It has long been assumed in physics that for information to travel between two parties in empty space, ``Alice'' and ``Bob,'' physical particles have to travel between them. Here, using the ``chained'' quantum Zeno effect, we show how, in the ideal asymptotic limit, information can be transferred between Alice and Bob without any physical particles traveling between them.

Quantum teleportation circumvents the uncertainty principle using dual channels: a quantum one consisting of previously-shared entanglement, and a classical one, together allowing the disembodied transport of an unknown quantum state over distance. It has recently been shown that a classical bit can be counterfactually communicated between two parties in empty space, “Alice” and “Bob”. Here, by using our “dual” version of the chained quantum Zeno effect to achieve a counterfactual CNOT gate, we propose a protocol for transporting an unknown qubit counterfactually, that is without any physical particles travelling between Alice and Bob—no classical channel and no previously-shared entanglement.

DOI: http://dx.doi.org/10.1103/PhysRevLett.112.208902 © 2014 American Physical Society

In a recent paper [ Phys. Rev. A 94, 032115 (2016)], Griffiths questioned—based on an interesting consistent-histories (CH) argument—the counterfactuality, for one of the bit choices, of the protocol of Salih et al. for communicating without sending physical particles [ Phys. Rev. Lett. 110, 170502 (2013)]. Here, we first show that for the Mach-Zehnder version used to explain our protocol, contrary to Griffiths's claim, no family of consistent histories exists where any history has the photon traveling through the communication channel, thus rendering the question of whether the photon was in the communication channel meaningless from a CH viewpoint. We then show that for the actual Michelson-type protocol, there is a consistent-histories family for each cycle that includes histories where the photon travels through the communication channel. We show that the probability of finding the photon in the communication channel at any time is zero—proving complete counterfactuality.

We present a way of directly manipulating an arbitrary qubit, without the exchange of any particles. This includes as an application the exchange-free preparation of an arbitrary quantum state at Alice by a remote classical Bob. As a result, we are able to propose a protocol that allows one party to directly enact, by means of a suitable program, any computation exchange-free on a remote second party's unknown qubit. Further, we show how to use this for the exchange-free control of a universal two-qubit gate, thus opening the possibility of directly enacting any desired algorithm remotely on a programmable quantum circuit.

We show how two distrustful parties, ``Bob'' and ``Charlie,'' can share a secret key with the help of a mutually trusted ``Alice'' counterfactually; that is, with no information-carrying particles traveling between any of the three.