Quantum Information Theory
Quantum Reverse Shannon Theorems Quantify Resource Tradeoffs for Noisy Channel Simulation
Quantum reverse Shannon theorems characterize efficient simulation of noisy channels using noiseless ones or other noisy channels, requiring auxiliary resources like shared randomness classically or entanglement quantumly. For tensor-power sources, ebits suffice; general sources demand additional re…
Quantum Clique is QMA-Complete; Holevo Capacity and Minimum Entropy are NP-Complete
The quantum clique problem, defined as deciding whether a quantum channel admits k zero-error distinguishable states, is QMA-complete, providing a quantum analogue to the classical NP-complete clique problem via zero-error channel capacity. Computing the Holevo capacity and minimum entropy of quantu…
Quantum Channel Classical Capacity Trade-Off with Limited Entanglement Assistance
Peter Shor's paper derives the full trade-off curve for the classical capacity of a quantum channel as a function of the entanglement consumed by sender and receiver. The curve endpoints are the unassisted Holevo-Schumacher-Westmoreland (HSW) capacity and the entanglement-assisted capacity, defined …
Quantum Channel Capacity for Joint Classical-Quantum Transmission
Devetak and Shor derive an expression for the admissible rate pairs enabling simultaneous transmission of classical and quantum information over a quantum channel, generalizing the individual classical and quantum capacities. The formula requires regularization over multiple channel uses but simplif…
Entanglement-Assisted Classical Capacity of Quantum Channels Equals Input + Output Entropies Minus Joint Entropy
The entanglement-assisted classical capacity of a quantum channel is the maximum over input states ρ of H(ρ) + H(channel(ρ)) - H(ρ, channel(ρ)), where the joint entropy uses an entangled purification. This formula mirrors the classical channel capacity expression. The paper computes this for the qub…
Almost-IID States and Information Theory Robustness
The paper investigates the operational justification of independent and identically distributed (IID) state assumptions in information theory. It demonstrates that resources described by "almost-IID" states, arising from operationally motivated symmetry assumptions via de Finetti theorems, are as ef…
New Measures Bound Forward Classical Capacity of Bipartite Quantum Channels
Researchers introduce multiple measures of forward classical communication for bipartite quantum channels, which specialize to known bounds on point-to-point quantum channel classical capacity from prior work. These measures serve as upper bounds on the forward classical capacity of bipartite channe…
Classical Feedback Does Not Increase Quantum Channel Capacity Beyond Maximum Output Entropy
The classical capacity of any quantum channel with free classical feedback is upper-bounded by the channel's maximum average output entropy. This bound implies no capacity gain from feedback for quantum erasure channels and, under energy constraints, for pure-loss bosonic channels. The proof leverag…
Additive Capacity Formula for Classical Communication over Noisy Quantum Channels with Receiver-Side Noisy Entanglement
The paper derives an additive capacity formula for classical information transmission over noisy quantum channels using separable sender encoding and receiver-provided noisy entanglement via mixed signal-ancilla states purified by a witness. This formula quantifies the utility of limited or noisy en…