31 citations
Publisher

Abstract

We propose a scheme for enhancing the information capacity to more than 2 bits in dense coding quantum communication that involves transmitting a polarization entangled twin photon and a subsequent joint measurement with a Bell-state analyzer. Although direct modulation of the timing position and optical frequency of the photon play no role in dense coding quantum communication, we show that the frequency-dependent phase correlation of polarization entangled twin photons can be used for this enhancement if photon twins are generated through optical parametric down-conversion. With our proposed Bell-state analyzer containing a nonlinear optical gate, the capacity can be enhanced from the reported 2 bits to 3 bits by the local operation of a frequency-dependent phase shift on the transmitted photon.

DOI
10.1103/physreva.59.1092

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We propose a scheme for enhancing the information capacity to more than 2 bits in dense coding quantum communication that involves transmitting a polarization entangled twin photon and a subsequent joint measurement with a Bell-state analyzer. Although direct modulation of the timing position and optical frequency of the photon play no role in dense coding quantum communication, we show that the frequency-dependent phase correlation of polarization entangled twin photons can be used for this enhancement if photon twins are generated through optical parametric down-conversion. With our proposed Bell-state analyzer containing a nonlinear optical gate, the capacity can be enhanced from the reported 2 bits to 3 bits by the local operation of a frequency-dependent phase shift on the transmitted photon.
Dense coding is a new concept of quantum communication using the nonlocal feature of quantum entangled states. Bob, the information receiver, prepares polarization-entangled photon twins and sends one of them to Alice, the information sender, while retaining the other. She can prepare each of the four Bell states by operating an appropriate manipulation only on the transmitted photon and thus she can encode 2 bits of information. To decode the 2 bits, Bob must execute a joint measurement of the returned and retained photons with a Bell-state analyzer, such as a Hong-Ou-Mandel type of two-photon interferometer. The information capacity of the transmitted photon is limited by the number of usable nonlocal quantum states which can be prepared through the local operation on one photon. A question arises as to whether Alice can enhance the capacity or not, by adopting an additional degree of freedom by use of pulse position modulation or optical frequency modulation for the transmitted photon. At a glance, capacity enhancement appears to be possible by introducing another degree of freedom. The question here is, however, whether or not it is possible by manipulating only one of photon twins. In the paper, however, we show that the information capacity in dense coding can be enhanced from the reported 2 bits to 3 bits provided that photon twins have spectral correlation and a perfect Bell state analyzer is available.
Entanglement can effectively increase communication channel capacity as evidenced by dense coding that predicts a capacity gain of 1 bit when compared to entanglement-free protocols. However, dense coding relies on Bell states and when implemented using photons the capacity gain is bounded by 0.5850.5850.585 bits due to one's inability to discriminate between the four optically encoded Bell states. In this paper we study the following question: Are there alternative entanglement-assisted protocols that rely only on linear optics, coincidence photon counting and separable single photon input states and at the same time provide a greater capacity gain than 0.5850.5850.585 bits. We show that besides the Bell states there is a class of bipartite four-mode two-photon entangled states that facilitate an increase in channel capacity. We also discuss how the proposed scheme can be generalized to the case of two-photon NNN-mode entangled states for N=6,8N=6,8N=6,8.
We report on the experimental realization of the analogy of quantum dense coding in classical optical communication using classical optical correlations. Compared to quantum dense coding that uses pairs of photons entangled in polarization, we find that the proposed design exhibits many advantages. Considering that it is convenient to realize in optical communication, the attainable channel capacity in the experiment for dense coding can reach 2 bits, which is higher than that of the usual quantum coding capacity (1.585 bits). This increased channel capacity has been proven experimentally by transmitting ASCII characters in 12 quaternary digitals instead of the usual 24 bits.
Entanglement can effectively increase communication channel capacity as evidenced by dense coding that predicts a capacity gain of 1bit1\phantom{\rule{4.pt}{0ex}}\text{bit}1bit when compared to entanglement-free protocols. However, dense coding relies on Bell states and when implemented using photons the capacity gain is bounded by 0.585bits0.585\phantom{\rule{4.pt}{0ex}}\text{bits}0.585bits due to one's inability to discriminate between the four optically encoded Bell states. In this paper we study the following question: Are there alternative entanglement-assisted protocols that rely only on linear optics, coincidence photon counting, and separable single-photon input states and at the same time provide a greater capacity gain than 0.585bits0.585\phantom{\rule{4.pt}{0ex}}\text{bits}0.585bits? We show that besides the Bell states there is a class of bipartite four-mode two-photon entangled states that facilitate an increase in channel capacity. We also discuss how the proposed scheme can be generalized to the case of two-photon NNN-mode entangled states for N=6,8N=6,8N=6,8.
Quantum entanglement is known to enable otherwise impossible feats in various communication protocols, such as quantum key distribution and super-dense coding. Here we describe efforts to further enhance the usual benefits, by incorporating quantum states that are simultaneously entangled in multiple degrees of freedom – “hyperentangled”. Via the process of spontaneous parametric down conversion, we have demonstrated photon pairs simultaneously entangled in polarization and spatial mode, and have used these to realize remote entangled state preparation, full polarization Bell-state analysis, and the highest reported capacity quantum dense coding.
Quantum communication, as a vital area of quantum information science, aims to leverage quantum phenomena—particularly entanglement—to achieve tasks that are impossible or inefficient in classical systems. It plays a key role in the development of secure communication protocols and advanced information processing. This paper focuses on one such protocol, dense coding, which enables the transmission of two classical bits using only one entangled quantum particle.”We introduce the mathematical and physical foundations of quantum communication, such as the entangled state and Kronecker product. Then we propose the quantum communication protocol, namely dense coding using Bell states. It offer unique advantages that are beyond the classical parts. For this purpose, we in detail analyze the quantum measurements using Pauli gates and identity matrix, as well as the transmission of particle from Alice to Bob. They are necessary steps for dense coding. Then we analyze how Bob finishes the protocol using measurement over two qubits.