Quantum Resource Theory

Is every \(n\)-qubit state of purity at most \(1/(2^n-1/2)\) a convex mixture of stabilizer states?

• Quantum Resource Theory
• Quantum magic

Can every Wigner-negative state in the depolarized qutrit Strange-state family be distilled arbitrarily accurately by catalyst-free stabilizer operations?

• Quantum Resource Theory
• Quantum magic
• Resource conversion

Do normalized one-dimensional Chen–Kastoryano–Gilyén Gibbs samplers have a positive modified log-Sobolev constant uniformly in system size at every fixed finite temperature?

• Quantum Resource Theory
• Quantum Algorithm
• Quantum thermodynamics
• Quantum state preparation
• Quantum relative entropy

Does any finite qutrit stabilizer-code protocol distill depolarized Strange states above the ternary Golay code’s threshold?

• Quantum Resource Theory
• Quantum Error Correction
• Quantum magic
• Quantum coding theory
• Resource conversion

What is the optimal catalyst-free asymptotic \(T\)-state yield of a dephased single-qubit \(T\) state?

• Quantum Resource Theory
• Quantum magic
• Resource conversion
• Additivity and regularization

What is the optimal success probability for a fixed catalyst-free stabilizer protocol that converts eight copies of an arbitrary unknown pure qubit into an exact \(|CCZ\rangle\) state?

• Quantum Resource Theory
• Quantum magic
• Resource conversion
• One-shot and finite-blocklength bounds

Is every fixed-temperature Gibbs state of a bounded finite-range qubit Hamiltonian on the square lattice an exact convex combination of PEPS with system-size-independent bond dimension?

• Quantum Resource Theory
• Quantum thermodynamics
• Quantum state preparation

Is there a closed-form formula for the squashed entanglement \(E_{\mathrm{sq}}\) of an arbitrary two-qubit Bell-diagonal state, or a certified approach to determining it numerically?

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

Does an absolutely maximally entangled state of eight ququarts exist?

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

What is the entanglement cost of the Werner state \(\rho_{d,p}\) for every integer \(d\geq2\) and every antisymmetric weight \(1/2<p\leq1\), and in particular, does it equal the entanglement of formation?

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

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

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

What is the entanglement cost of the isotropic state \(\sigma_{d,F}\) for every integer \(d\geq2\) and every fidelity \(1/d<F<1\)?

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

Can two bipartite quantum states with zero distillable secret key yield positive distillable secret key when used jointly?

• Quantum Cryptography
• Quantum Resource Theory
• Superactivation
• Secret-key distillation

Is the two-way assisted quantum capacity of the Holevo–Werner channel \(\mathcal W_d\) zero for every integer \(d\geq3\)?

• Quantum Communication
• Quantum Resource Theory
• Quantum capacity
• Bound entanglement
• Entanglement distillation

What is the exact LOCC entanglement cost of a finite-energy PPT-entangled Gaussian state?

• Quantum Resource Theory
• Gaussian quantum information
• Bound entanglement
• Entanglement cost

Is unrestricted entanglement of formation additive on tensor powers of every finite-energy two-mode Gaussian state?

• Quantum Resource Theory
• Gaussian quantum information
• Entanglement cost
• Additivity and regularization

Does there exist an absolute constant \(C>0\) and a deterministic algorithm that, for each integer \(k\geq2\) supplied in unary, runs in time \(k^{O(1)}\) and outputs a \(k\)-vertex-minor-universal graph with at most \(Ck^2\) vertices?

• Quantum Resource Theory
• Quantum Algorithm
• Quantum state preparation
• Resource conversion
• Computational complexity and computability

Is the exact deterministic LOCC entanglement cost of the two-qubit elegant joint measurement \(\mathcal M_{\mathrm{EJM}}\) equal to one ebit when arbitrary finite-dimensional pure entangled resources are allowed?

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

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

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 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

Is the Rains bound asymptotically achievable by completely positive-partial-transpose-preserving (completely PPT-preserving) channels for every full-rank two-qubit Bell-diagonal state, and what channel family achieves it?

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

What is the exact two-way distillable entanglement of a finite-energy mixed two-mode Gaussian state?

• Quantum Resource Theory
• Gaussian quantum information
• Entanglement distillation

What is the maximal success probability for preparing an approximate two-mode squeezed vacuum from finitely many copies of a non-Gaussian state?

• Quantum Resource Theory
• Gaussian quantum information
• Entanglement distillation
• One-shot and finite-blocklength bounds

What is the optimal asymptotic conversion rate between finite-energy bosonic states under passive linear-optical protocols?

• Quantum Resource Theory
• Gaussian quantum information
• Resource conversion

Can every set of three orthogonal maximally entangled pure states on \(\mathbb C^d\otimes\mathbb C^d\), for every integer \(d\geq4\), be distinguished exactly from one copy using unrestricted two-way local operations and classical communication (LOCC)?

• Quantum Metrology
• Quantum Resource Theory
• Quantum state discrimination
• Local operations and classical communication

Does there exist a family of bipartite unitaries requiring exponentially many shared Bell pairs for fixed-error implementation when classical communication is limited to one simultaneous exchange?

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

Does there exist an absolute constant \(a\geq0\) such that \(N_{\mathrm P}(k)=O(k[\log_2(k+1)]^a)\) as the integer \(k\geq2\) tends to infinity?

• Quantum Resource Theory
• Quantum state preparation
• Resource conversion

Does the semidefinite hierarchy for exact PPT entanglement cost collapse at its second level for every finite-dimensional bipartite density operator \(\rho_{AB}\)?

• Quantum Resource Theory
• Entanglement cost
• PPT-preserving operations
• Entanglement measures

Does a deterministic classical algorithm running in \(n^{O(1)}\) time decide local-unitary equivalence of arbitrary graph states on \(n\) labelled qubits?

• Quantum Algorithm
• Quantum Resource Theory
• Local unitary equivalence
• Computational complexity and computability

Determine the optimal symmetric discrimination exponents for two faithful noncommuting states when measurements must be separable across copies or implemented by local operations and classical communication (LOCC) among the copies.

• Quantum Metrology
• Quantum Resource Theory
• Quantum hypothesis testing
• Local operations and classical communication
• Quantum separability

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

Is the entanglement of purification additive on tensor products?

• Quantum Resource Theory
• Entanglement measures
• Additivity and regularization

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

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

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

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

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

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

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 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

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

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

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

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

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

Is every finite-dimensional extensibly causal process matrix purifiable?

• Quantum Resource Theory
• Indefinite causal order

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

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