A Quantum Paradox of Choice and Purported Classical Analogues

TL;DR

This paper explores a quantum paradox of choice where more options make a task harder, introduces new conditions for quantum state summoning, and discusses classical analogues, highlighting fundamental differences.

Contribution

It establishes necessary and sufficient conditions for quantum state summoning with multiple calls and introduces the concept of a quantum paradox of choice.

Findings

More options can make quantum tasks impossible, unlike classical intuition.

New stronger conditions are required for summoning when multiple calls are possible.

Classical analogues of the paradox are argued to be disanalogous.

Abstract

We recently considered the task of summoning an unknown quantum state and proved necessary and sufficient conditions for Alice to be able to guarantee to complete the task when there may be several possible calls, of which she need only respond to one. We showed that these are strictly stronger conditions than those previously established by Hayden and May for the case where Alice knows there will only be one call. We introduced the concept of a {\it quantum paradox of choice} to summarize the implications of these results: Alice is given more options to complete our version of the task, yet one can easily construct examples where our version is impossible and the apparently simpler version considered by Hayden-May is possible. Finkelstein has argued that one can identify analogous classical paradoxes of choice in a relativistic setting. We examine Finkelstein's proposed classical tasks and explain why they seem to us disanalogous.