Implications of Negative Channels

James M. McCracken

James M. McCracken

Joris Kattemölle, Balázs Gulácsi, Guido Burkard

Noise forms a central obstacle to effective quantum information processing. Recent experimental advances have enabled the tailoring of noise properties through Pauli twirling, transforming arbitrary noise channels into Pauli channels. This underpins theoretical descriptions of fault-tolerant quantum computation and forms an essential tool in noise characterization and error mitigation. Pauli-Lindblad channels have been introduced to aptly parameterize quasi-local Pauli errors across a quantum register, excluding negative Pauli-Lindblad parameters relying on the Markovianity of the underlying noise processes. We point out that caution is required when parameterizing channels as Pauli-Lindblad channels with nonnegative parameters. For this, we study the effects of Pauli twirling on Markovianity. We use the notion of Markovianity of a channel (rather than that of an entire semigroup) and prove a general Pauli channel is non-Markovian if and only if at least one of its Pauli-Lindblad parameters is negative. Using this, we show that Markovian quantum channels often become non-Markovian after Pauli twirling. The Pauli-twirling induced non-Markovianity necessitates the use of negative Pauli-Lindblad parameters for a correct noise description in experimentally realistic scenarios. An important example is the implementation of the $\sqrt{X}$-gate under standard Markovian noise. As such, our results have direct implications for quantum error mitigation protocols that rely on accurate noise characterization.

James M. McCracken

Huangjun Zhu

Quasiprobability representations, such as the Wigner function, play an important role in various research areas. The inevitable appearance of negativity in such representations is often regarded as a signature of nonclassicality, which has profound implications for quantum computation. However, little is known about the minimal negativity that is necessary in general quasiprobability representations. Here we focus on a natural class of quasiprobability representations that is distinguished by simplicity and economy. We introduce three measures of negativity concerning the representations of quantum states, unitary transformations, and quantum channels, respectively. Quite surprisingly, all three measures lead to the same representations with minimal negativity, which are in one-to-one correspondence with the elusive symmetric informationally complete measurements. In addition, most representations with minimal negativity are automatically covariant with respect to the Heisenberg-Weyl groups. Furthermore, our study reveals an interesting tradeoff between negativity and symmetry in quasiprobability representations.

Bivas Mallick, Ananda G. Maity, Nirman Ganguly +1 more

Higher-dimensional entanglement is a valuable resource for several quantum information processing tasks, and is often characterized by the Schmidt number and specific classes of entangled states beyond qubit-qubit and qubit-qutrit systems. We propose a criterion to detect higher-dimensional entanglement, focusing on determining the Schmidt number of quantum states and identifying significant classes of positive partial transposition and negative partial transposition entangled states. Our approach relies on evaluating moments of generalized positive maps which can be efficiently simulated in real experiments without the requirement of full-state tomography. We demonstrate the effectiveness of our detection scheme through various illustrative examples. As a direct application, we explore the implications of our moment-based detection schemes in identifying useful quantum channels such as non-Schmidt-number breaking channels and non-entanglement breaking channels. Finally, we present an operational implication of our proposed moment criterion through its manifestation in channel discrimination tasks.