Quantum Resource Theory

Is the entanglement of purification additive on tensor products?

• Quantum Resource Theory
• Entanglement measures
• Additivity and regularization

What is the squashed entanglement \(E_{\mathrm{sq}}(\Lambda_p)\) of the qubit depolarizing channel, defined for a mixing parameter \(p\in[0,1]\) by

• Quantum Resource Theory
• Quantum Communication
• Entanglement measures
• Quantum capacity
• Private capacity

Construct a simple closed-form or practically computable counterexample to additivity of the Holevo capacity or the entanglement of formation, together with a rigorous certificate of a strict violation.

• Quantum Communication
• Quantum Resource Theory
• Classical capacity
• Additivity and regularization
• Entanglement measures

Must the composition of any two compatible PPT completely positive maps be entanglement breaking?

• Quantum Resource Theory
• Quantum Communication
• Quantum separability
• Quantum channel structure

What is the optimal quasiprobability overhead of implementing the complex conjugate of an unknown quantum channel from \(n\) queries?

• Quantum algorithm
• Quantum Resource Theory
• Channel simulation
• Superchannels and quantum combs
• Quantum error mitigation

What is the asymptotic classical-communication cost of simulating a bipartite quantum channel with bidirectional classical communication and non-signalling assistance?

• Quantum Communication
• Quantum Resource Theory
• Channel simulation
• Quantum communication complexity
• Quantum relative entropy
• One-shot and finite-blocklength bounds

What computable expression, if any, equals the regularized exact PPT distillable entanglement of a bipartite state?

• Quantum Resource Theory
• Entanglement distillation
• PPT-preserving operations
• Additivity and regularization
• One-shot and finite-blocklength bounds

Can classically simulable operations purify an unknown depolarized pure state from any number of copies?

• Quantum Resource Theory
• Quantum algorithm
• Quantum magic
• Resource conversion
• Quantum state preparation

Characterize the finite-dimensional quantum channels for which joint classical–entanglement coding strictly outperforms time sharing between unassisted and unlimited-entanglement classical communication.

• Quantum Communication
• Quantum Resource Theory
• Classical capacity
• Entanglement-assisted communication
• Additivity and regularization

Does quantum control of causal order yield a persistent asymptotic metrological advantage over parallel access for some smooth finite-dimensional channel family?

• Quantum metrology
• Quantum Resource Theory
• Quantum estimation
• Indefinite causal order

For every local dimension \(d\geq3\), determine the entanglement of formation of an arbitrary Weyl–Bell-diagonal state.

• Quantum Resource Theory
• Entanglement measures
• Bell-diagonal states

Do there exist integers \(N,d\geq 2\) for which the absolutely maximally entangled states of \(N\) qudits of local dimension \(d\) form finitely many, but more than one, local-unitary equivalence classes?

• Quantum Resource Theory
• Absolutely maximally entangled states
• Local unitary equivalence

Let \(\mathcal N:\mathcal L(A)\to\mathcal L(B)\) be a finite-dimensional quantum channel.

• Quantum Resource Theory
• Quantum metrology
• Quantum hypothesis testing
• Channel discrimination
• Quantum relative entropy

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

• Quantum Resource Theory
• 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 Resource Theory
• Secret-key distillation
• Device-independent cryptography
• Bell nonlocality

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 Resource Theory
• Bell nonlocality
• Resource conversion

For which of the parameter pairs specified below does an absolutely maximally entangled state exist?

• Quantum Resource Theory
• Quantum Error Correction
• Absolutely maximally entangled states
• Quantum coding theory

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 Resource Theory
• Bell nonlocality
• Resource conversion

Does Gaussian entanglement of formation equal unrestricted entanglement of formation for every non-bisymmetric multimode Gaussian state?

• Quantum Resource Theory
• Gaussian quantum information
• Entanglement measures

Consider distilling the bipartite Bell-diagonal state

• Quantum Resource Theory
• Entanglement distillation
• PPT-preserving operations
• Bell-diagonal states

What are the exact one-shot coherence and work costs of implementing an arbitrary Gibbs-preserving channel by thermal operations?

• Quantum Resource Theory
• Quantum thermodynamics
• Channel simulation
• One-shot and finite-blocklength bounds
• 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 Communication
• Quantum Resource Theory
• 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 Resource Theory
• Bell nonlocality

Does there exist a finite-dimensional bipartite state with non-positive partial transpose (NPT) that is undistillable by local operations and classical communication (LOCC)?

• Quantum Resource Theory
• Entanglement distillation
• Bound entanglement
• Local operations and classical communication

Determine, for every integer \(d\geq 2\), the largest number \(\mathcal N(d)\) of \(d\)-level parties that admit an absolutely maximally entangled state of minimal computational-basis support.

• Quantum Resource Theory
• Quantum Error Correction
• Absolutely maximally entangled states
• Quantum coding theory

What is the entanglement cost of the Choi state of the qubit amplitude-damping channel

• Quantum Resource Theory
• Entanglement cost
• Local operations and classical communication

Can discarding one local qubit reduce two-way distillable entanglement by an arbitrarily large amount?

• Quantum Resource Theory
• Entanglement distillation
• Entanglement measures
• Local operations and classical communication

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 Resource Theory
• Quantum metrology
• Bell nonlocality
• Quantum hypothesis testing

Is every finite-dimensional extensibly causal process matrix purifiable?

• Quantum Resource Theory
• Indefinite causal order

What is the entanglement cost of a qubit Bell-diagonal state for an arbitrary probability vector \(\mathbf p=(p_I,p_X,p_Y,p_Z)\)?

• Quantum Resource Theory
• Entanglement cost
• Bell-diagonal states
• Local operations and classical communication

Characterize the spectra of bipartite states that remain separable under every global unitary, and decide whether absolute separability equals absolute positivity under partial transpose in higher local dimensions.

• Quantum Resource Theory
• Quantum separability

Does an absolutely maximally entangled state of eight ququarts exist?

• Quantum Resource Theory
• Quantum Error Correction
• Absolutely maximally entangled states
• Quantum coding theory

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

• Quantum Resource Theory
• Bell nonlocality

What is the distillable entanglement \(D(\rho_{\mathbf p})\) under local operations and classical communication (LOCC) for the Bell-diagonal state

• Quantum Resource Theory
• Entanglement distillation
• Bell-diagonal states
• Local operations and classical communication

Does every finite-dimensional entangled bipartite state have positive asymptotic distillable secret key?

• Quantum Cryptography
• Quantum Resource Theory
• Secret-key distillation
• Bound entanglement
• Local operations and classical communication

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 Resource Theory
• Quantum metrology
• Bell nonlocality

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

• Quantum Resource Theory
• Bell nonlocality

Find a closed formula for the relative entropy of entanglement of every two-qubit density operator \(\rho\), including an explicit closest separable state.

• Quantum Resource Theory
• Entanglement measures
• Quantum separability
• Quantum relative entropy

Let \(H\) be a \(d\)-dimensional Hilbert space.

• Quantum Resource Theory
• Quantum Communication
• Quantum hypothesis testing
• Quantum relative entropy
• One-shot and finite-blocklength bounds

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 Resource Theory
• Bell nonlocality

What is the computational complexity of testing bipartite separability with a constant trace-distance promise gap?

• Quantum algorithm
• Quantum Resource Theory
• Quantum separability
• Computational complexity and computability

Can loss of one qubit held by an honest party reduce the two-way distillable secret key by an arbitrarily large amount?

• Quantum Cryptography
• Quantum Resource Theory
• Secret-key distillation
• Local operations and classical communication

Does there exist an \(\operatorname{AME}(4,6)\) state whose coefficients are real in a product basis?

• Quantum Resource Theory
• Absolutely maximally entangled states