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arXiv:1502.00554 · Physical Review A

Channel-capacity gain in entanglement-assisted communication protocols based exclusively on linear optics, single-photon inputs, and coincidence photon counting

Pavel Lougovski, Dmitry B. Uskov

Published Aug 4, 2015• 5 citations
arXivHTMLPDF

Abstract

Entanglement can effectively increase communication channel capacity as evidenced by dense coding that predicts a capacity gain of $1\phantom{\rule{4.pt}{0ex}}\text{bit}$ when compared to entanglement-free protocols. However, dense coding relies on Bell states and when implemented using photons the capacity gain is bounded by $0.585\phantom{\rule{4.pt}{0ex}}\text{bits}$ 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 $0.585\phantom{\rule{4.pt}{0ex}}\text{bits}$? 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 $N=6,8$.

DOI
10.1103/physreva.92.022303

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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.
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.
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.
According to the theory that quantum entanglement can be used in quantum dense coding and increase the classical information capacity of a quantum channel, we discuss and compare the upper bound of capacity for dense coding in two case of using entangled input states and using product input states though a noiseless channel, when using a pure entanglement resource and get the result,i. e. , the capacity of dense coding using entangled input states is no larger than the capacity for product input states.
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 the seminal example of how entanglement can boost qubit communication, from sending one bit to sending two bits. This is made possible by projecting separate particles onto a maximally entangled basis. We investigate more general communication tasks, in both theory and experiment, and show that simpler measurements enable strong and sometimes even optimal entanglement-assisted qubit communication protocols. Using only partial Bell state analysers for two qubits, we demonstrate quantum correlations that cannot be simulated with two bits of classical communication. Then, we show that there exists an established and operationally meaningful task for which product measurements are sufficient for the strongest possible quantum predictions based on a maximally entangled two-qubit state. Our results reveal that there are scenarios in which the power of entanglement in enhancing quantum communication can be harvested in simple and scalable optical experiments.