Quantum Foundations

Does the four-party Zhang–Yeung inequality hold for the von Neumann entropies of every finite-dimensional quantum state?

• Quantum Foundations
• Quantum Communication
• Matrix and entropy inequalities

Does every entangled bipartite state become Bell nonlocal under collective local measurements on some finite number of copies?

• Quantum Foundations
• Quantum Resource Theory
• Superactivation
• Bell nonlocality
• Quantum separability

What is the exact steering threshold for arbitrary POVMs on a higher-dimensional Werner state?

• Quantum Foundations
• Quantum steering

Does every finite-alphabet Bell-nonlocal behavior have a strictly positive asymptotic secret-key rate against arbitrary individual nonsignalling attacks?

• Quantum Cryptography
• Quantum Foundations
• Secret-key distillation
• Device-independent cryptography
• Bell nonlocality

Does a symmetric informationally complete positive-operator-valued measure exist in every finite dimension \(d\ge2\)?

• Quantum Foundations
• Symmetric informationally complete measurements

For every partially entangled two-qubit pure state, does some fixed finite-alphabet nonsignalling resource give an exact noncommunicating simulation of all local projective measurements?

• Quantum Foundations
• Quantum Resource Theory
• Bell nonlocality
• Resource conversion

Can shared randomness and at most two Popescu–Rohrlich boxes exactly simulate every pair of local projective measurements on every two-qubit state, without communication?

• Quantum Foundations
• Quantum Resource Theory
• Bell nonlocality
• Resource conversion

Can shared randomness and one classical bit exactly simulate every pair of local projective measurements on every pure entangled two-qubit state?

• Quantum Foundations
• Quantum Communication
• Bell nonlocality
• Quantum communication complexity

Does the vacuum of a massive free scalar Bose field violate the CHSH inequality between bounded localization regions at arbitrarily large spacelike separation?

• Quantum Foundations
• Bell nonlocality

Does every finite dimension admit a symmetric informationally complete measurement that is a single Weyl–Heisenberg orbit?

• Quantum Foundations
• Symmetric informationally complete measurements

For every \(d\geq3\), do the standard CGLMP Fourier–phase measurements maximize the relative-entropy statistical strength against local realism among all projective \(d\)-outcome measurements on the fixed state \(\lvert\Phi_d\rangle=d^{-1/2}\sum_{j=0}^{d-1}\lvert j,j\rangle\), when the setting distribution is also optimized?

• Quantum Foundations
• Bell nonlocality
• Quantum hypothesis testing

Is every finite-dimensional extensibly causal process matrix purifiable?

• Quantum Foundations
• Indefinite causal order

Is the closure of the finite-dimensional tensor-product correlation set semialgebraic in every fixed bipartite Bell scenario?

• Quantum Foundations
• Bell nonlocality

For each integer \(d\geq2\), determine the maximum number \(\mu(d)\) of pairwise mutually unbiased orthonormal bases of \(\mathbb C^d\).

• Quantum Foundations
• Mutually unbiased bases

For every \(d\geq3\), do the standard Fourier–phase measurements optimize the CGLMP violation of the maximally entangled state among all projective \(d\)-outcome measurements?

• Quantum Foundations
• Bell nonlocality

Must every nontrivial facet Bell inequality in a finite bipartite scenario have a quantum violation?

• Quantum Foundations
• Bell nonlocality

Determine complete facet descriptions for local-behavior polytopes beyond the presently solved Bell scenarios, either for a specified unresolved finite scenario or for a nontrivial infinite family with additional structure.

• Quantum Foundations
• Bell nonlocality

Does every finite dimension admit a Weyl–Heisenberg SIC fiducial that is an eigenvector of a Zauner Clifford unitary?

• Quantum Foundations
• Symmetric informationally complete measurements