Capacity of optical reading, Part 1: Reading boundless error-free bits using a single photon

We show that nature imposes no fundamental upper limit to the number of information bits per expended photon that can, in principle, be read reliably when classical data is encoded in a medium that can only passively modulate the amplitude and phase of the probe light. We show that with a coherent-state (laser) source, an on-off (amplitude-modulation) pixel encoding, and shot-noise-limited direct detection (an overly-optimistic model for commercial CD/DVD drives), the highest photon information efficiency achievable in principle is about 0.5 bit per transmitted photon. We then show that a coherent-state probe can read unlimited bits per photon when the receiver is allowed to make joint (inseparable) measurements on the reflected light from a large block of phase-modulated memory pixels. Finally, we show an example of a spatially-entangled non-classical light probe and a receiver design---constructable using a single-photon source, beam splitters, and single-photon detectors---that can in principle read any number of error-free bits of information. The probe is a single photon prepared in a uniform coherent superposition of multiple orthogonal spatial modes, i.e., a W-state. The code, target, and joint-detection receiver complexity required by a coherent-state transmitter to achieve comparable photon efficiency performance is shown to be much higher in comparison to that required by the W-state transceiver.