# Sharing Nonfungible Information Requires Shared Nonfungible Information

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Identification Formalism

## 3. Fungible Information Is Insufficient for System Identification

**Theorem**

**1.**

**Lemma**

**1.**

**Proof of Lemma 1.**

**Proof of Theorem 1.**

**Example**

**1.**

**Example**

**2.**

**Example**

**3.**

## 4. Implemented System Identification Operators Are Nonfungible

**Theorem**

**2.**

**Proof.**

## 5. Uncertainty about Operator Sharing Induces Decoherence

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

QRF | Quantum reference frame |

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**Figure 1.**Alice sends distant Bob a fungible encoding of her observational outcomes and a nonfungible token (dashed lines) of her local Cartesian frame. Both Alice and Bob must identify the same token for the sharing protocol to be successfully executed.

**Figure 2.**Alice and Bob each cycle through identifying ($\{{M}_{j}^{Xk}\}$ and $\{{M}_{j}^{Yk}\}$) and then determining the pointer state of ($\{{M}_{l}^{Pk}\}$ and $\{{M}_{l}^{Qk}\}$) their shared (${X}_{k}$) and local (${Y}_{k}$) Cartesian frames.

**Figure 3.**Quantum Darwinism [19,20]: Observers k interact with disjoint partitions ${E}^{k}$ of the environment E of S, each of which encodes the eigenvalues of ${H}_{SE}$. Redundancy of encoding and hence agreement among the observers k clearly requires that ${H}_{SE}$ be independent of the partitioning of E into the ${E}^{k}$.

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## Share and Cite

**MDPI and ACS Style**

Fields, C.; Marcianò, A. Sharing Nonfungible Information Requires Shared Nonfungible Information. *Quantum Rep.* **2019**, *1*, 252-259.
https://doi.org/10.3390/quantum1020022

**AMA Style**

Fields C, Marcianò A. Sharing Nonfungible Information Requires Shared Nonfungible Information. *Quantum Reports*. 2019; 1(2):252-259.
https://doi.org/10.3390/quantum1020022

**Chicago/Turabian Style**

Fields, Chris, and Antonino Marcianò. 2019. "Sharing Nonfungible Information Requires Shared Nonfungible Information" *Quantum Reports* 1, no. 2: 252-259.
https://doi.org/10.3390/quantum1020022