Let $L_{>\lambda}(\mathcal{A})$ and $L_{\geq\lambda}(\mathcal{A})$ be the languages recognized by {\em measure many 1-way quantum finite automata (MMQFA)} (or,{\em enhanced 1-way quantum finite automata(EQFA)}) $\mathcal{A}$ with strict, resp. non-strict cut-point $\lambda$ . We consider the languages equivalence problem, showing that \begin{itemize} \item {both strict and non-strict languages equivalence are undecidable;} \item {to do this, we provide an additional proof of the undecidability of non-strict and strict emptiness of MMQFA(EQFA), and then reducing the languages equivalence problem to emptiness problem;} \item{Finally, some other Propositions derived from the above results are collected.} \end{itemize}Let $L_{>\lambda}(\mathcal{A})$ and $L_{\geq\lambda}(\mathcal{A})$ be the languages recognized by {\em measure many 1-way quantum finite automata (MMQFA)} (or,{\em enhanced 1-way quantum finite automata(EQFA)}) $\mathcal{A}$ with strict, resp. non-strict cut-point $\lambda$. We consider the languages equivalence problem, showing that \begin{itemize} \item {both strict and non-strict languages equivalence are undecidable;} \item {to do this, we provide an additional proof of the undecidability of non-strict and strict emptiness of MMQFA(EQFA), and then reducing the languages equivalence problem to emptiness problem;} \item{Finally, some other Propositions derived from the above results are collected.} \end{itemize}

arXiv:1308.3301Aug 15, 20130 citations

Secure quantum-enhanced measurements on a network of sensors

Sean William Moore, Jacob Dunningham

Two-party secure quantum remote sensing protocols enable quantum-enhanced measurements at remote locations with guaranteed security against eavesdroppers. This idea can be scaled up to networks of nodes where one party can directly measure functions of parameters at the different nodes using entangled states. However, the security on such networks decreases exponentially with the number of nodes. Here we show how this problem can be overcome in a hybrid protocol that utilizes both entangled and separable states to achieve quantum-enhanced measurement precision and security on networks of any size.Two-party secure quantum remote sensing protocols enable quantum-enhanced measurements at remote locations with guaranteed security against eavesdroppers. This idea can be scaled up to networks of nodes where one party can directly measure functions of parameters at the different nodes using entangled states. However, the security on such networks decreases exponentially with the number of nodes. Here we show how this problem can be overcome in a hybrid protocol that utilizes both entangled and separable states to achieve quantum-enhanced measurement precision and security on networks of any size.

arXiv:2406.19285Physical Review AJan 14, 20254 citations

On the Quantum Measurement Problem

Časlav Brukner

arXiv:1507.05255The frontiers collectionNov 14, 2016152 citations

Let

L_{>\lambda}(\mathcal{A})

and

L_{\geq\lambda}(\mathcal{A})

be the languages recognized by {\em measure many 1-way quantum finite automata (MMQFA)} (or,{\em enhanced 1-way quantum finite automata(EQFA)})

\mathcal{A}

with strict, resp. non-strict cut-point

\lambda

. We consider the languages equivalence problem, showing that \begin{itemize} \item {both strict and non-strict languages equivalence are undecidable;} \item {to do this, we provide an additional proof of the undecidability of non-strict and strict emptiness of MMQFA(EQFA), and then reducing the languages equivalence problem to emptiness problem;} \item{Finally, some other Propositions derived from the above results are collected.} \end{itemize}