Local operations and classical communication

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

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

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

What is the two-way quantum capacity \(\mathcal{Q}_2(\mathcal A_p)\) of the qubit amplitude-damping channel

• Quantum Communication
• Quantum capacity
• Local operations and classical communication

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

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

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

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

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 exact secret-key capacity \(K(\mathcal A_p)\) of the qubit amplitude-damping channel for every damping probability \(p\in[0,1]\)?

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

What is the exact LOCC distillable entanglement \(E_D(\rho_{\mathrm{as}}^{(d)})\) of the \(d\times d\) antisymmetric state, for each integer \(d\ge3\)?

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

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

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

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