bibkey: guptamurshidbandyopadhyay2024sequences
authors: Tathagata Gupta; Shayeef Murshid; Somshubhro Bandyopadhyay
year: 2024
title: "Unambiguous discrimination of sequences of quantum states"
doi: 10.1103/PhysRevA.109.052222
url: https://arxiv.org/abs/2402.06365v2
claim: "The paper shows that for sequences drawn with repetition from a parent set with equal real inner products, optimal unambiguous sequence discrimination is achieved by measuring the members individually, and asks whether collective measurements help for sequences without repetition."
strata_touched:
  - D5/S3/Quantum/PureState/NoRepetitionSequenceUnambiguousDiscrimination
license: citation-only
triage: anchor

Unambiguous discrimination of sequences of quantum states

T. Gupta, S. Murshid and S. Bandyopadhyay, arXiv:2402.06365v2 [quant-ph]; Phys. Rev. A 109, 052222 (2024). Quotations are from the v2 TeX source.

The no-repetition question:

In our scenario, as well as in more general ones (which we could not solve), repetitions of states are allowed in a sequence. The third problem considers the situation where it is not. Restrict $k<N$ and by $S_{N,k}^{\prime }$ denote the set of sequences of length $k$, where no element is repeated. If we let $\mathcal{G}(k,N)$ be the set of injective functions from $\left[k\right]$ to $\left[N\right]$, then $S_{N,k}^{\prime }=\left\{|{\psi }_{\tau (1)}⟩\otimes \cdots \otimes |{\psi }_{\tau (k)}⟩:\tau \in \mathcal{G}(k,N)\right\}$

(the display is written inline here).

Now assume that the inner products of the states $|{\psi }_i⟩$ are equal and positive, say, $s>0$. Then $S_{N,k}^{\prime }\subset S_{N,k}$, where $S_{N,k}$ is the set of sequences considered in this paper. Under these restricted conditions, numerical experiments ($N=3$, $k=3$) still suggest that the optimal probability for distinguishing between the elements of $S_{N,k}^{\prime }$ unambiguously once again obeys $(1-s{)}^k$. However, for arbitrary values of both $N$ and $k$, whether one could benefit from collective measurements in this scenario is an interesting problem to consider in the future.

Verified locator

Source: https://arxiv.org/abs/2402.06365v2

• URL: https://arxiv.org/abs/2402.06365v2 (single-file TeX source, md5 a3c17bf5369a6647a1dc646ac2ba07da, 1002 lines):
  • the no-repetition question, l. 883–903.
• DOI: 10.1103/PhysRevA.109.052222 (https://doi.org/10.1103/PhysRevA.109.052222; Crossref lists Physical Review A, volume 109, article 052222, published 22 May 2024).