Local Inaccessibility of Random Classical Information and Their Implications in the Change Point Problem

TL;DR

The paper introduces Local Random Authentication (LRA), an input-dependent LOCC discrimination task that tests whether a shared multipartite quantum state matches a particular orthogonal member under a classical query. It establishes a formal framework distinguishing complete and partial LRA, proves that LOCC discrimination implies LRA but not vice versa, and shows that product states can always be authenticated while entanglement is necessary for impossibility results, revealing a form of conditional nonlocality. It further analyzes conclusive variants of LRA, showing that pure-state sets always admit conclusive LRA whereas mixed-state cases exhibit richer, sometimes more restrictive behavior. Finally, LRA is linked to the quantum change point problem, showing that adaptive LOCC strategies can, under i.i.d. assumptions, be reduced to constant per-round LOCC protocols, with practical implications for device verification and quantum metrology.

Abstract

Discrimination of quantum states under local operations and classical communication (LOCC) is an intriguing question in the context of local retrieval of classical information, encoded in the multipartite quantum systems. All the local quantum state discrimination premises, considered so far, mimic a basic communication set-up, where the spatially separated decoding devices are independent of any additional input. Here, exploring a generalized communication scenario, we introduce a framework for input-dependent local quantum state discrimination, which we call local random authentication (LRA). We report that impossibility of LRA certifies the presence of entangled states in the ensemble, a feature absent from erstwhile nonlocality arguments based on local state discrimination. Additionally, we explore the salient features of this state discrimination prototype for arbitrary set of orthogonal quantum states and compare them with the traditional notion of local quantum state discrimination. Finally, our results reveal a fundamental information-theoretic implications in the local estimation of quantum change point problems.

Figures (2)

• Figure 1: Task of LRA in bipartite settings. A state $\ket{\psi_k}$, randomly chosen from the set of orthogonal quantum states $\mathcal{S}$, is distributed between $B_1$ and $B_2$ and the question $\mathcal{Q}_i$ is asked. Depending upon the question they will execute a LOCC protocol and answer a bit $y\in\{0,1\}$, which stands for " No" and " Yes" respectively. Since the framework considers unrestricted classical communication between the parties, w.l.g we can assume that the final answer will be given by $B_1$.
• Figure 2: A schematic diagram for the relation between LRA and LOCC discrimination. In the figure LOCCD abbreviates the phrase LOCC distinguishable. All the solid directed arrows represents the results established in the present work, while the dashed arrows are already known implications. The red cross-marks are used to depict that the corresponding implications do not hold true.

Theorems & Definitions (27)

• Definition 1
• Definition 2
• Theorem 1
• proof
• Theorem 2
• proof
• Corollary 1
• Proposition 1
• proof
• Lemma 1