Experimental investigation of Markovian and non-Markovian channel addition

Abstract

The study of memory effects in quantum channels helps in developing characterization methods for open quantum systems and strategies for quantum error correction. Two main sets of channels exist, corresponding to system dynamics with no memory (Markovian) and with memory (non-Markovian). Interestingly, these sets have a non-convex geometry, allowing one to form a channel with memory from the addition of memoryless channels and vice-versa. Here, we experimentally investigate this non-convexity in a photonic setup by subjecting a single qubit to a convex combination of Markovian and non-Markovian channels. We use both divisibility and distinguishability as criteria for the classification of memory effects, with associated measures. Our results highlight some practical considerations that may need to be taken into account when using memory criteria to study system dynamics given by the addition of Markovian and non-Markovian channels in experiments.

Digital Simulation of Convex Mixtures of Markovian and Non-Markovian Single Qubit Channels on NISQ Devices

“…The result of this work is to show that, through simulations using NISQ devices, convex mixtures of Markovian channels can lead to a non-Markovian channel (M+M=nM) and vice versa (nM+nM=M). Furthermore, for the convex mixtures from [16], our simulations yielded better approximations of the intended channels than the simulations in [16]. For our designed convex mixture of two non-Markovian channels, the resulting channel obtained could be more definitively verified as Markovian.…”

“…There has been much interest in the study of the non-Markovian dynamics of an open quantum system [6][7][8][10][11][12][13][14][15]. Recently, simulations of open quantum systems have been used to further understand non-Markovian dynamics [16,17].…”

“…Using a linear optical setup, Uriri et al [16] simulated convex mixtures of two Markovian channels leading to a non-Markovian channel (M + M = nM) and convex mixtures of two non-Markovian channels leading to a Markovian channel (nM + nM = M). However, in [16], the intended Markovian channels could not be definitively verified as Markovian due to experimental error and channel design challenges.…”

“…Using a linear optical setup, Uriri et al [16] simulated convex mixtures of two Markovian channels leading to a non-Markovian channel (M + M = nM) and convex mixtures of two non-Markovian channels leading to a Markovian channel (nM + nM = M). However, in [16], the intended Markovian channels could not be definitively verified as Markovian due to experimental error and channel design challenges. Utilizing a general approach to the simulation of the open quantum systems on NISQ devices implemented in [17], this work will focus on the quantum simulation of the convex mixtures of quantum channels.…”

Experimental realization of high-fidelity teleportation via a non-Markovian open quantum system

“…These developments have influenced, and have been influenced by, the increasing ability to realize experimentally reservoir engineering [10], various fundamental open system models in non-Markovian regimes [11], and the control of open system dynamics [12]. Indeed, a number of various physical platforms have been used for this purpose including, e.g., optical systems [11][12][13][14][15][16][17][18][19][20][21], NV centers [22,23], trapped ions [24], and NMR systems [25,26]. In addition to fundamental studies and tests, recent experimental work also includes some of the first exploitations of non-Markovian memory effects in basic quantum information protocols including, e.g., single-qubit Deutsch-Josza algorithm [27].…”