Requiring each sum-of-squares term to involve only one of Alice's measurement questions can impose an unbounded certification cost. In the simplest Bell scenario, we prove that no finite level of the Alice-conditioned NPA hierarchy contains all standard level-two Bell certificates. An explicit family of truncated positive functionals on the infinite dihedral group exceeds the tilted-CHSH quantum bound at every prescribed finite level, while a standard degree-two certificate is exact. A Fejer-weighted trace reduces positivity to a rank-one subtraction from a moving-average Gram matrix. The required conditioned level grows at least as $(2-\alpha)^{-1/2}$ near the endpoint tilt. This bounds the degree of exact nice-SOS inputs to compiled-game soundness proofs. Consequently, no finite conditioned level certifies the entire optimal CHSH randomness tradeoff against quantum side information, although standard level two does. Away from the endpoint, we prove a sharp one-level cost throughout $\alpha\in[13/10,3/2]$, using optimal-strategy kernels and exact Bernstein matrix positivity to certify a continuous interval. The results separate ordinary SOS degree from the resources keyed by single-question certificate structure.
We give the first exponential quantum advantage in the general interactive three-party Numbers-on-Forehead (NOF) model for a decision problem. Previous separations hold only for restricted protocols like one-way communication for a relation. We construct an explicit partial Boolean function, the Interleaved Unitary Pro...
Non-local quantum computation (NLQC) consists on the implementation of a bipartite unitary $U_{AB}$ by two cooperating distant players by means of a two-round protocol with a single intermediate round of simultaneous communication. It is a major open question to know whether there exists a unitary $U_{AB}$ whose implem...
Isabel M. Moreno-Cuadrado, David Pérez-García, C. Palazuelos· 1 citation
We establish exact thresholds for the failure of simultaneous quantum typicality: three parties for mixed states and four for pure states. For the four-qubit Higuchi--Sudbery state, every sequence satisfying the expected purity bounds on three overlapping marginals, with sufficiently small fixed positive entropy slack,...
The noise threshold below which the qubit depolarizing channel retains positive quantum capacity has been studied since 1996. The classic constructions come with exact finite formulae, but in every reported threshold to date -- most recently the record of Agarwal et al. -- the final step, the sign of the coherent infor...
We prove an exponential strong converse for the unassisted private capacity of every finite-dimensional degradable quantum channel. We use a single error criterion: the infidelity between the actual message-estimate-environment state and an ideal state consisting of uniformly distributed, perfectly correlated messages...
We introduce a relation problem constructed from the Clauser--Horne--Shimony--Holt (CHSH) game, which we call the two-round one-dimensional CHSH problem. Its two-round structure ensures that the CHSH questions are supplied only after the relevant Pauli-frame data have been fixed, thereby ruling out a simple classical s...
