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Dense Coding with Linear Optics without Bell State Measurements

Pavel Lougovski, Dmitry B. Uskov

Published Feb 2, 2015• 0 citations
OpenAlex

Abstract

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 $0.585$ 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 $0.585$ 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 $N$-mode entangled states for $N=6,8$.

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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.
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.
Here, we study the classical information capacity of a quantum channel, assuming linear optical encoding, as a function of available photons and optical modes. We present a formula for general channel capacity and show that this capacity is achieved without requiring the use of entangling operations typically required for scalable universal quantum computation, e.g., Knill-Laflamme-Milburn measurement-assisted transformations. As an example, we provide an explicit encoding scheme using the resources required of standard dense coding using two dual-rail qubits (two photons in four modes). In this case, our protocol encodes one additional bit of information. Greater gains are expected for larger systems.
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.
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.
With the assistance of auxiliary two-dimensional polarization entanglement, we theoretically present an efficient Bell state measurement (BSM) method for photonic four-dimensional entanglement in the path degree of freedom, in which just simple linear optical elements and common single-photon detectors are utilized. With this approach, the 16 mutually orthogonal four-dimensional path Bell states can be classified into eight distinguishable groups, which allows the transmission of 3 bits of classical information by just sending one photon in our quantum superdense coding protocol. Compared with previous quantum dense coding protocols that are also based on linear-optical BSM, our protocol has certain advantages and will be useful for other quantum communication protocols based on high-dimensional entanglement.