Photonic information processing needs quantum design rules

In the century since Einstein postulated light's quantum nature—an event celebrated last year, along with SPIE's 50th birthday—the quantum revolution has progressed from formalizing the mathematical theory of the electron and photon, to a second wave that uses quantum phenomena for new information-processing technologies. These applications are found in fields as diverse as communications, cryptography, computing, and even imaging.

Since photons are the de facto information-encoding entity, this means photonic information processing often amounts to quantum information processing, which can be carried out on chips fabricated with very large scale integration (VLSI) techniques, such as the array of single-photon detectors shown in Figure 1, for significant cost reduction. Our experience with VLSI has taught us the importance of having good rules^B1 that abstract away the underlying physics and allow engineers to design chips. This inspired us to consider an analogous set of quantum design rules (QDRs) for VLSI photonics.^2,3

To establish correct engineering guidelines, we first need to understand the quantum rules that photons obey. We adopt the quantum path integral (QPI) formalism⁴ to avoid traps that arise from treating the photon as either a classical particle or a classical wave. Under this formalism, a photon propagating in free space is represented by an infinite set of QPI amplitudes φ_i between source s and detector d.

The probability for detecting a physical photon is determined by summing over all of these paths, and then taking the squared modulus of the result. Some eight quantum rules^2,3 of this type will correctly calculate probabilities in VLSI information-processing devices. For example, in Figure 2, which shows a scattering event ε, path φ₁ would be computed as the product of the two legs, φ_1a and φ_1b, an example of the ‘AND-ing’ rule. We have shown elsewhere that flawed claims can result when these rules are ignored.²

We have extended QPI formalism to entanglement.^2,3 The most common method for producing entangled ‘biphotons’ pumps a nonlinear crystal, such as beta-barium borate (BBO), with UV photons to create photon pairs whose total momenta and energy equal that of each pump photon. An entangled pair acts like the two-segment QPI amplitude shown in Figure 2. Figure 3 depicts the BBO crystal as the scattering event ε in Figure 2, and detectors D₁ and D₂ as the source and detector, respectively. One biphoton (signal) propagates from ε to detector D₂ in the expected way, but the idler photon propagates backward from D₁ to ε. The coincidence counter (CC) forms a closed circuit of paths.

Figure 3, as adapted in Figure 4, also explains how quantum ghost imaging^5,6 works. Detector D₁ acts like a source for the idler photon passing through a focusing lens to the BBO crystal, which propagates the signal photon to the detector array D₂. The ghost image appears only in the coincidence counts, focused in accordance with the thin lens equation.

With the photon rules in hand, we can discern some engineering-level QDRs. (i) Photons don't interact with photons, but only the material comprising the device. (ii) The minutest change to the material comprising a quantum information device can completely alter its operation. (iii) The distinction between amplitudes and intensities made in Fourier optics becomes redundant: only quantum amplitudes lead to probabilities. (iv) The thin lens equation d₁^-1 + d_o^-1 = f^-1 still holds for quantum-ghost imaging devices.⁵ More experiments are needed to enumerate other QDRs, and that is a major thrust of our current research conducted in the Quantum Architecture Group at the Swiss Federal Institute of Technology Lausanne (EPFL; Figure 5).