Revisiting the Quantum Open System Dynamics of Central Spin Model

In this work, we revisit the theory of open quantum systems from the perspective of fermionic baths. Specifically, we concentrate on the dynamics of a central spin half particle interacting with a spin bath. We have calculated the exact reduced dynamics of the central spin and constructed the Kraus operators in relation to that. Further, the exact Lindblad type canonical master equation corresponding to the reduced dynamics is constructed. We have also briefly touched upon the aspect of non-Markovianity from the backdrop of the reduced dynamics of the central spin.Quanta 2021; 10: 55–64.

On the effect of decoherence on quantum tunnelling

This work proposes a series of quantum experiments that can, at least in principle, allow for examining microscopic mechanisms associated with decoherence. These experiments can be interpreted as a quantum-mechanical version of non-equilibrium mixing between two volumes separated by a thin interface. One of the principal goals of such experiments is in identifying non-equilibrium conditions when time-symmetric laws give way to time-directional, irreversible processes, which are represented by decoherence at the quantum level. The rate of decoherence is suggested to be examined indirectly, with minimal intrusions—this can be achieved by measuring tunnelling rates that, in turn, are affected by decoherence. Decoherence is understood here as a general process that does not involve any significant exchanges of energy and governed by a particular class of the Kraus operators. The present work analyses different regimes of tunnelling in the presence of decoherence and obtains formulae that link the corresponding rates of tunnelling and decoherence under different conditions. It is shown that the effects on tunnelling of intrinsic decoherence and of decoherence due to unitary interactions with the environment are similar but not the same and can be distinguished in experiments.

Kraus operators and symmetric groups

In the contest of open quantum systems, we study a class of Kraus operators whose definition relies on the defining representation of the symmetric groups. We analyze the induced orbits as well as the limit set and the degenerate cases.

Influence of Noise Channel in Quantum One Time Password Authentication

This paper presents an overview of quantum errors and noise channels, their mathematical modeling and its implementation in quantum one time password (QOTP) based user authentication. Quantum noise plays a pivotal role in understanding quantum information theory which is important to build up quantum communication theory. The Kraus operators provide a powerful mathematical tool in understanding and modeling various quantum channels. Use of QOTP provides an impressive method of carrying out user authentication involving quantum operations based on user biometrics. However, the efficiency of this method can be better envisaged by incorporating noise models during qubit transmission.

Device-independent characterization of quantum instruments

Among certification techniques, those based on the violation of Bell inequalities are appealing because they do not require assumptions on the underlying Hilbert space dimension and on the accuracy of calibration methods. Such device-independent techniques have been proposed to certify the quality of entangled states, unitary operations, projective measurements following von Neumann's model and rank-one positive-operator-valued measures (POVM). Here, we show that they can be extended to the characterization of quantum instruments with post-measurement states that are not fully determined by the Kraus operators but also depend on input states. We provide concrete certification recipes that are robust to noise.

Stationary states of weak coupling limit-type Markov generators and quantum transport models

We prove that every stationary state in the annihilator of all Kraus operators of a weak coupling limit-type Markov generator consists of two pieces, one of them supported on the interaction-free subspace and the second one on its orthogonal complement. In particular, we apply the previous result to describe in detail the structure of a slightly modified quantum transport model due to Arefeva et al. (modified AKV’s model) studied first in [J. C. García et al., Entangled and dark stationary states of excitation energy transport models in many-particles systems and photosynthesis, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 21(3) (2018), Article ID: 1850018, p. 21, doi:10.1142/S0219025718500182], in terms of generalized annihilation and creation operators.

Density-operator evolution: Complete positivity and the Keldysh real-time expansion

We study the reduced time-evolution of general open quantum systems by combining insights from quantum-information and statistical field theory. Inspired by prior work [Eur. Phys. Lett.~102, 60001 (2013) and Phys. Rev. Lett.~111, 050402 (2013)] we establish the explicit structure guaranteeing the complete positivity (CP) and trace-preservation (TP) of the real-time evolution expansion in terms of the microscopic system-environment coupling.This reveals a fundamental two-stage structure of the coupling expansion: Whereas the first stage naturally defines the dissipative timescales of the system -before having integrated out the environment completely- the second stage sums up elementary physical processes, each described by a CP superoperator. This allows us to establish the highly nontrivial functional relation between the (Nakajima-Zwanzig) memory-kernel superoperator for the reduced density operator and novel memory-kernel operators that generate the Kraus operators of an operator-sum. We illustrate the physically different roles of the two emerging coupling-expansion parameters for a simple solvable model. Importantly, this operational approach can be implemented in the existing Keldysh real-time technique and allows approximations for general time-nonlocal quantum master equations to be systematically compared and developed while keeping the CP and TP structure explicit.Our considerations build on the result that a Kraus operator for a physical measurement process on the environment can be obtained by `cutting' a group of Keldysh real-time diagrams `in half'. This naturally leads to Kraus operators lifted to the system plus environment which have a diagrammatic expansion in terms of time-nonlocal memory-kernel operators. These lifted Kraus operators obey coupled time-evolution equations which constitute an unraveling of the original Schroedinger equation for system plus environment. Whereas both equations lead to the same reduced dynamics, only the former explicitly encodes the operator-sum structure of the coupling expansion.

Asymptotics of quantum channels: conserved quantities, an adiabatic limit, and matrix product states

This work derives an analytical formula for the asymptotic state---the quantum state resulting from an infinite number of applications of a general quantum channel on some initial state. For channels admitting multiple fixed or rotating points, conserved quantities---the left fixed/rotating points of the channel---determine the dependence of the asymptotic state on the initial state. The formula stems from a Noether-like theorem stating that, for any channel admitting a full-rank fixed point, conserved quantities commute with that channel’s Kraus operators up to a phase. The formula is applied to adiabatic transport of the fixed-point space of channels, revealing cases where the dissipative/spectral gap can close during any segment of the adiabatic path. The formula is also applied to calculate expectation values of noninjective matrix product states (MPS) in the thermodynamic limit, revealing that those expectation values can also be calculated using an MPS with reduced bond dimension and a modified boundary.

Local available quantum correlations for Bell Diagonal states and Markovian decoherence

Local available quantum correlations (LAQCs), as dened by Mundarain et al. [19], are analytically determined for Bell Diagonal states. Using the Kraus operators formalism [10], we analyze the dissipative dynamics of 2-qubit LAQCs under Markovian decoherence. This is done for Werner states under the depolarizing [20] and phase damping channels [21]. Since Werner states are among those that exhibit the so called entanglement sudden death [27], the results are compared with the ones obtained for Quantum Discord [22], as analyzed by Werlang et al. [24], as well as for entanglement, i.e. Concurrence[7]. The LAQCs quantier, as Quantum Discord does, only vanishes asymptotically.