PUBLIC CLAIM STATEMENT - VERSION 1

Canonical blog URL:
https://zoeabcd.github.io/blog/common-mask-unclonability-results/

CLAIM 1 - COMMON-MASK GOLDREICH-LEVIN

For any finite-dimensional UE token ensemble and any decision strategy with
joint success p_D >= 1/2, there exist local one-copy recovery measurements,
using no post-split communication, whose joint search success satisfies

    p_S >= (2 p_D - 1)^4.

In particular, p_D = 1/2 + epsilon implies p_S >= 16 epsilon^4. The post-split
state may be arbitrarily entangled. The reduction is information-theoretic and
may be inefficient and nonuniform.

CLAIM 2 - UNIFORM-MASK I/X/Z PARITY GAME

Let omega_n be the supremum, over all finite-dimensional splitting channels
and local decoders, of the joint success probability in the following game:
x, theta, and r are independent and uniform in {0,1}^n; one copy of the BB84
state |x_theta> is split before the common question (theta,r) is revealed; and
both recipients, without communicating, must output <r,x> mod 2.

For every n >= 1,

    omega_n <= 1/2 [1 + (sqrt(3)/2)^n].

An explicit product Breidbart strategy gives

    omega_n >= 1/2 + 1/2 [(1 + 1/sqrt(2))/2]^n.

These bounds do not establish the exact value of omega_n, tightness, a product
theorem, or a bound for infinite-dimensional or commuting-operator strategies.

SOURCE MANUSCRIPT SHA-256 DIGESTS

IXZ_UE.pdf:
10f7a0ab94887f4658304cc5aa03d8f243bf51bd08f8f260455b86aac42991cb

search_to_decision.pdf:
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