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Correcting Quantum Errors with Entanglement
TLDR
The entanglement-assisted quantum codes described do not require the dual-containing constraint necessary for standard quantum error–correcting codes, thus allowing us to “quantize” all of classical linear coding theory.
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Entanglement-Assisted Capacity of Quantum Multiple-Access Channels
TLDR
A regularized formula for the entanglement-assisted (EA) capacity region for quantum multiple-access channels (QMAC) is found and the Holevo-Schumacher-Westmoreland theorem may be obtained from a modification of the EA protocol.
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Entanglement-Assisted Communication of Classical and Quantum Information
TLDR
The main result is a capacity theorem that gives a 3-D achievable rate region that justifies the need for simultaneous coding of classical and quantum information over an EAQ channel.
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Catalytic Quantum Error Correction
TLDR
The theory of entanglement-assisted quantum error-correcting (EAQEC) codes is developed, a generalization of the stabilizer formalism to the setting in which the sender and receiver have access to presharedEntanglement, which greatly simplifies their construction.
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High Performance Entanglement-Assisted Quantum LDPC Codes Need Little Entanglement
TLDR
It is shown that the above conjecture is wrong by providing families of EAQECCs with an entanglement consumption rate that diminishes linearly as a function of the code length, and indicates that EAZECCs are not only theoretically interesting, but also physically implementable.
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Channel Simulation and Coded Source Compression
TLDR
The result reveals that a helper's scheme which separately conducts a measurement and a compression is suboptimal, and measurement compression seems necessary to achieve the optimal rate region, and the direct coding theorem of the result is proved via the measurement compression theory of Winter, a quantum-to-classical channel simulation.
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The Expressive Power of Parameterized Quantum Circuits
TLDR
It is proved that PQCs with a simple structure already outperform any classical neural network for generative tasks, unless the polynomial hierarchy collapses, and they are employed as an application for Bayesian learning.
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Trading classical communication, quantum communication, and entanglement in quantum Shannon theory
TLDR
A “unit-resource” capacity theorem is proved that applies to the scenario where only the above three noiseless resources are available for consumption or generation, and the optimal strategy mixes the three fundamental protocols of teleportation, superdense coding, and entanglement distribution.
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The information-theoretic costs of simulating quantum measurements
TLDR
An extension of the Devetak–Winter theorem on classical data compression with quantum side information to the case in which the sender is not required to receive the outcomes of the simulated measurement, and a single-letter converse theorem demonstrating optimality is proved.
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Quantum noise protects quantum classifiers against adversaries
TLDR
By taking advantage of depolarisation noise in quantum circuits for classification, a robustness bound against adversaries can be derived where the robustness improves with increasing noise, which is the first quantum protocol that can be used against the most general adversaries.
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