Quantum Uniqueness

Peter D. Pešić

Povilas Marcinkevicius, İbrahim Ethem Bağcı, Nema M. Abdelazim +3 more

A Unique Object (UNO) is a physical object with unique characteristics that can be measured externally. The usually analogue measurement can be converted into a digital representation - a fingerprint - which uniquely identifies the object. For practical applications it is necessary that measurements can be performed without the need of specialist equipment or complex measurement setup. Furthermore, a UNO should be able to defeat simulation attacks; an attacker may replace the UNO with a device or system that produces the expected measurement. Recently a novel type of UNOs based on Quantum Dots (QDs) and exhibiting unique photo-luminescence properties has been proposed. The uniqueness of these UNOs is based on quantum effects that can be interrogated using a light source and a camera. The so called Quantum Confinement UNO (QCUNO) responds uniquely to different light excitation levels which is exploited for simulation attack protection, as opposed to focusing on features too small to reproduce and therefore difficult to measure. In this paper we describe methods for extraction of fingerprints from the QCUNO. We evaluate our proposed methods using 46 UNOs in a controlled setup. Focus of the evaluation are entropy, error resilience and the ability to detect simulation attacks.

Peter D. Pešić

Joel Klassen

The quantum marginal problem asks whether a family of quantum marginals are compatible with a global quantum state. It is of central importance to a wide range of topics in both quantum many body physics and quantum information. Often it can be the case that when a family of quantum marginals are compatible with a global quantum state, that global state is unique. This thesis explores the role of uniqueness in the quantum marginal problem, in particular the distinction between uniqueness among pure states and uniqueness among all states. A particularly important vari- ant of the quantum marginal problem is the symmetric extendibility problem. This thesis makes headway on characterizing the extremal points of a particular class of symmetric extendibility problems, and demonstrates the importance of understand- ing the distinction between being uniquely determined among mixed states and being uniquely determined among pure states in making further progress in this direction.

Ji‐Hwan Kim, Donghoon Ha, Younghun Kwon

This study considers the minimum error discrimination of two quantum states in terms of a two-party zero-sum game, whose optimal strategy is a minimax strategy. A minimax strategy is one in which a sender chooses a strategy for a receiver so that the receiver may obtain the minimum information about quantum states, but the receiver performs an optimal measurement to obtain guessing probability for the quantum ensemble prepared by the sender. Therefore, knowing whether the optimal strategy of the game is unique is essential. This is because there is no alternative if the optimal strategy is unique. This paper proposes the necessary and sufficient condition for an optimal strategy of the sender to be unique. Also, we investigate the quantum states that exhibit the minimum guessing probability when a sender's minimax strategy is unique. Furthermore, we show that a sender's minimax strategy and a receiver's minimum error strategy cannot be unique if one can simultaneously diagonalize two quantum states, with the optimal measurement of the minimax strategy. This implies that a sender can confirm that the optimal strategy of only a single side (a sender or a receiver but not both of them) is unique by preparing specific quantum states.

Peter D. Pešić