Quantum pattern recognition

Summary form only given. In quantum cryptography, non-cloning properties of quantum states are exploited to achieve quantum security. At the same time, typically one optical mode is used, for instance that of a single-mode optical fiber, effectively reducing the problem to a one-dimensional system. Only recently have researchers begun to exploit higher dimensions for quantum cryptography [1]. High dimensional spaces appear naturally in imaging applications.We here experimentally investigate the question if it is possible to recognize an arbitrary pattern in a physical object using much fewer photons than the complexity of the pattern. Theoretically it has already been proposed to use a quantum computer for pattern recognition and that this can be achieved with very few photons [2]. To avoid using a quantum computer, we exploit a spatial light modulator, which can map a single incoming optical mode on thousands outgoing optical modes in a programmable way. In this way, a weak light pulse containing only a few or even a single photon can be distributed over the high number of pixels of a complex 2-dimensional image. The inverse is just as feasible: a known complex pattern can be mapped onto a single mode. We use this principle to analyze the light from a physical object when illuminated with, e.g., a plane wave. After reflection of or transmission through the object under investigation, the response can be projected onto a single mode. The signal in that mode can be analyzed with the standard repertoire of quantum optical measurements, determining, e.g., the field amplitude, the intensity or the number of photons.We use coherent pulses of light which have mean photon numbers much smaller than the thousands of modes of the complex image. We introduce the parameter S=K/n as the ratio of the number of modes, K, of the response field pattern and the number of photons, n, that is used for the illumination. This measurement is in the quantum domain if S>>1. We read- out objects with S=4, well in the quantum regime. The method can be extended by preshaping the illumination light, with applications in authentication of physical objects [3,4].