28 entries matching the current filters. Sorted by recently added.
For the nonrelativistic Coulomb Hamiltonian of fermionic spin-1/2 electrons and a fixed point nucleus of charge Z , prove that the maximal number of bound electrons satisfies N c(Z) le Z+C , with C independent of Z .
For a specified generator or finite-memory model, preparation/measurement access and estimation norm, determine matching experimental and computational bounds for identifying the dynamics, including robustness to…
For a specified set of multi-time interventions, determine optimal tests for quantum memory and the minimal memory dimension or simulation cost needed to reproduce the accessible statistics within error varepsilon .
For a specified Bell functional, normalization and target, determine the tight extractability-fidelity bound as a function of the violation deficit; treat norm-distance bounds and measurement certification as separate…
Identify natural restricted families of finite nonlocal games whose finite-dimensional tensor-product value admits two-sided additive approximation with a certified stopping rule; separately determine efficient…
Determine the maximal number M(6) of mutually unbiased bases in mathbb C ^6 ; in particular decide whether M(6)=3 or whether four or more exist.
For a specified class of local Hamiltonians and allowed local or quasilocal basis changes, characterize obstructions to stoquasticity. Separate finite-input basis-curing complexity from a phase-invariant obstruction…
Determine how the physically realizable process class changes when specified closed-laboratory, spacetime-localization or background-causality assumptions are relaxed, and give operational implementations or…
For a specified symmetry group and constrained dynamics, bound errors in changing and composing finite-resource quantum frames, including interacting clock backreaction and repeated-use degradation under an explicit…
Extend the certified existence/nonexistence table for mathrm AME (n,d) with explicit constructions or impossibility proofs for unresolved parameter pairs, keeping minimal-support and unrestricted AME questions distinct.
For specified mixed or multipartite LOCC conversion families, characterize feasibility and catalyst cost separately for exact product return, exact marginal return with correlations, and approximate return with a stated…
Give a structural characterization of finite-dimensional bipartite states satisfying E C( rho)=E D( rho) under ordinary asymptotic LOCC with vanishing error and no catalysts.
For finitely specified bipartite channels or instruments, develop certified varepsilon -membership tests for the closure of LOCC in a stated operational norm, and distinguish this task from exact finite-round or…
For rational finite-dimensional density matrices, identify structured families admitting efficient separability tests with a specified norm and promise gap, and bound the dimension and accuracy dependence of convergent…
For explicitly budgeted spatially/temporally correlated or adversarial noise, establish fault-tolerance thresholds and space-time overhead bounds for two- or three-dimensional local architectures. Specify local…
Given a full classical description of an arbitrary reference state sigma and copies of an unknown N -qubit state rho , determine the optimal copy complexity of testing rho= sigma versus | rho- sigma | 1 ge varepsilon ,…
Prove average-case approximate hardness for complex-Gaussian permanents, together with a robust reduction strong enough to rule out polynomial-time classical sampling within inverse-polynomial total-variation error for…
Do universal constants c,C 0 exist such that every multilinear p: -1,1 ^ n to[0,1] of degree d ge1 and positive variance has some variable i with operatorname Inf i(p) ge c( operatorname Var (p)/d)^C ? Use the uniform…
Determine whether mathsf StoqMA = mathsf MA . A central route is to establish general completeness-and-soundness error amplification for StoqMA while preserving the verifier model.
Determine whether mathsf QMA (2)= mathsf QMA , or whether two polynomial-size witnesses promised to be unentangled increase verification power.
Is Psi circ Phi entanglement breaking for every pair of compatible finite-dimensional complex completely positive, trace-preserving maps whose Choi matrices have positive partial transpose?
For mathcal D q( rho)=(1-q) rho+ frac q3(X rho X+Y rho Y+Z rho Z) , determine the unassisted memoryless quantum capacity, or at least q = sup q in[0,3/4]:Q( mathcal D q) 0 .
For a specified two-receiver memoryless quantum broadcast channel, characterize the region for independent classical private messages, with no preshared entanglement, feedback or receiver cooperation; treat common…
For explicitly specified channel or noncommutative-graph families, evaluate asymptotic zero-error capacity with message type and assistance fixed. A concrete classical benchmark is the exact Shannon capacity Theta(C 7) .
For every finite-dimensional memoryless channel mathcal N , does unassisted entanglement transmission at a fixed rate above Q( mathcal N) force entanglement fidelity to tend to zero for all code sequences? Prove the…