# Semi-device-independent quantum money with coherent states

## TL;DR

This paper presents a security proof for semi-device-independent quantum money using coherent states, accounting for practical imperfections and analyzing protocol security over time with quantum memory.

## Contribution

It provides a novel security analysis for quantum money protocols with classical verification in realistic settings using semidefinite programming.

## Key findings

- Secure regimes identified in fixed and randomized phase settings.
- Protocol security evolution analyzed with decohering quantum memory.
- Secure credit card lifetimes determined for specific configurations.

## Abstract

The no-cloning property of quantum mechanics allows unforgeability of quantum banknotes and credit cards. Quantum credit card protocols involve a bank, a client and a payment terminal, and their practical implementation typically relies on encoding information on weak coherent states of light. Here, we provide a security proof in this practical setting for semi-device-independent quantum money with classical verification, involving an honest bank, a dishonest client and a potentially untrusted terminal. Our analysis uses semidefinite programming in the coherent state framework and aims at simultaneously optimizing over the noise and losses introduced by a dishonest party. We discuss secure regimes of operation in both fixed and randomized phase settings, taking into account experimental imperfections. Finally, we study the evolution of protocol security in the presence of a decohering optical quantum memory and identify secure credit card lifetimes for a specific configuration.