On the Impossibility of Interaction-Free Quantum Sensing for Small I/O Bandwidth

Abstract

A method for ( nearly ) interaction-free measurement ( IFM ) specifies the design of a quantum optical sensing system that is able to determine with arbitrarily high likelihood if an obstructing body has been inserted into the system, without moving or modifying its optical components, and uses at most an arbitrarily small multiplicative factor of the input intensity to do the sensing when the obstructing body is present. Kwiat et al. (1995, Phys. Rev. Lett. 74 , 4763–4766) have given a method for IFM. We give a precise mathematical formulation of IFM and as an example, we use this formulation to specify the IFM method of Kwiat et al. We similarly define ( nearly ) interaction-free sensing ( IFS ), except that we impose an upper bound on the intensity to do the sensing (which again is an arbitrarily small multiplicative factor of the input intensity) whether or not the obstructing body is present. A quantum optical method for IFS (but not IFM) may be used to do I/O with bandwidth reduced by an arbitrarily small multiplicative factor of the bandwidth required for conventional optical or electronic I/O methods (i.e., without using quantum effects). We prove that there is no method for IFS with unitary transformations. Hence we conclude that I/O bandwidth can not be significantly reduced by such quantum methods for sensing. This is one of relatively few known proofs of the non-existence of a class of quantum devices (e.g., for instantaneous communication and EPR) and apparently the first for a quantum device relevant to computational I/O bandwidth. We use an interesting proof method, where we first show that no unitary transformation can do quantum amplification detection : that is, significantly increase the amplitude on detection of a small amplitude basis state. Then we show that the existence of a method for IFS implies a unitary quantum amplification detection method, which is impossible.