Tighter POVM Bounds for Sequential Conjugate Coding

Computational investigation of whether the O(epsilon^1/4) security bound in sequential conjugate coding can be improved to O(epsilon^1/2) or better.

Quantum Physics (quant-ph) | arXiv:2601.13258 |

Key Findings

0.45

Best structured exponent (rotated)

0.44

Adversarial exponent (m=3)

0.85

Tilted POVM exponent

1.00

Asymmetric POVM exponent

Main result: All tested POVM families produce excess guessing probability scaling with exponent alpha > 0.25, providing computational evidence that the epsilon^(1/4) bound is not tight and can likely be improved to O(epsilon^(1/2)).

Interactive Explorer

Qubits (m): POVM Type:

Excess Guessing Probability vs Epsilon

Fitted Exponents by POVM Family

Adversarial Optimization

Random POVM Sampling Distribution

Exponent Summary

POVM	m=1	m=2	m=3
Tilted	0.8522	0.8522	0.8522
Rotated	0.4470	0.4532	0.4605
Asymmetric	1.0000	1.0000	1.0000
Adversarial	-0.0075	0.1592	0.4395

Adversarial Results (m=3)

epsilon	p_comp	p_had	Delta p	eps^(1/4)
0.001	0.9991	0.1250	0.0000	0.1778
0.010	0.9912	0.1250	0.0000	0.3162
0.050	0.9406	0.1324	0.0074	0.4729
0.100	0.8938	0.1388	0.0138	0.5623
0.200	0.8405	0.1428	0.0178	0.6687
0.300	0.7804	0.1428	0.0178	0.7401
0.400	0.7328	0.1453	0.0203	0.7953

Random Sampling Statistics (200 samples each)

epsilon	m=1 mean	m=1 max	m=2 mean	m=2 max	m=3 mean	m=3 max
0.01	0.0034	0.0191	0.0016	0.0033	0.0007	0.0011
0.05	0.0169	0.0954	0.0079	0.0163	0.0037	0.0053
0.10	0.0335	0.1908	0.0157	0.0326	0.0074	0.0105
0.20	0.0656	0.3394	0.0314	0.0652	0.0148	0.0211
0.30	0.0930	0.3394	0.0471	0.0977	0.0223	0.0316