Counterfactual distribution of Schrödinger cat states

Abstract

In the counterfactual cryptography scheme proposed by Noh (2009), the sender Alice probabilistically transmits classical information to the receiver Bob without the physical travel of a particle. Here we generalize this idea to the distribution of quantum entanglement. The key insight is to replace their classical input choices with quantum superpositions. We further show that the scheme can be generalized to counterfactually distribute multi-partite cat states.

Addendum: Protocol for Counterfactually Transporting an Unknown Qubit

“…This can be ignored, however, for large M. Given ideal implementation, the fidelity of our protocol for counterfactual transport approaches unity for N ≫ M ≫ 1, where N and M are the number of inner and outer cycles respectively. We draw the reader's attention to the fact that the posting of our protocol on the arXiv in 2014 [2] has triggered a number of related papers including, Guo et al [3], Li et al [4], Vaidman [5], and Shenoy-Hejamadi and Srikanth [6]. We plan a separate reply to Vaidman's Comment [5].…”

How Quantum is Quantum Counterfactual Communication?

“…Once Salih et al published their protocol, various implementations began to appear [23,[43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61]. While many of these don't make use of polarisation, some do, alongside wider modal-style analyses of the protocol [41,62].…”

Quantum Cryptography: Key Distribution and Beyond

“…Though counterfactual quantum cryptography may not be so useful for long-distance communication, it is interesting conceptually [104,105]. Schemes to improve the efficiency of counterfactual quantum key distribution protocols [106,107], security analysis of such schemes under various attacks such as intercept-resend and counterfactual attacks [108][109][110], experimental realisation using different set-ups [25,111,112], direct communication protocols [113] and counterfactual generation and distribution of entanglement [114] have contributed towards better understanding of applying counterfactuality. The basic idea of the direct communication protocol is to ensure counterfactual transfer of information using the chained beamsplitter approach mentioned earlier.…”