Quantum Communication

What is the smallest output dimension in which the minimum output von Neumann entropy of quantum channels fails to be additive?

• Quantum Communication
• Additivity and regularization
• Matrix and entropy inequalities
• Quantum channel structure

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

What is the private classical capacity \(P(\Lambda_p)\) of the qubit depolarizing channel, defined for a mixing parameter \(p\in[0,1]\) by

• Quantum Communication
• Quantum Cryptography
• Private capacity
• 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

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

Does amortization collapse for the max-relative entropy and geometric Rényi divergence of arbitrary finite-dimensional quantum superchannels?

• Quantum metrology
• Quantum Communication
• Channel discrimination
• Quantum relative entropy
• Superchannels and quantum combs

Can Holevo–Schumacher–Westmoreland codebooks operating at every rate below their ensemble Holevo information be chosen so that their square-root, or pretty-good, measurements have uniform quantum implementations whose cost is polynomial in the blocklength and…

• Quantum algorithm
• Quantum Communication
• Decoding algorithms
• Classical capacity
• Quantum state discrimination

Is Guha’s multimode Strong Conjecture 2 true for every correlated input state?

• Quantum Communication
• Bosonic channels
• Matrix and entropy inequalities

Is the ordinary unassisted quantum capacity a computable function of a finite description of a finite-dimensional quantum channel?

• Quantum Communication
• Quantum algorithm
• Quantum capacity
• Computational complexity and computability

Does the ordinary, unrotated Petz map universally recover a tripartite state with fidelity controlled by its conditional mutual information?

• Quantum Communication
• Quantum recovery
• Matrix and entropy inequalities

Does the pure-loss bosonic channel admit the following candidate second-order classical converse under a maximum-photon-number occupation constraint?

• Quantum Communication
• Bosonic channels
• Classical capacity
• One-shot and finite-blocklength bounds

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 general finite-dimensional i.i.d.

• Quantum Communication
• Quantum source coding
• Strong converses

Does the max-relative entropy of finite-dimensional quantum channels satisfy an asymptotic equipartition property under uniform diamond-norm smoothing?

• Quantum Communication
• Quantum relative entropy
• One-shot and finite-blocklength bounds

What is the unconstrained, unassisted quantum capacity of the single-mode Gaussian random-displacement channel?

• Quantum Communication
• Quantum capacity
• Bosonic channels

Can every finite-dimensional quantum channel be written as the uniform mixture of \(d_B\) channels whose Choi ranks are at most the input dimension?

• Quantum Communication
• Quantum channel structure

Does there exist an integer \(d\geq2\) and a pair of distinct channels \(\mathcal M,\mathcal N:\mathcal L(A)\to\mathcal L(B)\), with \(A\simeq B\simeq\mathbb C^d\), that both have Choi rank exactly \(d\), are mutually degradable, and are each nondegradable?

• Quantum Communication
• Channel degradability
• Quantum channel structure

For every integer \(d\geq3\), every \(x\in(0,1)\), and every \(1<p<2\), is the maximal output Schatten \(p\)-norm of the polarized Werner–Holevo channel multiplicative on two identical copies?

• Quantum Communication
• Additivity and regularization
• Quantum channel structure
• Matrix and entropy inequalities

Does there exist a finite-dimensional quantum channel whose minimum output Rényi entropy is additive for every tensor power below some order and first becomes strictly subadditive at that order?

• Quantum Communication
• Additivity and regularization
• Matrix and entropy inequalities
• Quantum channel structure

Does every finite-dimensional transpose-degradable channel satisfy an exponential strong converse for quantum communication at its single-letter quantum capacity?

• Quantum Communication
• Quantum capacity
• Channel degradability
• Strong converses

Does there exist a finite-dimensional transpose-degradable quantum channel that is not degradable?

• Quantum Communication
• Channel degradability
• Quantum channel structure

What are the componentwise-minimal dimension triples \((d_A,d_B,d_E)\) that admit a transpose-degradable but nondegradable channel?

• Quantum Communication
• Channel degradability
• Quantum channel structure

Let \(\mathcal N,\mathcal M:\mathcal L(A)\to\mathcal L(B)\) be quantum channels on finite-dimensional systems.

• Quantum metrology
• Quantum Communication
• Channel discrimination
• Quantum hypothesis testing
• Quantum relative entropy
• Strong converses

For \(0<\eta<1\) and \(0<\nu<\infty\), let the single-mode bosonic thermal attenuator be

• Quantum Communication
• Quantum capacity
• Bosonic channels

What is the quantum capacity \(\mathcal{Q}(\Lambda_{\mathbf p})\) of the qubit Pauli channel defined by

• Quantum Communication
• Quantum capacity

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

Is the normalized trace average of all words in two positive-definite matrices always bounded below by the corresponding trace exponential?

• Quantum Communication
• Matrix and entropy inequalities

Let \(\Phi_{\eta,\nu}\) be the single-mode bosonic thermal attenuator with transmissivity \(0<\eta<1\) and environmental mean photon number \(0<\nu<\infty\), defined by

• Quantum Communication
• Quantum capacity
• Bosonic channels

Does an explicit total Boolean family require polynomial shared-state cost for bounded-error one-round \(f\)-routing?

• Quantum Communication
• Quantum Cryptography
• Quantum communication complexity
• Position-based quantum cryptography

For \(0<\eta<1\) and \(0<\nu<\infty\), let the single-mode bosonic thermal attenuator be

• Quantum Communication
• Quantum capacity
• Bosonic channels

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

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