arXiv subjects

A. T. Rezakhani

Publications and source records attributed to A. T. Rezakhani.

At least 19 recordsLinked to original sources

arXiv2026

State-Based Quantum Operations: Chameleon Gates

We introduce chameleon gates as a natural generalization of conventional quantum controlled-gates. Chameleon gates are state-based quantum controlled-operations that retain standard elements such as control and target systems, while introducing a new feature: the quantum knob. This knob is a quantum signal (state) that determines the operation performed by the gate. Consequently, the action and form of a chameleon gate depend dynamically on the quantum knob, allowing the gate to adapt its operation and implement transformations that are not necessarily unitary. This shapeshifting property is in stark contrast to conventional quantum controlled-gates, whose actions are fixed and cannot be modified. We also propose how chameleon gates can be realized using conventional quantum gates available in current quantum technologies. We then employ chameleon gates as a useful building block within the recently proposed state-based quantum computation (SBQC) framework. Using this approach, we demonstrate the simulation of state-dependent (nonlinear) quantum evolutions.

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arXiv2025

Feature- and process-based optimal control of quantum dynamics

Preparing desired quantum states and quantum operations (processes) is essential for numerous tasks in quantum computation. Several approaches have been developed for optimal control of quantum states, whereas optimal strategies for preparation of a given quantum process have remained fairly less explored. For some applications, rather than a specific desired state or process, it may suffice to obtain states or processes with specific desired features such as (high) coherence or purity. In such cases, fidelity-based measures alone are inadequate for evaluating the performance of a quantum control strategy, and hence proper feature-based figures of merit should be employed. Here we develop a feature-based optimal coherent control formalism for open quantum processes under Markovian evolutions which demonstrate high coherence and purity features. In particular, we observe that performance of the feature-based Krotov optimization algorithm can be improved by choosing educated initial guess fields. In addition, in a model for a qutrit Rydberg system, it is shown that the convex overlap-based fidelity outperforms other process-based as well as state-based fidelities. This analysis underscores the utility of feature-based optimal control strategies for quantum processes.

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arXiv2025

Does Quantum Mechanics Breed Larger, More Intricate Quantum Theories? The Case for Experience-Centric Quantum Theory and the Interactome of Quantum Theories

We pose and address the radical question that whether quantum mechanics, known for its firm internal structure and enormous empirical success, carries in itself the genome of larger quantum theories which have higher internal intricacies and phenomenological versatilities. That is, on the basic level of closed quantum systems and regardless of interpretational aspects, whether standard quantum theory (SQT) harbors quantum theories with context-based deformed principles or structures, having definite predictive power within broader scopes. We answer the question in affirmative following complementary evidence and reasoning arising from quantum-computation-based quantum simulation and fundamental, general, abstract rationales in the frameworks of information theory, fundamental or functional emergence, and participatory agency. In this light, as we show, one is led to the recently proposed experience-centric quantum theory (ECQT), which is a larger and richer theory of quantum behaviors with drastically generalized quantum dynamics. ECQT allows the quantum information of the closed quantum system's developed state history to continually contribute to defining manybody interactions, Hamiltonians, and even internal elements and ``particles'' of the total system. Hence the unitary evolutions are continually impacted and become guidable by the agent-system's experience. The intrinsic interplay of unitarity and non-Markovianity in ECQT brings about a host of diverse behavioral phases, which concurrently infuse closed and open quantum system characteristics and even surpasses the theory of open systems in SQT. In the broader perspective, an upshot of our investigation is the existence of the quantum interactome--the interactive landscape of all coexisting, independent context-based quantum theories which emerge from inferential participatory agencies--and its predictive phenomenological utility.

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arXiv2025

State-Based Quantum Simulation: Releasing the Powers of Quantum States and Copies

Quantum computing employs controllable interactions to perform sequences of logical gates and entire algorithms on quantum registers. This paradigm has been widely explored, e.g., for simulating dynamics of manybody systems by decomposing their Hamiltonian evolution in a series of quantum gates. Here, we introduce a method for quantum simulation in which the Hamiltonian is decomposed in terms of states and the resulting evolution is realized by only controlled-swap gates and measurements applied on a set of auxiliary systems whose quantum states define the system dynamics. These auxiliary systems can be identically prepared in an arbitrary number of copies of known states at any intermediate time. This parametrization of the quantum simulation goes beyond traditional gate-based methods and permits simulation of, e.g., state-dependent (nonlinear) Hamiltonians and open quantum systems. We show how classical nonlinear and time-delayed ordinary differential equations can be simulated with the state-based method, and how a nonlinear variant of shortcut to adiabaticity permits adiabatic quantum computation, preparation of eigenstates, and solution of optimization tasks.

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arXiv2024

Unfolding system-environment correlation in open quantum systems: Revisiting master equations and the Born approximation

Understanding system-bath correlations in open quantum systems is essential for various quantum information and technology applications. Derivations of most master equations (MEs) for the dynamics of open systems require approximations that mask dependence of the system dynamics on correlations, since the MEs focus on reduced system dynamics. Here we demonstrate that the most common MEs indeed contain hidden information about explicit system-environment correlation. We unfold these correlations by recasting the MEs into a universal form in which the system-bath correlation operator appears. The equations include the Lindblad, Redfield, second-order time-convolutionless, second-order Nakajima-Zwanzig, and second-order universal Lindblad-like cases. We further illustrate our results in an example, which implies that the second-order universal Lindblad-like equation captures correlation more accurately than other standard techniques.

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arXiv2022

Entropy-Based Formulation of Thermodynamics in Arbitrary Quantum Evolution

Given the evolution of an arbitrary open quantum system, we formulate a general and unambiguous method to separate the internal energy change of the system into an entropy-related contribution and a part causing no entropy change, identified as heat and work, respectively. We also demonstrate that heat and work admit geometric and dynamical descriptions by developing a universal dynamical equation for the given trajectory of the system. The dissipative and coherent parts of this equation contribute exclusively to heat and work, where the specific role of a work contribution from a counterdiabatic drive is underlined. Next we define an expression for the irreversible entropy production of the system which does not have explicit dependence on the properties of the ambient environment; rather, it depends on a set of the system's observables excluding its Hamiltonian and is independent of internal energy change. We illustrate our results with three examples.

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arXiv2021

Correlation-Enabled Energy Exchange in Quantum Systems without External Driving

We study the role of correlation in mechanisms of energy exchange between an interacting bipartite quantum system and its environment by decomposing the energy of the system to local and correlation-related contributions. When the system Hamiltonian is time-independent, no external work is performed. In this case, energy exchange between the system and its environment occurs only due to the change in the state of the system. We investigate possibility of a special case where the energy exchange with the environment occurs exclusively due to changes in the correlation between the constituent parts of the bipartite system, while their local energies remain constant. We find sufficient conditions for preserving local energies. It is proven that under these conditions and within the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) dynamics this scenario is not possible for all initial states of the bipartite system. Nevertheless, it is still possible to find special initial states for which the local energies remain unchanged during the associated evolution and the whole energy exchange is only due to the change in the correlation energy. We illustrate our results with an example.

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arXiv2021

Enhancing energy transfer in quantum systems via periodic driving: Floquet master equations

We provide a comprehensive study of the energy transfer phenomenon -- populating a given energy level -- in 3- and 4-level quantum systems coupled to two thermal baths. In particular, we examine the effects of an external periodic driving and the coherence induced by the baths on the efficiency of the energy transfer. We consider the Floquet-Lindblad and the Floquet-Redfield scenarios, which both are in the Born-Markov, weak-coupling regime but differ in the treatment of the secular approximation, and for the latter, we develop an appropriate Floquet-type master equation by employing a partial secular approximation. Throughout the whole analysis we keep Lamb-shift corrections in the master equations. We observe that, especially in the Floquet-Redfield scenario, the driving field can enhance the energy transfer efficiency compared to the nondriven scenario. In addition, unlike degenerate systems where Lamb-shift corrections do not contribute significantly on the energy transfer, in the Redfield and the Floquet-Redfield scenarios these corrections have nonnegligible effects.

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arXiv2021

Temperature in Nonequilibrium Quantum Systems

We extend on ideas from standard thermodynamics to show that temperature can be assigned to a general nonequilibrium quantum system. By choosing a physically motivated complete set of observables and expanding the system state thereupon, one can read a set of relevant, independent thermodynamic variables which include internal energy. This expansion allows us to read a nonequilibrium temperature as the partial derivative of the von Neumann entropy with respect to internal energy. We show that this definition of temperature is one of a set of thermodynamics parameters unambiguously describing the system state. It has appealing features such as positivity for passive states and consistency with the standard temperature for thermal states. By attributing temperature to correlations in a bipartite system, we obtain a universal relation which connects the temperatures of subsystems, total system as a whole, and correlation. All these temperatures can be different even when the composite system is in a well-defined Gibbsian thermal state.

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arXiv2021

Coherent dynamical control of quantum processes

Manipulation of a quantum system requires the knowledge of how it evolves. To impose that the dynamics of a system becomes a particular target operation (for any preparation of the system), it may be more useful to have an equation of motion for the dynamics itself--rather than the state. Here we develop a Markovian master equation for the process matrix of an open system, which resembles the Lindblad Markovian master equation. We employ this equation to introduce a scheme for optimal local coherent process control at target times, and extend the Krotov technique to obtain optimal control. We illustrate utility of this framework through several quantum coherent control scenarios, such as optimal decoherence suppression, gate simulation, and passive control of the environment, in all of which we aim to simulate a given terminal process at a given final time.

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arXiv2021

Adaptive Quantum Heat Engines

For heat engines working between two heat baths, functionality is often conditioned on a set of fixed constraints such as given internal structure of the engine and given temperatures for the baths. It is, however, important to devise heat engines which can function adaptively, in particular when the engine is a quantum system and the baths are subject to fluctuations. Here we study a model for an adaptive quantum heat engine whose heat baths can have variable temperatures. We obtain conditions under which such an engine can still operate. Moreover, we propose an enhancement of the heat engine by coupling it with an appropriate controller which changes the internal structure of the engine. Interestingly, we prove that this enhanced engine can always operate and we also obtain conditions for maximum power extraction from this engine for all temperatures of the heat baths.

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arXiv2020

Shortcuts to Adiabaticity in Driven Open Quantum Systems: Balanced Gain and Loss and Non-Markovian Evolution

A universal scheme is introduced to speed up the dynamics of a driven open quantum system along a prescribed trajectory of interest. This framework generalizes counterdiabatic driving to open quantum processes. Shortcuts to adiabaticity designed in this fashion can be implemented in two alternative physical scenarios: one characterized by the presence of balanced gain and loss, the other involves non-Markovian dynamics with time-dependent Lindblad operators. As an illustration, we engineer superadiabatic cooling, heating, and isothermal strokes for a two-level system, and provide a protocol for the fast thermalization of a quantum oscillator.

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arXiv2020

Correlation Picture Approach to Open-Quantum-System Dynamics

We introduce a new dynamical picture, referred to as correlation picture,' which connects a correlated state to its uncorrelated counterpart. Using this picture allows us to derive an exact dynamical equation for a general open-system dynamics with system--environment correlations included. This exact dynamics is in the form of a Lindblad-like equation even in the presence of initial system-environment correlations. For explicit calculations, we also develop a weak-correlation expansion formalism that allows us to perform systematic perturbative approximations. This expansion provides approximate master equations which can feature advantages over existing weak-coupling techniques. As a special case, we derive a Markovian master equation, which is different from existing approaches. We compare our equations with corresponding standard weak-coupling equations by two examples, where our correlation picture formalism is more accurate, or at least as accurate as weak-coupling equations.

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arXiv2019

Mutual Information is not a Reliable Measure for Variations in Total Correlations

Correlations disguised in various forms underlie a host of important phenomena in classical and quantum systems, such as information and energy exchanges. The quantum mutual information and the norm of the correlation matrix are both considered as proper measures of total correlations. We demonstrate that, when applied to the same system, these two measures can actually show significantly different behavior except at least in two limiting cases: when there are no correlations and when there is maximal quantum entanglement. We further quantify the discrepancy by providing analytic formulas for time derivatives of the measures for an interacting bipartite system evolving unitarily. We argue that to properly account for correlations, one should consider the full information provided by the correlation matrix (and reduced states of the subsystems). Scalar quantities such as the norm of the correlation matrix or the quantum mutual information can only capture a part of the complex features of correlations. As a concrete example, we show that in describing heat exchange associated with correlations, neither of these quantities can fully capture the underlying physics.

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arXiv2019

Continuity of the quantum Fisher information

In estimating an unknown parameter of a quantum state the quantum Fisher information (QFI) is a pivotal quantity, which depends on the state and its derivate with respect to the unknown parameter. We prove the continuity property for the QFI in the sense that two close states with close first derivatives have close QFIs. This property is completely general and irrespective of dynamics or how states acquire their parameter dependence and also the form of parameter dependence---indeed this continuity is basically a feature of the classical Fisher information that in the case of the QFI naturally carries over from the manifold of probability distributions onto the manifold of density matrices. We demonstrate that in the special case where the dependence of the states on the unknown parameter comes from one dynamical map (quantum channel), the continuity holds in its reduced form with respect to the initial states. In addition, we show that when one initial state evolves through two different quantum channels, the continuity relation applies in its general form. A situation in which such scenario can occur is an open-system metrology where one of the maps represents the ideal dynamics whereas the other map represents the real (noisy) dynamics. In the making of our main result, we also introduce a regularized representation for the symmetric logarithmic derivative which works for general states even with incomplete rank, and its features continuity similarly to the QFI.

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arXiv2019

Binding energy of bipartite quantum systems: Interaction, correlations, and tunneling

We provide a physically motivated definition for the binding energy (or bond-dissociation) of a bipartite quantum system. We consider coherently applying an external field to cancel out the interaction between the subsystems, to break their bond and separate them as systems from which no work can be extracted coherently by any cyclic evolution. The minimum difference between the average energies of the initial and final states obtained this way is defined as the binding energy of the bipartite system. We show the final optimal state is a passive state. We also discuss how required evolution can be realized through a sequence of control pulses. We illustrate utility of our definition through two examples. In particular, we also show how quantum tunneling can assist or enhance bond-breaking process. This extends our definition to probabilistic events.

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arXiv2018

Quantum detailed balance conditions and fluctuation relations for thermalizing quantum dynamics

Quantum detailed balance conditions and quantum fluctuation relations are two important concepts in the dynamics of open quantum systems: both concern how such systems behave when they thermalize because of interaction with an environment. We prove that for thermalizing quantum dynamics the quantum detailed balance conditions yield the validity of a quantum fluctuation relation (where only forward-time dynamics is considered). This implies that to have such a quantum fluctuation relation (which in turn enables a precise formulation of the second law of thermodynamics for quantum systems) it suffices to fulfill the quantum detailed balance conditions. We, however, show that the converse is not necessarily true; indeed, there are cases of thermalizing dynamics which feature the quantum fluctuation relation without satisfying detailed balance. We illustrate our results with three examples.

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arXiv2018

How Quantum is a "Quantum Walk"?

We characterize quantumness of the so-called quantum walks (whose dynamics is governed by quantum mechanics) by introducing two computable measures which are stronger than the variance of the walker's position probability distribution. The first measure is based on comparing probability distributions of a quantum walk and all classical random walks (through the classical relative entropy of the distributions), and it quantifies non-Gaussianity of the probability distribution of the walk. Next, after assigning a density matrix to classical walks, we introduce a more powerful measure by employing quantum relative entropy. We show that this measure exceeds the first one by the quantum coherence of the walk. There are walks labeled classical by the variance whereas our measures identify some quantumness therein. As an application, we study a model of quantum (energy) transport on a simple lattice, and compare the behavior of its relative transport efficiencies with that of the quantumness. Our measures help partly explain why in some quantum transport phenomena a considerably high efficiency may appear---this is where quantumness is appreciable.

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