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Frontiers in Optics

Information in a Photon When Loss Encodes the Bit

Saikat Guha, Zachary Dutton, Jonathan L. Habif

Published Jan 1, 2011• 0 citations
Publisher

Abstract

We investigate quantum limits on the information that can be reliably extracted by a photon, when the information is encoded using linear loss. Applications range across transverse optical imaging to optical reading and continuous-variable tomography.
DOI
10.1364/fio.2011.jtua42

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We address the problem of how efficiently information can be encoded into and read out reliably from a passive reflective surface that encodes classical data by modulating the amplitude and phase of incident light. We show that nature imposes no fundamental upper limit to the number of bits that can be read per expended probe photon and demonstrate the quantum-information-theoretic trade-offs between the photon efficiency (bits per photon) and the encoding efficiency (bits per pixel) of optical reading. We show that with a coherent-state (ideal laser) source, an on-off (amplitude-modulation) pixel encoding, and shot-noise-limited direct detection (an overly optimistic model for commercial CD and DVD drives), the highest photon efficiency achievable in principle is about 0.5 bits read 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 nonclassical light probe and a receiver design---constructible 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 WWW state. The code 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 WWW-state transceiver, although this advantage rapidly disappears with increasing loss in the system.
Exploration of the Universe requires communication with Earth, either on a direct path or through a cascade of proximate celestial bodies. Microwaves have traditionally been used for space communication, but electromagnetic waves of higher frequencies, such as in the optical domain, will enable probing farther in space due to their considerably lower diffraction loss. The ultimate range limit to point-to-point optical communication, at a given transmitter power, is determined by the photon information efficiency (PIE), which measures the number of information bits extracted per photon incident on a detector. As distances across space and, consequently, path loss increases, systems achieving the highest PIE can enable communication at the longest distances. We report here an experimental demonstration of optical detection at a record PIE of 14.5 bits per incident photon, or 17.8 bits per detected photon, after 87.5 dB of attenuation. Expressed in terms of energy per bit, this corresponds to 8.84 zeptojoules per bit, or 0.069 photons per bit at 1550 nm. To our knowledge, this is the highest PIE or lowest energy per bit detection system ever demonstrated at optical frequencies. Such a sensitive detection system holds promise for a wide range of applications.
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