bibkey: emeriau2020torpedo authors: Pierre-Emmanuel Emeriau; Mark Howard; Shane Mansfield year: 2022 title: “Quantum Advantage in Information Retrieval” doi: 10.1103/PRXQuantum.3.020307 url: https://arxiv.org/abs/2007.15643v2 claim: “In the dimension-d Torpedo Game, Alice receives x, z in Z_d, sends one dit, and Bob, asked q in {infinity, 0, …, d-1}, must answer a != x (q = infinity) or a != qx - z; the classical value is theta^C_2 = 3/4, theta^C_3 = 11/12, perfect classical strategies were found for 5 <= d <= 23, and the authors conjecture theta^C_(d>=5) = 1 (eq. (11)).” strata_touched:

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Quantum Advantage in Information Retrieval

P.-E. Emeriau, M. Howard and S. Mansfield, arXiv:2007.15643 (v1 2020-07-30, v2 2020-11-19); PRX Quantum 3, 020307 (2022). Subject: quant-ph.

The paper studies information retrieval tasks in prepare-and-measure scenarios. In the dimension-d Torpedo Game Alice receives two dits x, z, sends a single (qu)dit, and Bob is asked one of d + 1 questions q ∈ {∞, 0, …, d − 1}; the winning relations are w_∞(x, z) = {a ≠ x} and w_q(x, z) = {a ≠ qx − z}, arithmetic modulo d (eq. (2)). The classical value θ^C_d is the greatest average winning probability over encodings and decodings with shared randomness (eq. (cval)). The authors find θ^C_2 = 3/4, θ^C_3 = 11/12, and write:

We have, however, found perfect classical strategies, i.e. strategies that win with probability 1, for d = 5 (see Fig. 9) up to d = 23. This leads us to conjecture that there exists a perfect classical strategy for all d > 5, Conjecture: θ^C_{d≥5} = 1.

The thesis of P.-E. Emeriau (arXiv:2204.08782, 2022) restates the conjecture for dimension 4 and above.

Verified locator

• DOI: https://doi.org/10.1103/PRXQuantum.3.020307 (open access): the section on the Torpedo Game, eq. (11), Fig. 9.
• URL: https://arxiv.org/abs/2007.15643v2 (source retrieved 2026-09-30): S1_QRAC.tex (winning relations), S3_Torpedo.tex (eq. cval, the conjecture PerfectClassical), cl_dimension5.tex (Fig. 9).