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Physical Review A

Dense coding by means of the displaced photon

Sergey A. Podoshvedov, Jaewan Kim

Published Mar 12, 2008• 18 citations
Publisher

Abstract

We propose an optical scheme to perform a complete Bell-state measurement of four entangled displaced states. The principal feature of the scheme is the use of the phase of the displaced photon. The main ingredients of the scheme are the resources of single photons, coherent radiation, and optical linear elements (beam splitters, phase-shifting devices). The optical scheme works with on-off photodetectors that cannot discriminate different numbers of detected photons. This type of measurement is adjusted for dense coding and a communication rate per photon is calculated for one partial case.

DOI
10.1103/physreva.77.032319

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We propose an optical scheme to perform a complete Bell-state measurement of four entangled displaced states. The principal feature of the scheme is the use of the phase of the displaced photon. The main ingredients of the scheme are the resources of single photons, coherent radiation, and optical linear elements (beam splitters, phase-shifting devices). The optical scheme works with on-off photodetectors that cannot discriminate different numbers of detected photons. This type of measurement is adjusted for dense coding and a communication rate per photon is calculated for one partial case.
We extend the analysis of dense coding protocol based on displaced photon states. The phase transformations with a displaced qubit allow for someone to transform five states to each other. Each ``particle-carrier'' (displaced qubit) carries an equal number of photons. On the receiving side, it is possible to decode all five outcomes using a linear optical scheme with beam splitters and on-off photodetectors that cannot discriminate different number of detected photons. Summarizing, interacting with only a single displaced qubit, it is possible to transmit two bits of information more. Optimal conditions to guarantee maximal communication rate log25{\mathrm{log}}_{2}5log2​5 per ``particle-carrier'' (displaced qubit) and influence of decoherence on the communication rate are considered.
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.
In this paper, we propose an optical scheme to almost completely teleport a two-mode four-component entangled coherent state in terms of optical devices such as nonlinear Kerr media, beam splitters, phase shifters and photon detectors. Different from those previous schemes in which exact photon number discrimination is needed, in our scheme one only needs to make ‘yes’ and ‘no’ measurements upon the photon numbers in related modes. This scheme can also be understood as an entanglement swapping protocol.
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.
We propose a simple scheme for complete Bell-state measurement of photons using hyperentangled states---entangled in multiple degrees of freedom. In addition to hyperentanglement, our scheme requires only linear optics and single photon detectors, and is realizable with current technology. At the cost of additional classical communication, our Bell-state measurement can be implemented nonlocally. We discuss the possible application of these results to quantum dense coding and quantum teleportation.
We propose a nearly perfect optical scheme for the quantum teleportation of entangled coherent states using optical devices such as nonlinear Kerr media, beam splitters, phase shifters, and photon detectors. Different from those previous schemes, our scheme needs only ``yes'' or `no' measurements of the photon number of the related modes, i.e. nonzero- and zero-photon measurements, while in previous schemes one has to exactly identify the even or odd parity character of the photon numbers detected by detectors.