The superadditivity effects of quantum capacity decrease with the dimension for qudit depolarizing channels

Abstract

Quantum channel capacity is a fundamental quantity in order to understand how good can quantum information be transmitted or corrected when subjected to noise. However, it is generally not known how to compute such quantities, since the quantum channel coherent information is not additive for all channels, implying that it must be maximized over an unbounded number of channel uses. This leads to the phenomenon known as superadditivity, which refers to the fact that the regularized coherent information of $n$ channel uses exceeds one-shot coherent information. In this article, we study how the gain in quantum capacity of qudit depolarizing channels relates to the dimension of the systems considered. We make use of an argument based on the no-cloning bound in order to proof that the possible superadditive effects decrease as a function of the dimension for such family of channels. In addition, we prove that the capacity of the qudit depolarizing channel coincides with the coherent information when $d\to \infty$. We also discuss the private classical capacity and obain similar results. We conclude that when high dimensional qudits experiencing depolarizing noise are considered, the coherent information of the channel is not only an achievable rate but essentially the maximum possible rate for any quantum block code.

arXiv comment10 pages, 2 figures

References in corpus (47)

• Surface codes: Towards practical large-scale quantum computation
• Encoding a qubit in an oscillator
• Distillation of secret key and entanglement from quantum states
• The capacity of the noisy quantum channel
• Exact and Approximate Unitary 2-Designs: Constructions and Applications
• Entanglement-Assisted Classical Capacity of Noisy Quantum Channels
• Superadditivity of communication capacity using entangled inputs
• Optimal Universal and State-Dependent Quantum Cloning
• From Classical to Quantum Shannon Theory
• Capacities of Quantum Erasure Channels
• Quantum Communication With Zero-Capacity Channels
• Quantum Channel Capacity of Very Noisy Channels
• Probabilistic error cancellation with sparse Pauli-Lindblad models on noisy quantum processors
• Symmetrised Characterisation of Noisy Quantum Processes
• The XZZX Surface Code
• Quantum cloning and the capacity of the Pauli channel
• On Quantum Fidelities and Channel Capacities
• Degenerate Quantum Codes for Pauli Channels
• The structure of degradable quantum channels
• Unbounded number of channel uses are required to see quantum capacity
• The private classical capacity with a symmetric side channel and its application to quantum cryptography
• Quantum channels with a finite memory
• Approximate Degradable Quantum Channels
• Experimentally scalable protocol for identification of correctable codes
• Dephrasure channel and superadditivity of coherent information
• Binding entanglement channels
• Minimal qudit code for a qubit in the phase-damping channel
• Useful states and entanglement distillation
• Conjugate Degradability and the Quantum Capacity of Cloning Channels
• Private and Quantum Capacities of More Capable and Less Noisy Quantum Channels
• Bounds on classical information capacities for a class of quantum memory channels
• Quantum and private capacities of low-noise channels
• Quantum flags, and new bounds on the quantum capacity of the depolarizing channel
• Quantum capacity analysis of multi-level amplitude damping channels
• Superadditivity of private information for any number of uses of the channel
• Quantum Codes from Neural Networks
• Exact solution for the quantum and private capacities of bosonic dephasing channels
• Positivity and nonadditivity of quantum capacities using generalized erasure channels
• Error Thresholds for Arbitrary Pauli Noise
• Pursuing the fundamental limits for quantum communication
• Channel covariance, twirling, contraction, and some upper bounds on the quantum capacity
• Detecting positive quantum capacities of quantum channels
• Capacity of trace decreasing quantum operations and superadditivity of coherent information for a generalized erasure channel
• Multi-qubit time-varying quantum channels for NISQ-era superconducting quantum processors
• Resonant Multilevel Amplitude Damping Channels
• Exploring super-additivity of coherent information of noisy quantum channels through Genetic algorithms
• Bounding quantum capacities via partial orders and complementarity

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