Problems

Can one construct a plain-model, efficient, information-theoretically secure one-time unclonable-encryption scheme for one classical bit with exponentially small adversarial advantage?

For four particles and local dimension D ≥ 4, can a complete edge-coloured, complex-weighted graph have unit perfect-matching amplitude for every monochromatic inherited colouring and zero for every nonmonochromatic one? Ruled out for the…

Does the value of a two-player quantum game decay exponentially under parallel repetition, as Raz's theorem gives for classical games? Yes: an exponential parallel repetition theorem holds for arbitrary finite two-player quantum games.

Friedland and coauthors proposed a quantum analogue of the p-Wasserstein distance and conjectured that, though only a semidistance in general, it is a true distance for a particular quantum cost matrix and for cost matrices near it. The…

For an even cycle of size N and depth p with 2p + 2 ≤ N, is the optimal QAOA approximation ratio for MaxCut exactly 2p+1/2p+2, as Farhi, Goldstone and Gutmann conjectured?

Englert and Rehacek conjectured which measurement is globally information-optimal for an ensemble of equiangular equiprobable pure states. Their conjecture holds, via the remaining entropy inequalities of Holevo and Utkin.

We prove that every PPT linear map has finite entanglement-breaking index, thereby establishing the eventual entanglement-breaking property of PPT channels in full generality. Furthermore, by utilizing completely positive maps with low…

Does quantum memory give a query-complexity advantage for learning an unknown quantum channel, when protocols without it must measure after each channel use and keep only a classical transcript? It does, and the paper also determines how…

Online Shadow Tomography with log m dependence, while retaining poly(log(d)/ε) dependence. Also, matching the best classical bounds for Adaptive Data Analysis

Can a complete edge-coloured, complex-weighted graph realize perfect-matching amplitudes of one on every monochromatic inherited vertex colouring and zero otherwise? Nonexistence is proved in the diagonal family N = D for every even N ≥ 4,…

Does every nonlocal game admitting a perfect entangled strategy admit one using a maximally entangled state? Described in the paper as one of the longstanding open problems in quantum nonlocality. Answered negatively by an explicit…

Whether negative-partial-transpose states undistillable from one copy become distillable from finitely many copies is a basic open problem in entanglement theory. In the canonical two-parameter DiVincenzo family used as its…

Whether perfectly complete quantum key agreement can be built from quantumly secure one-way functions in a black-box way. It cannot: for any protocol where Alice and Bob exchange only classical messages, make at most q_A and q_B quantum…

Is the irreversibility of entanglement manipulation robust in the strong-converse sense - a strict separation between the exponential strong-converse distillable entanglement and the entanglement cost, as conjectured by Lami and Regula?…

Holevo and Werner's 1999 lower bound on the quantum capacity of the bosonic thermal attenuator comes from thermal inputs. Is it optimal? The paper proves it is exactly the supremum over single-mode Gaussian states, then exhibits a…

Does bipartite bound information exist: classical correlations between two parties and an eavesdropper that cost secret bits to create, yet from which no secret key can ever be distilled?

What is the optimal uniform continuity bound for quantum conditional entropy in trace distance, depending only on the dimension of the conditioned system? The sharp bound h_2(δ) + δ log(d^2 - 1) up to δ = 1 - d^-2, conjectured by Wilde, is…

Is a Werner state that is not one-copy distillable ever two-copy distillable? The first open rung of the NPT bound-entanglement ladder, open since 2000.