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arXiv:1801.05578 · Physical Review A

Paradoxical consequences of multipath coherence: Perfect interaction-free measurements

Z. Zhao, S. Mondal, M. Markiewicz, A. Rutkowski, Borivoje Dakić, Wiesław Laskowski, Tomasz Paterek

Published Aug 6, 2018• 3 citations
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Abstract

Quantum coherence can be used to infer the presence of a detector without triggering it. Here we point out that, according to quantum mechanics, such interaction-free measurements cannot be perfect, i.e., in a single-shot experiment one has strictly positive probability to activate the detector. We formalize the extent to which such measurements are forbidden by deriving a trade-off relation between the probability of activation and the probability of an inconclusive interaction-free measurement. Our description of interaction-free measurements is theory independent and allows derivations of similar relations in models generalizing quantum mechanics. We provide the trade-off for the density cube formalism, which extends the quantum model by permitting coherence between more than two paths. The trade-off obtained hints at the possibility of perfect interaction-free measurements and indeed we construct their explicit examples. Such measurements open up a paradoxical possibility where we can learn by means of interference about the presence of an object in a given location without ever detecting a probing particle in that location. We therefore propose that absence of perfect interaction-free measurement is a natural postulate expected to hold in all physical theories. As shown, it holds in quantum mechanics and excludes the models with multipath coherence.

DOI
10.1103/physreva.98.022108

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Quantum coherence can be used to infer the presence of a detector without triggering it. Here we point out that, according to quantum mechanics, such interaction-free measurements cannot be perfect, i.e., in a single-shot experiment one has strictly positive probability to activate the detector. We formalize the extent to which such measurements are forbidden by deriving a trade-off relation between the probability of activation and the probability of an inconclusive interaction-free measurement. Our description of interaction-free measurements is theory independent and allows derivations of similar relations in models generalizing quantum mechanics. We provide the trade-off for the density cube formalism, which extends the quantum model by permitting coherence between more than two paths. The trade-off obtained hints at the possibility of perfect interaction-free measurements and indeed we construct their explicit examples. Such measurements open up a paradoxical possibility where we can learn by means of interference about the presence of an object in a given location without ever detecting a probing particle in that location. We therefore propose that absence of perfect interaction-free measurement is a natural postulate expected to hold in all physical theories. As shown, it holds in quantum mechanics and excludes the models with multipath coherence.
Recently, it has been pointed out that it is possible to make a quantum-mechanical interaction-free measurement (IFM), in which the existence of an object in a given region of space may be determined seemingly without interacting with it.1,2 In the embodiment first proposed by Elitzur and Vaidman,3 a standard Michelson interferometer is aligned so that incident single photons (obtained in our experiment by using parametric downconversion; see Fig. 1) must exit by the same port in which they entered, in the absence of any object within the interferometer. The presence of an object (e.g., the mirror leading to detector DB) in one of the arms completely changes the possible outcomes because the constructive interference is interrupted. Now it is possible that the photon will exit from the other exit port, to detector DIfm. By detecting the photon in this case, one can claim with certainty that an object was within the interferometer, even though the photon could not have interacted with it. If the beam splitter has a very low reflectivity, then the fraction of IFMs approaches 1/2.
Summary form only given.Using the complementary wave-like and particle-like natures of photons, one can make interaction-free measurements (IFM)-the presence of an object can be determined with no photons being absorbed. By using an application of the quantum Zeno effect (weakly and repeatedly testing for the object's presence so that the otherwise coherent evolution of the interrogating photon is inhibited), we have demonstrated the feasibility of IFMs with an efficiency of >85%, higher than that possible in the original IFM scheme, where, at most, half of the measurements could be interaction free. We also investigate various interaction-free imaging systems, demonstrate imaging with a resolution <5 /spl mu/m, and define the limits to these systems. We also discuss in which sense interaction-free measurements really are not.
A quantum-mechanical measurement process is analyzed in terms of a model Hamiltonian describing the interaction between a quantum system (a ``particle'') and a macroscopic apparatus (a ``detector''), which is assumed to be made up of N two-level elementary constituents (``molecules''). The description of the molecule locations introduces an effective fluctuating coupling constant, and this provokes a loss of quantum-mechanical coherence in the limit of large N. It is argued that coherence is lost statistically, as a result of the interaction: The collapse of the wave function is indeed obtained when the same experiment is performed many times, as a result of the microscopic differences among macroscopically identical initial states of the detector. In this way, insight is obtained into the mechanism engendering the loss of coherence suffered by a quantum-mechanical system when interacting with a macroscopic apparatus, and the concept of ``wave-function collapse'' is replaced by that of a statistically defined dephasing process. No classical behavior of the detection system is postulated and the presence of no external observer is required.
Interaction-free measurement (IFM) certifies the presence of an absorbing object without a photon ever being absorbed by it. When several candidate locations are available, existing protocols can also identify which one holds the absorber, but they do so by testing paths sequentially through two-path interferometers, resolving a binary presence question at each step. We propose a different approach: probing all candidate locations at once, with the photon prepared in a coherent superposition across every path before a single measurement resolves the outcome. We prove that a three-stage protocol built on a ddd-path interferometer attains the exact one-shot optimum for this task, and we extend it to kkk absorbers among ddd paths, where the no-absorption branch encodes the entire absorber subset coherently rather than revealing individual locations one by one. The dark port therefore ceases to be a mere witness of presence and becomes a location-resolving signal. We then move beyond single-pass strategies using the quantum-comb formalism, casting the problem as an exact optimization over all multi-pass strategies and showing that adaptive protocols surpass the one-shot ceiling. Enriching the interferometer geometry with one additional path guaranteed to be empty, we show that sequential scanning, bright-port recycling, and Zeno-type interrogation all become particular feasible strategies within this same optimization, rather than separate benchmarks to compare against. This unified formulation identifies the optimal interaction-free localization strategy for any given set of resources, opening a route toward loss-resilient quantum imaging protocols for the study of fragile, absorption-sensitive samples.
In 1993 Elitzur and Vaidmannl (EV) demonstrated that quantum mechanics permits the use of light quanta to examine an object without a single photon having actually interacted with the object, requiring only the possibility of such an interaction. The EV scenario has recently been carried out in the laboratory and its predictions verified. EV discussed their scenario in terms of the Copenhagen interpretation of quantum mechanics, in which the interaction-free result is rather mysterious, using a “knowledge” not available classically. They also used the Everett-Wheeler interpretation and suggested that the information indicating the presence of the opaque object comes from an interaction in a separate Everett-Wheeler universe, with the information communicated to our universe through the absence of interference. In the present work, we will examine the EV interaction-free scenario in terms of the transactional interpretation of quantum mechanics2 and will provide a more plausible account of the physical processes that make possible quantum interaction-free measurements.
We investigate the extent to which ``interaction-free'' measurements perturb the state of quantum systems. We show that the absence of energy exchange during the measurement is not a sufficient criterion to preserve that state, as the quantum system is subject to measurement-dependent decoherence. While it is possible in general to design interaction-free measurement schemes that do preserve that state, the requirement of quantum coherence preservation rapidly leads to a very low efficiency. Our results, which have a simple interpretation in terms of ``which-way'' arguments, open up the way to novel quantum nondemolition techniques.