Interaction-free measurement is a quantum process where, in the ideal situation, an object can be detected as if no interaction took place with the probing photon. Here we show that the problem of interaction-free measurement can be regarded as a problem of quantum-channel discrimination. In particular, we look for the optimal photonic states that can minimize the detection error and the photon loss in detecting the presence or absence of the object, which is taken to be semitransparent, and the number of the interrogation cycle is assumed to be finite. Furthermore, we also investigated the possibility of minimizing the detection error through the use of entangled photons, which is essentially a setting of quantum illumination. However, our results indicate that entanglement does not exhibit a clear advantage; the same performance can be achieved with unentangled photonic states.
Interaction-free measurement is a quantum process where, in the ideal situation, an object can be detected as if no interaction took place with the probing photon. Here we show that the problem of interaction-free measurement can be regarded as a problem of quantum-channel discrimination. In particular, we look for the optimal photonic states that can minimize the detection error and the photon loss in detecting the presence or absence of the object, which is taken to be semitransparent, and the number of the interrogation cycle is assumed to be finite. Furthermore, we also investigated the possibility of minimizing the detection error through the use of entangled photons, which is essentially a setting of quantum illumination. However, our results indicate that entanglement does not exhibit a clear advantage; the same performance can be achieved with unentangled photonic states.
Interaction-free measurement infers the presence of an absorbing object from a photon that, in the counterfactual sense, never interacted with it, and is widely described as a route to minimally invasive sensing. We ask what it actually buys, in estimation-theoretic terms. Written as a channel-estimation problem, the Elitzur-Vaidman interferometer carries exactly half the Fisher information about the object's transmissivity that direct transmission probing does, and the two schemes deliver identical Fisher information per absorbed photon. For measuring how transparent something is, the interferometer buys nothing. The advantage lies in discrimination, and we show that what it requires is not that the object be opaque but that the competing hypothesis be the object's absence. Against empty space the Chernoff information per absorbed photon grows almost linearly, as the number of Zeno cycles times its logarithm, even for a weakly absorbing object; between two partial transparencies it does not grow at all. Parasitic loss in the cycle caps the advantage. The number of conclusive interrogations per absorbed photon reaches a maximum inversely proportional to the loss per cycle, at an optimal cycle number that is likewise inversely proportional to it, which identifies the loss per cycle as the figure of merit governing how far interaction-free sensing can be pushed. Finally, the negative result is not special to the interferometer. For a single photon meeting a memoryless, non-dispersive object any number of times through arbitrary fixed optics, the accessible quantum Fisher information never exceeds that of the same incident flux spent on independent single-pass probes, and is generically far below it. This recovers the bound of Massar, Mitchison and Pironio for this class, by a short argument that also identifies when it is tight.
An interaction-free measurement system with a polarization-based Mach-Zehnder interferometer structure is analyzed for semitransparent objects. Here, it is shown that the interaction-free measurement of such objects with 100% detection efficiency is possible in principle if the system loss is negligible. The influence of two system imperfections, the system loss and the low quantum efficiency of the photon detectors, on the interaction-free measurement is also analyzed. Although the two system imperfections limit the maximal detection efficiency that can be achievable, the quantum efficiency of the photon detectors is less important when the system loss becomes small.
Abstract In this work, we investigate the question of which objects can be discriminated by totally “interaction-free” measurements. To this end, we interpret the Elitzur–Vaidman bomb-tester experiment as a quantum channel discrimination problem and generalize the notion of “interaction-free” measurement to arbitrary quantum channels. Our main result is a necessary and sufficient criterion for when it is possible or impossible to discriminate quantum channels in an “interaction-free” manner (i.e., such that the discrimination error probability and the “interaction” probability can be made arbitrarily small). For the case where our condition holds, we devise an explicit protocol with the property that both probabilities approach zero with an increasing number of channel uses, N. More specifically, the “interaction” probability in our protocol decays as N1 1 N and we show that this rate is the optimal achievable one. Furthermore, our protocol only needs at most one ancillary qubit and might thus be implementable in near-term experiments. For the case where our condition does not hold, we prove an inequality that quantifies the trade-off between the error probability and the “interaction” probability.
The characterisation of Quantum Channel Discrimination (QCD) offers critical insight for future quantum technologies in quantum metrology, sensing and communications. The task of multi-channel discrimination creates a scenario in which the discrimination of multiple quantum channels can be equated to the idea of pattern recognition, highly relevant to the tasks of quantum reading, illumination and more. Whilst the optimal quantum strategy for many scenarios is an entangled idler-assisted protocol, the extension to a multi-hypothesis setting invites the exploration of discrimination strategies based on unassisted, multipartite probe states. In this work, we expand the space of possible quantum enhanced protocols by formulating general classes of unassisted multi-channel discrimination protocols which are not assisted by idler modes. Developing a general framework for idler-free protocols, we perform an explicit investigation in the bosonic setting, studying prominent Gaussian channel discrimination problems for real world applications. Our findings uncover the existence of strongly quantum advantageous, idler-free protocols for the discrimination of bosonic loss and environmental noise. This circumvents the necessity for idler assistance to achieve quantum advantage in some of the most relevant discrimination settings, significantly loosening practical requirements for prominent quantum sensing applications.
We study the power of measurements implementable with local quantum operations and classical communication (LOCC) measurements in the setting of quantum channel discrimination. More precisely, we consider discrimination procedures that attempt to identify an unknown channel, chosen uniformly from two known alternatives, that take the following form: (i) the input to the unknown channel is prepared in a possibly entangled state with an ancillary system, (ii) the unknown channel is applied to the input system, and (iii) an LOCC measurement is performed on the output and ancillary systems, resulting in a guess for which of the two channels was given. The restriction of the measurement in such a procedure to be an LOCC measurement is of interest because it isolates the entanglement in the initial input-ancillary systems as a resource in the setting of channel discrimination. We prove that there exist channel discrimination problems for which restricted procedures of this sort can be at either of the two extremes: they may be optimal within the set of all discrimination procedures (and simultaneously outperform all strategies that make no use of entanglement), or they may be no better than unentangled strategies (and simultaneously suboptimal within the set of all discrimination procedures).
Abstract The characterisation of Quantum Channel Discrimination (QCD) offers critical insight for future quantum technologies in quantum metrology, sensing and communications. The task of multi-channel discrimination creates a scenario in which the discrimination of multiple quantum channels can be equated to the idea of pattern recognition, highly relevant to the tasks of quantum reading, illumination and more. Although the optimal quantum strategy for many scenarios is an entangled idler-assisted protocol, the extension to a multi-hypothesis setting invites the exploration of discrimination strategies based on unassisted, multipartite probe states. In this work, we expand the space of possible quantum-enhanced protocols by formulating general classes of unassisted multi-channel discrimination protocols which are not assisted by idler modes. Developing a general framework for idler-free protocols, we perform an explicit investigation in the bosonic setting, studying prominent Gaussian channel discrimination problems for real-world applications. Our findings uncover the existence of strongly quantum advantageous, idler-free protocols for the discrimination of bosonic loss and environmental noise. This circumvents the necessity for idler assistance to achieve quantum advantage in some of the most relevant discrimination settings, significantly loosening practical requirements for prominent quantum-sensing applications.