# Multiple-copy state discrimination of noisy qubits

## TL;DR

This paper compares local and collective quantum state discrimination schemes for noisy qubits, revealing that both schemes have a shared success limit and that local schemes outperform collective ones under noise.

## Contribution

It provides the first detailed analysis of success probabilities for local and collective schemes under preparation noise in quantum state discrimination.

## Key findings

- Both schemes share a common success limit less than one.
- The local scheme outperforms the collective scheme in noisy conditions.
- Preparation noise significantly impacts the optimal discrimination strategy.

## Abstract

Multiple-copy state discrimination is a fundamental task in quantum information processing. If there are two, pure, non-orthogonal states then both local and collective schemes are known to reach the Helstrom bound, the maximum probability of successful discrimination allowed by quantum theory. For mixed states, it is known that only collective schemes can perform optimally, so it might be expected that these schemes are more resilient to preparation noise. We calculate the probability of success for two schemes, one local and one collective, in the regime of imperfect preparation fidelity. We find two surprising results. Firstly, both schemes converge upon the same many-copy limit, which is less than unity. Secondly, the local scheme performs better in all cases. This highlights the point that one should take into account noise when designing state discrimination schemes.