Evaluation of counterfactuality in counterfactual communication protocols

Abstract

We provide an in-depth investigation of parameter estimation in Nested Mach-Zehnder interferometers (NMZIs) using two information measures: the Fisher information and the Shannon mutual information. Protocols for counterfactual communition (CFC) have, so far, been based on two different definitions of counterfactuality. In particular, some schemes are been based on NMZI devices, and have recently been subject to criticism. We provide a methodology for evaluating the counterfactuality of these protocols, based on an information theoretical framework. More specifically, we make the assumption that any realistic quantum channel in MZI structures will have some weak uncontrolled interaction. We then use the Fisher information of this interaction to measure counterfactual violations. The measure is used to evaluate the suggested counterfactual communication protocol of Salih et al. [1]. The protocol of Arvidsson-Shukur and Barnes [2], based on a different definition, is evaluated with a probability measure. Our results show that the definition of Arvidsson-Shukur and Barnes is satisfied by their scheme, whilst that of Salih et al. is only satisfied by perfect quantum channels. For realistic devices the latter protocol does not achieve its objective.

Quantum advantage in postselected metrology

“…Postselection can also raise the rate of information per final measurement in a quantum setting. But classical postselection is intuitive, whereas an intense discussion surrounds postselected quantum experiments [17][18][19][20][21][22][23][24][25][26][27][28][29] . The ontological nature of postselected quantum states, and the extent to which they exhibit nonclassical behavior, is subject to an ongoing debate.…”

Trace-free counterfactual communication with a nanophotonic processor

“…In practice, however, imperfections in the interferometers will lead to cases in which the photon re-enters Alice's laboratory and she incorrectly records a logic 1. This leads to a rare counterfactual violation, as the wavefunction "leaks" from Bob's to Alice's laboratory, 15 leaving a weak trace in Bob's lab, while the photon is detected in Alice's laboratory. The high-fidelity operations enabled by our PNP allows us to make the probability of such violations vanishingly small.…”

“…11,12,14 (2) An analysis of the Fisher information flow indicates that to retain counterfactuality in Salih's protocol, perfect quantum channels are needed. 15 (3) If one performs a weak measurement in Bob's lab, one can detect the presence of photons that are later found in Alice's laboratory. Some authors have argued that the presence of the "weak trace" renders the counterfactuality of the protocol invalid, [16][17][18][19] but others have dismissed the weak trace as a consequence of the unwanted weak measurement's disturbance.…”

“…In our scheme single photons travel from Alice to Bob but information from Bob to Alice; this has been dubbed type-II CFC, in contrast to type-I schemes, where the photon should remain with Alice throughout the protocol. 15 In both types the particles and the information never co-propagate, thereby making the communication counterfactual. Note that the very recent proposals 23,24 discussing means of making the Salih scheme trace-free still require the post-selected removal of noncounterfactual events, as well as thousands of ideal optical operations.…”

Genuine Counterfactual Communication with a Nanophotonic Processor

“…The quantum Zeno effect allows Bob to transmit a message to Alice by encoding information in particles he never interacts with 4,5 . The first suggested protocol 6 not only required thousands of ideal optical components, but also resulted in a so-called "weak trace" 7 of the particles having travelled from Bob to Alice, calling the scalability and counterfactuality of previous proposals [8][9][10][11][12] and experiments 13,14 into question. Here we overcome these challenges, implementing a new protocol 15 in a programmable nanophotonic processor, based on reconfigurable silicon-on-insulator waveguides that operate at telecom wavelengths 16 .…”