Fermionic model of unitary transport of qubits from a black hole Boguslaw Broda * Department of Theoretical Physics, Faculty of Physics and Applied Informatics, University of Lód´ z, Pomorska 149/153, 90-236 Lód´ z, Poland (Received 22 July 2020; accepted 11 December 2020; published 25 January 2021) Inspired by a recent model of Osuga and Page, we propose an explicitly unitary fermionic toy model for transferring information from a black hole to the outgoing radiation. The model treats the unitary evolution as a composition of the Hawking pair creation outside the black hole and of pair annihilation inside the black hole. DOI: 10.1103/PhysRevD.103.025022 I. INTRODUCTION The black hole (BH) information (loss) paradox con- cerns difficulties around the issue of unitarity of BH evaporation (for recent reviews see e.g., [1–4]). There are a lot of approaches proposed to date to analyze and resolve the paradox—some of them suggest to study simplified situations embodied in various qubit models (see e.g., [5–12]). A successful model of BH evolution should include a description of particle pair production according to the Hawking prescription, following gradual evaporation (“vanishing”) of the BH, and it should be unitary. A model strictly motivated by actual physical phenomena would certainly be greatly appreciated, but in fact any model respecting at least general physical laws, even without any real physical mechanism built in, would be welcome as a “proof of concept. ” Recently Osuga and Page [12] (inspired by [13]) have proposed an explicitly unitary toy qubit transport model for BH evaporation (without firewalls). Another version of the model (with additional features) has been presented in [14]. In the present paper, building on both models, we propose yet another toy qubit transport model for BH evaporation, which is explicitly unitary. Since the model, by assumption, operates on qubits and the particle pair production scheme exactly follows the Hawking mechanism for fermions, we shall work in terms of fermionic modes rather than bosonic ones. A new and important feature of our present proposal is explicit incorporation of the (fermionic) Hawking pair creation mechanism into the chain of unitary processes. In other words, the global unitary evolution considered is given by the composition U ¼ U 00 · U 0 , where U 0 corre- sponds to creation of fermionic pairs outside a BH according to the Hawking prescription, whereas U 00 cor- responds to annihilation of fermion pairs inside the BH (as described in [14]). For the reader’ s convenience, we will follow the notation of [12] (and [14]) as closely as possible. II. THE TOY MODEL An initial total quantum state describing a newly formed (fermionic) BH and “fermionic radiation” in the vacuum state is assumed in the following (partially product) form [14] (cf. [12]): jΨi¼ X 1 q 1 ;q 2 ;…;q N ¼0 A q 1 q 2 q N ⊗ N k¼1 jq k i a k ⊗ jOi b k c k : ð1Þ Here A q 1 q 2 q N are amplitudes for inner BH modes a k , which encode a quantum state of the BH, and the vacuum state for fermionic radiation is jOi b k c k ≡ j0i b k ⊗ j0i c k ; ð2Þ where the Hawking (fermionic) modes b k and c k are infalling and outgoing modes, respectively. The same range of indices (k ¼ 1; 2; …;N) postulated for BH modes a k and b k , c k pairs is not only a convenient computational simplification in our model but also it is a physically justified assumption, at least approximately (see e.g., [14]). In the language of k-mode blocks, the first step of (unitary) evolution denoted by U 0 k yields the Hawking (fermion) pair for a single “k” mode, i.e., U 0 k ðjq k i a k ⊗ jOi b k c k Þ¼jq k i a k ⊗ jH 1 i b k c k ; ð3Þ where the fermionic Hawking state can be chosen in the form [cf. Eq. (116) in [15] ] * boguslaw.broda@uni.lodz.pl Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP 3 . PHYSICAL REVIEW D 103, 025022 (2021) 2470-0010=2021=103(2)=025022(5) 025022-1 Published by the American Physical Society