Quantum Communication

Does the entropy photon-number inequality hold for every pair of independent finite-energy bosonic inputs?

• Quantum Communication
• Bosonic channels
• Matrix and entropy inequalities

What is the unassisted quantum capacity of a general qubit Pauli channel?

• Quantum Communication
• Quantum capacity

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

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

What necessary and sufficient structural conditions characterize the finite-dimensional channels of zero quantum capacity, and separately those of zero private capacity, that acquire a positive capacity of the same kind when used in parallel with some antidegradable…

• Quantum Communication
• Quantum Cryptography
• Superactivation
• Quantum capacity
• Private capacity
• Channel degradability

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

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

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

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

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

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

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

What is the unassisted quantum capacity of a single-mode thermal attenuator at every strictly positive finite environment temperature?

• 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

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 high-dimensional crossover fidelity of optimized deterministic port-based teleportation?

• Quantum Communication
• Channel simulation
• One-shot and finite-blocklength bounds

Does the quantum erasure-channel upper information-combining bound hold for two independent uniform bits with arbitrary quantum side information?

• Quantum Communication
• Matrix and entropy inequalities

Does there exist a norm-continuous semigroup \((\Phi_t)_{t\geq0}\) of unital completely positive trace-preserving maps on \(\mathcal L(\mathbb C^d)\), for some finite integer \(d\geq3\), such that \(\Phi_s\) is mixed unitary and \(\Phi_t\) is not mixed unitary for some \(0<s<t\)?

• Quantum Communication
• Quantum channel structure

Does the quantum Mrs.

• Quantum Communication
• Matrix and entropy inequalities

Can two quantum channels with zero two-way-assisted secret-key capacity have positive secret-key capacity when used jointly?

• Quantum Cryptography
• Quantum Communication
• Superactivation
• Secret-key distillation

Is there a single-mode phase-insensitive Gaussian amplifier or additive-noise channel of zero finite-energy quantum capacity that acquires positive finite-energy quantum capacity when used in parallel with a two-mode positive-partial-transpose Gaussian channel…

• Quantum Communication
• Superactivation
• Quantum capacity
• Bosonic channels

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

Does free shared classical randomness make the Holevo information achievable for visible compression of every finite mixed-state ensemble?

• Quantum Communication
• Quantum source coding
• Channel simulation

Is minimum output von Neumann entropy additive whenever one channel is a qubit channel?

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

Is energy-constrained Holevo information additive for a squeezed thermal attenuator below its water-filling threshold?

• Quantum Communication
• Classical capacity
• Bosonic channels
• Additivity and regularization

What is the two-way quantum capacity of a thermal amplifier for every gain and thermal noise level?

• Quantum Communication
• Quantum capacity
• Bosonic channels

What is the unassisted quantum capacity of a thermal amplifier for every gain and thermal noise level?

• Quantum Communication
• Quantum capacity
• Bosonic channels

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 achievable rate region for independent local compression of an arbitrary finite ensemble of bipartite pure states.

• Quantum Communication
• Quantum source coding

What is the unassisted quantum capacity of a depolarizing channel in every finite dimension \(d\geq3\)?

• Quantum Communication
• Quantum capacity
• Additivity and regularization

For every odd integer \(d\geq5\), do there exist \(r=d(d+1)/2\) unitary operators \(U_1,\ldots,U_r\) on \(\mathbb C^d\) such that

• Quantum Communication
• Quantum channel structure

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

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

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

• Quantum Communication
• Quantum capacity
• Bosonic channels

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 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 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

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

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

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

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

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