Negative Channels

James M. McCracken

P. V. Srinidhi, Indranil Chakrabarty, Samyadeb Bhattacharya +1 more

Counterintuitive to classical notions, quantum conditional entropy can be negative, playing a pivotal role in information-processing tasks. This article delves deeply into quantum channels, emphasizing negative conditional entropy breaking (NCEB) channels and introducing negative conditional entropy annihilating (NCEA) channels. We characterize these channels from topological and information-theoretic perspectives, examining their properties when combined serially. We also examine NCEB channels in parallel. Our exploration extends to complimentary channels associated with NCEB, leading to the introduction of information-leaking channels. Utilizing the parameters of the standard depolarizing channel, we provide tangible examples and further characterization. We demonstrate the relationship of NCEB and NCEA with newly introduced channels like coherent information (CIB) breaking and mutual information (MIB) breaking, along with standard channels like zero capacity channels. The preservation of quantum resources is an integral constituent of quantum information theory. Recognizing this, we lay prescriptions to detect channels that do not break the negativity of conditional entropy, ensuring the conservation of this quantum resource.

Alireza Seif, Moein Malekakhlagh, Swarnadeep Majumder +1 more

Pauli channels are widely used to describe errors in quantum computers, particularly when noise is shaped via Pauli twirling. A common assumption is that such channels admit a Markovian generator, namely a Pauli-Lindblad model with non-negative rates, but the validity of this assumption has not been systematically examined. Here, using CP-indivisibility as our criterion for non-Markovianity, we study multi-qubit Pauli channels from a single snapshot of the dynamics. We find that while the generator always has the same structure as the standard Pauli-Lindblad model, the rates may be negative or complex. We show that random Pauli channels are almost always non-Markovian, with the probability of encountering a negative rate converging doubly exponentially to unity with the number of qubits. For physically motivated noise models shaped by Pauli twirling, including single-qubit over-rotations and two-qubit amplitude damping errors, we find that negative rates are generic, even when the underlying physical noise is Markovian. We generalize probabilistic error amplification and cancellation to non-Markovian generators, and quantify the sampling overhead introduced by negative and complex rates. Experiments on superconducting qubits confirm that allowing negative rates in the learned noise model yields more accurate predictions than restricting to non-negative rates.

Natalia M. Litchinitser, Ildar R. Gabitov, Andrei I. Maimistov

We discuss a novel kind of nonlinear coupler with one channel filled with a negative index metamaterial. The opposite directionality of the phase velocity and the energy flow in the negative index metamaterial channel facilitates an effective feedback mechanism that leads to optical bistability and gap soliton formation.

G. Giedke, Michael M. Wolf

Mário S. Alvim, Konstantinos Chatzikokolakis A, Annabelle K. McIver +3 more