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Quantum state exclusion with many copies

Debanjan Roy, Tathagata Gupta, Pratik Ghosal, Samrat Sen, Somshubhro Bandyopadhyay

TL;DR

The paper analyzes quantum state exclusion under multiple identical copies and proves that any ensemble of at least three pure states becomes antidistinguishable with a finite number of copies, though the required number $N$ can be arbitrarily large. It introduces a formal many-copy framework, derives a universal activation bound, and provides exact copy counts for special classes such as equi-overlap sets. It further shows that there is no universal finite bound on $N$ by constructing ensembles that require more and more copies, and demonstrates a complete characterization for three pure states with equal overlaps. Overall, the results reveal a robust activation phenomenon for state exclusion in the many-copy regime, with implications for quantum foundations and information-processing tasks that rely on exclusion.”

Abstract

Quantum state exclusion is the task of identifying at least one state from a known set that was not used in the preparation of a quantum system. In particular, a given set of quantum states is said to admit state exclusion if there exists a measurement such that, for each state in the set, some measurement outcome rules it out with certainty. However, state exclusion is not always possible in the single-copy setting. In this paper, we investigate whether access to multiple identical copies enables state exclusion. We prove that for any set of three or more pure states, state exclusion becomes possible with a finite number of copies. We further show that the required number of copies may be arbitrarily large -- in particular, for every natural number $N$, we construct sets of states for which exclusion remains impossible with $N$ or fewer copies.

Quantum state exclusion with many copies

TL;DR

The paper analyzes quantum state exclusion under multiple identical copies and proves that any ensemble of at least three pure states becomes antidistinguishable with a finite number of copies, though the required number can be arbitrarily large. It introduces a formal many-copy framework, derives a universal activation bound, and provides exact copy counts for special classes such as equi-overlap sets. It further shows that there is no universal finite bound on by constructing ensembles that require more and more copies, and demonstrates a complete characterization for three pure states with equal overlaps. Overall, the results reveal a robust activation phenomenon for state exclusion in the many-copy regime, with implications for quantum foundations and information-processing tasks that rely on exclusion.”

Abstract

Quantum state exclusion is the task of identifying at least one state from a known set that was not used in the preparation of a quantum system. In particular, a given set of quantum states is said to admit state exclusion if there exists a measurement such that, for each state in the set, some measurement outcome rules it out with certainty. However, state exclusion is not always possible in the single-copy setting. In this paper, we investigate whether access to multiple identical copies enables state exclusion. We prove that for any set of three or more pure states, state exclusion becomes possible with a finite number of copies. We further show that the required number of copies may be arbitrarily large -- in particular, for every natural number , we construct sets of states for which exclusion remains impossible with or fewer copies.
Paper Structure (12 sections, 12 theorems, 40 equations, 1 figure)

This paper contains 12 sections, 12 theorems, 40 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Exclusion of quantum states
  3. Antidistinguishable Sets
  4. Known Characterizations
  5. Many-copy Antidistinguishability
  6. Motivation
  7. Results
  8. All sets of pure states are many-copy antidistinguishable
  9. $N$-copy antidistinguishability of states with equal and real pairwise inner products
  10. Arbitrarily many copies may be required for activating antidistinguishability
  11. Complete characterisation of $N$-copy antidistinguishability of three pure states with equal overlaps
  12. Conclusions

Key Result

Proposition 2

A set $\mathcal{S} = \{\rho_1, \rho_2, \ldots, \rho_k\}$ is antidistinguishable only if where denotes the fidelity between $\rho_i$ and $\rho_j$.

Figures (1)

  • Figure 1: Number of copies necessary and sufficient to activate antidistinguishability for the set of three qubit states defined in Eq. \ref{['ex']}, as a function of the parameter $\theta$. A line break has been used as the required number of copies becomes arbitrarily large as $\theta$ approaches zero.

Theorems & Definitions (21)

  • Definition 1
  • Proposition 2: from bandyopadhyay2014conclusive
  • Proposition 3: from Heinosaari_2018
  • Proposition 4: from Johnston2025tightbounds
  • Proposition 5: from caves2002conditions
  • Lemma 6: from Johnston2025tightbounds
  • Theorem 7
  • proof
  • Definition 8: $N$-copy antidistinguishability
  • Lemma 9: from Johnston2025tightbounds
  • ...and 11 more