Quantum wavelength-division-multiplexing and multiple-access communication systems and networks: Global and unified approach

The march towards successful global quantum internet requires introducing all-quantum networks and signal processing techniques. In this paper, we develop and discuss methods for various wavelength-division-multiplexing and multiple-access (WDM) communication systems and networks in fully quantum mechanical terms to obtain all-quantum WDM (QWDM) systems and networks. We begin the paper with a detailed discussion on various possible narrow-band and wideband sources of light signals used in typical WDM systems, such as coherent, number, and Poissonian mixed states. After introducing a generic and fully quantum mechanical WDM network, we develop methodologies for obtaining the necessary mathematical evolutions through wavelength distributors such as arrayed-waveguide-grating multiplexers and demultiplexers, and wavelength-sensitive and -insensitive broadcasting star couplers. In particular, using the methodologies introduced, one can use the results to obtain a complete and exact expression for any evolved pure quantum light signal through a typical WDM network using the aforementioned optical components. To test the validity and robustness of our mathematical expression for the evolved QWDM light signals, we use two opposing and extreme signals, namely, coherent state and number state, as inputs to various WDM communication and network systems and architecture. The methodologies and the required mathematical QWDM models introduced here can be extended to any fully quantum network architecture deemed necessary in a future global quantum internet, e.g., fiber to the home, Lambdanet-based broadcast WDM networks, and quantum routers based on a waveguide grating router.

Figure 1

(a) Wavelength division multiplexing optical network via a multichannel point-to-point long-haul fiber link [7], (b) passive photonic loop [7], and (c) single-hop WDM access network topologies (Lambdanet [6]). See Appendix pp1 for more description. Tx and Rx, respectively, stand for transmitter and receiver systems. Mux and DeMux are abbreviations of multiplexing and demultiplexing, respectively.

Figure 2

Schematic of a generic quantum wavelength division multiplexing (QWDM) network. Depending on chosen network topology, $\underline{\text{G}}$ can be a star coupler, a combination of multiplexer/fiber/demultiplexer, and or a wavelength grating router (WGR). Depending on opted $\underline{\text{G}}$, quantum transmitters (QTs) can be narrow and/or broadband lasers or single-photon sources. Input signals can be either weak coherent pulses (WCHs) or single-photon pulses (SPPs). Quantum receivers (QR), depending on a particular choice of $\underline{\text{G}}$, are a demultiplexer and/or a single frequency filter. Quantum detectors (QDs) can be either single-photon detectors (SPDs) or conjugate homodyne detectors (CHDs). ${\text{PD}}_{jl}$ stands for a photodetector that receives the optical signal from the $l\mathrm{th}$ output of the $j\mathrm{th}$ receiver. LO is a local oscillator. X1 and X2 indicate field quadratures.

Figure 3

Evolution of a single-photon wave-packet operator ${\widehat{a}}_{i,{\zeta }_i}^{†\left(1\right)}$ through a generic communication system's components towards all the receivers' detectors.

Figure 4

Illustration of the distribution of field operators from the input (solid red line) of the general distributor to the specific output (blue dashed line) (a) from stage 1 to stage 2 and (b) vice versa. Note that ${\left({\underline{\text{G}}}^{†}\right)}_{ij}={\underline{\text{G}}}_{ji}^{*}$.

Figure 5

Schematic of a router-based model of a $3\times 3 {\underline{\text{QR}}}_j$ utilized in QWDM. Input port number is fixed to (a) $\mathit{s}=1$ and (b) $\mathit{s}=2$.

Figure 6

Schematic configuration of a QWDM system for two transmitters and two receivers. QTx1 and QTx2 are two narrow-band sources with central frequencies ${\omega }_{11}$ and ${\omega }_{21}$, respectively.