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We investigate the multiple use of a ferromagnetic spin chain for quantum and classical communications without resetting. We find that the memory of the state transmitted during the first use makes the spin chain a qualitatively different quantum channel during the second transmission, for which we find the relevant Kraus operators. We propose a parameter to quantify the amount of memory in the channel and find that it influences the quality of the channel, as reflected through fidelity and entanglement transmissible during the second use. For certain evolution times, the memory allows the channel to exceed the memoryless classical capacity (achieved by separable inputs) and in some cases it can also enhance the quantum capacity.
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Spin chains have been proposed as quantum wires for information transfer in solid state quantum architectures. We show that huge gains in both transfer speed and fidelity are possible using a minimalist control approach that relies only a single, local, on-off switch actuator. Effective switching time sequences can be determined using optimization techniques for both ideal and disordered chains. Simulations suggest that effective optimization is possible even in the absence of accurate models.
Employing a recently proposed measure for quantum non-Markovianity, we carry out a systematic study of the size of memory effects in the spin-boson model for a large region of temperature and frequency cutoff parameters. The dynamics of the open system is described utilizing a second-order time-convolutionless master equation without the Markov or rotating wave approximations. While the dynamics is found to be strongly non-Markovian for low temperatures and cutoffs, in general, we observe a special regime favoring Markovian behavior. This effect is explained as resulting from a resonance between the systems transition frequency and the frequencies of the dominant environmental modes. We further demonstrate that the corresponding Redfield equation is capable of reproducing the characteristic features of the non-Markovian quantum behavior of the model.
We consider the transfer of classical and quantum information through a memory amplitude damping channel. Such a quantum channel is modeled as a damped harmonic oscillator, the interaction between the information carriers - a train of qubits - and the oscillator being of the Jaynes-Cummings kind. We prove that this memory channel is forgetful, so that quantum coding theorems hold for its capacities. We analyze entropic quantities relative to two uses of this channel. We show that memory effects improve the channel aptitude to transmit both classical and quantum information, and we investigate the mechanism by which memory acts in changing the channel transmission properties.
We study the performance of a partially correlated amplitude damping channel acting on two qubits. We derive lower bounds for the single-shot classical capacity by studying two kinds of quantum ensembles, one which allows to maximize the Holevo quantity for the memoryless channel and the other allowing the same task but for the full-memory channel. In these two cases, we also show the amount of entanglement which is involved in achieving the maximum of the Holevo quantity. For the single-shot quantum capacity we discuss both a lower and an upper bound, achieving a good estimate for high values of the channel transmissivity. We finally compute the entanglement-assisted classical channel capacity.
Understanding temporal processes and their correlations in time is of paramount importance for the development of near-term technologies that operate under realistic conditions. Capturing the complete multi-time statistics defining a stochastic process lies at the heart of any proper treatment of memory effects. In this thesis, using a novel framework for the characterisation of quantum stochastic processes, we first solve the long standing question of unambiguously describing the memory length of a quantum processes. This is achieved by constructing a quantum Markov order condition that naturally generalises its classical counterpart for the quantification of finite-length memory effects. As measurements are inherently invasive in quantum mechanics, one has no choice but to define Markov order with respect to the interrogating instruments that are used to probe the process at hand: different memory effects are exhibited depending on how one addresses the system, in contrast to the standard classical setting. We then fully characterise the structural constraints imposed on quantum processes with finite Markov order, shedding light on a variety of memory effects that can arise through various examples. Lastly, we introduce an instrument-specific notion of memory strength that allows for a meaningful quantification of the temporal correlations between the history and the future of a process for a given choice of experimental intervention. These findings are directly relevant to both characterising and exploiting memory effects that persist for a finite duration. In particular, immediate applications range from developing efficient compression and recovery schemes for the description of quantum processes with memory to designing coherent control protocols that efficiently perform information-theoretic tasks, amongst a plethora of others.
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