Topic
Quantum capacity
13 records: 9 unsolved, 4 solved. Filter the catalog by this topic →
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Squashed entanglement of the qubit depolarizing channel
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
Unsolved -
Universal finite truncation of quantum and private capacities
Do there exist channel-independent finite integers \(m_Q\) and \(m_P\) that determine, respectively, the quantum capacity and the private classical capacity of every finite-dimensional quantum channel?
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Computability of ordinary quantum capacity
Is the ordinary unassisted quantum capacity a computable function of a finite description of a finite-dimensional quantum channel?
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Exactly solvable nondegradable quantum channels
Does there exist a finite-dimensional quantum channel that is neither degradable nor antidegradable and whose unassisted quantum capacity is known exactly?
Solved -
All-code exponential strong converse for degradable channels
Does every finite-dimensional degradable quantum channel satisfy an all-code exponential strong converse for quantum communication at its quantum capacity?
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Quantum capacity of the Gaussian random-displacement channel
What is the unconstrained, unassisted quantum capacity of the single-mode Gaussian random-displacement channel?
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Exponential strong converse for transpose-degradable channels
Does every finite-dimensional transpose-degradable channel satisfy an exponential strong converse for quantum communication at its single-letter quantum capacity?
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Positivity threshold for thermal-attenuator quantum capacity
For \(0<\eta<1\) and \(0<\nu<\infty\), let the single-mode bosonic thermal attenuator be
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Quantum capacity of a qubit Pauli channel
What is the quantum capacity \(\mathcal{Q}(\Lambda_{\mathbf p})\) of the qubit Pauli channel defined by
Unsolved -
Quantum capacity of a bosonic thermal attenuator
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
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Energy-constrained quantum capacity of a thermal attenuator
For \(0<\eta<1\) and \(0<\nu<\infty\), let the single-mode bosonic thermal attenuator be
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Two-way quantum capacity: amplitude-damping channel
What is the two-way quantum capacity \(\mathcal{Q}_2(\mathcal A_p)\) of the qubit amplitude-damping channel
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Capacity-achieving codes for amplitude damping
What is the constructive quantum code for achieving the quantum capacity \(\mathcal{Q}(\mathcal A_p)\) of the qubit amplitude-damping channel
Solved