arXiv subjects

Himanshu Badhani

Publications and source records attributed to Himanshu Badhani.

11 recordsLinked to original sources

arXiv2026

Conditional channel entropy sets fundamental limits on thermodynamic quantum information processing

The thermodynamic resourcefulness of quantum channels primarily depends on their underlying causal structure and their ability to generate quantum correlations. We quantify this interplay within the resource theory of athermality for bipartite quantum channels in the presence of a side channel acting as memory, referred to as the resource theory of conditional athermality. For channels with trivial output Hamiltonians, we characterize the optimal one-shot rates for distilling the identity gate from a given channel, as well as the cost of simulating the channel using the identity gate, under conditional Gibbs-preserving superchannels. We show that these rates have a direct trade-off relation with the conditional channel entropies, attributing operational significance to signaling in quantum processes. Furthermore, we establish an asymptotic equipartition property for the conditional channel min-entropy for classes of channels that are either tele-covariant or no-signaling from the non-conditioning input to the conditioning output. As a consequence, we demonstrate asymptotic reversibility of the resource theory for these channels. The asymptotic conditional athermality capacity of a tele-covariant channel is half the superdense coding capacity of its Choi state. Our work establishes the conditional channel entropy as a primitive information-theoretic concept for quantum processes, elucidating its potential for wider applications in quantum information science.

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arXiv2025

Thermodynamic work capacity of quantum information processing

We introduce the resource-theoretic free energy of a quantum channel as the maximal work extractable from the channel as its output equilibrates to a thermal state and its reference system remains locally intact. It is proportional to the relative entropy between the given channel and the absolutely thermal channel. It attains a clear operational meaning as twice the asymptotic rates of athermality distillation and formation under Gibbs preserving superchannels, which map one absolutely thermal channel to another for a given bath, thereby revealing the asymptotic reversibility of the resource theory of athermality for quantum channels. Consequently, we establish that the optimal extractable work in converting one channel to another through the asymptotic athermality distillation and formation tasks equals the difference in their free energies. We call this optimal work the thermodynamic work capacity of channel conversion. Quantum information processing and computing fundamentally concern the manipulation and transformation of quantum channels, which encompass quantum states, their transformations, and measurements. A quantitative characterization of the optimal thermodynamic work gain or expenditure in quantum information processing constitutes a key step toward formulating thermodynamics of quantum processes.

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arXiv2025

Thermodynamics of quantum processes: An operational framework for free energy and reversible athermality

We explore the thermodynamics of quantum processes (quantum channels) by axiomatically introducing the free energy for channels, defined via the quantum relative entropy with an absolutely thermal channel whose fixed output is in equilibrium with a thermal reservoir. This definition finds strong support through its operational interpretations in designated quantum information and thermodynamic tasks. We construct a resource theory of athermality for quantum processes, where free operations are Gibbs preserving superchannels and golden units are unitary channels with respect to absolutely thermal channel having fully degenerate output Hamiltonian. We exactly characterize the one-shot distillation and formation of quantum channels using hypothesis-testing and max-relative entropy with respect to the absolutely thermal channel. These rates converge asymptotically to the channel free energy (up to a multiplicative factor of half the inverse temperature), establishing its operational meaning and proving the asymptotic reversibility of the athermality. We show the direct relation between the resource theory of athermality and quantum information tasks such as private randomness and purity distillation, and thermodynamic tasks of erasure and work extraction. Our work connects the core thermodynamic concepts of free energy, energy, entropy, and maximal extractable work of quantum processes to their information processing capabilities.

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arXiv2025

Erasure cost of a quantum process: A thermodynamic meaning of the dynamical min-entropy

The erasure of information is fundamentally an irreversible logical operation, carrying profound consequences for the energetics of computation and information processing. We investigate the thermodynamic costs associated with erasing (and preparing) quantum processes. Specifically, we analyze an arbitrary bipartite unitary gate acting on logical and ancillary input-output systems, where the ancillary input is always initialized in the ground state. We focus on the adversarial erasure cost of the reduced dynamics - that is, the minimal thermodynamic work cost to erase the logical output of the gate for any logical input, assuming full access to the ancilla but no access to any purifying reference of the logical input state. We determine that this adversarial erasure cost is directly proportional to the negative min-entropy of the reduced dynamics, thereby giving the dynamical min-entropy a clear operational meaning. The dynamical min-entropy can take positive and negative values, depending on the underlying quantum dynamics. The negative value of the erasure cost implies that the extraction of thermodynamic work is possible instead of its consumption during the process. A key foundation of this result is the quantum process decoupling theorem, which quantitatively relates the decoupling ability of a process with its min-entropy. This insight bridges thermodynamics, information theory, and the fundamental limits of quantum computation.

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arXiv2025

Causal and Non-Causal Revivals of Information: A New Regime of Non-Markovianity in Quantum Stochastic Processes

The study of information revivals, witnessing the violation of certain data-processing inequalities, has provided an important paradigm in the study of non-Markovian quantum stochastic processes. Although often used interchangeably, we argue here that the notions of ``revivals'' and ``backflows'', i.e., flows of information from the environment back into the system, are distinct: an information revival can occur without any backflow ever taking place. In this paper, we examine in detail the phenomenon of non-causal revivals and relate them to the theory of short Markov chains and squashed non-Markovianity. We also provide an operational condition, in terms of system-only degrees of freedom, to witness the presence of genuine backflow that cannot be explained by non-causal revivals. As a byproduct, we demonstrate that focusing on processes with genuine backflows, while excluding those with only non-causal revivals, resolves the issue of non-convexity of Markovianity, thus enabling the construction of a convex resource theory of genuine quantum non-Markovianity.

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arXiv2025

Decomposition of a system in pseudo-Hermitian quantum mechanics

This work outlines a consistent method of identifying subsystems in finite-dimensional Hilbert spaces, independent of the underlying inner-product structure. Such Hilbert spaces arise in $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics, where a non-Hermitian Hamiltonian is made self-adjoint by changing the inner product using the so-called ``metric operator". This is the framework of pseudo-Hermitian quantum mechanics. For composite quantum systems in this framework, defining subsystems is generally considered feasible only when the metric operator is chosen to have a tensor product form so that a partial trace operation can be well defined. In this work, we use arguments from algebraic quantum mechanics to show that the subsystems can be well-defined in every metric space - irrespective of whether or not the metric is of tensor product form. This is done by identifying subsystems with a decomposition of the underlying C*-algebra into commuting subalgebras. Although the choice of the metric is known to have no effect on the system's statistics, we show that different choices of the metric can lead to inequivalent subsystem decompositions. Each of the subsystems can be tomographically constructed and these subsystems satisfy the no-signalling principle. With these results, we put all the choices of the metric operator on an equal footing for composite systems.

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arXiv2025

Exploring Non-Markovianity in Ergodic Channels: Measuring Memory Retention through Ergotropy

In this work we introduce and characterize a broad class of quantum operations with a unique fixed point, termed quantum ergodic channels. We derive Lindblad-type master equations for these channels in arbitrary finite dimensions and analyze their non-Markovian dynamics using established measures. When the fixed point is a passive state, the channels exhibit ergotropy dynamics with notable thermodynamic implications. Specifically, under Markovian processes, ergotropy, a measure of the extractable work from a system under unitary evolution monotonically decreases. However, in non-Markovian dynamics, ergotropy fluctuates, leading to a backflow effect that highlights memory-induced resource recovery. Our findings suggest that this ergotropy backflow could serve as an operationally meaningful indicator of non-Markovianity, offering new perspectives on the interplay between memory effects and thermodynamic behavior in open quantum systems. This study enhances the theoretical framework for understanding energy dynamics under ergodic channels and highlights new avenues for exploring the implications of memory effects in quantum batteries.

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arXiv2024

Non-Hermitian quantum walks and non-Markovianity: the coin-position interaction

A $\mathcal{PT}$-symmetric, non-Hermitian Hamiltonian in the $\mathcal{PT}$-unbroken regime can lead to unitary dynamics under the appropriate choice of the Hilbert space. The Hilbert space is determined by a Hamiltonian-compatible inner product map on the underlying vector space, facilitated by a ``metric operator". A more traditional method, however, involves treating the evolution as open system dynamics, and the state is constructed through normalization at each time step. In this work, we present a comparative study of the two methods of constructing the reduced dynamics of a system evolving under a $\mathcal{PT}$-symmetric Hamiltonian. Our system is a one-dimensional quantum walk with the spin and position degrees of freedom forming its two subsystems. We compare the information flow between the subsystems under the two methods. We find that under the metric formalism, a power law decay of the information backflow to the subsystem gives a clear indication of the transition from $\mathcal{PT}$-unbroken to the broken phase. This is unlike the information backflow under the normalized state method. We also note that even though non-Hermiticity models open system dynamics, pseudo-Hermiticity can increase entanglement between the subsystem in the metric Hilbert space, thus indicating that pseudo-Hermiticity cases can be seen as a resource in quantum mechanics.

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arXiv2023

Reduced dynamics in quasi-Hermitian systems

Evolutions under non-Hermitian Hamiltonians with unbroken $\mathcal{PT}$ symmetry can be considered unitary under appropriate choices of inner products, facilitated by the so-called metric operator. While it is understood that the choice of the metric operator has no bearing on the description of the system, in this work, we show that this choice does dictate the entanglement structure of the system. We show that the partial trace of the Hermitized density matrix gives the correct representation of the reduced subsystem, and based on such operations, we elucidate the metric dependency of the reduced dynamics and consequently the observable dependence of the subsystem decomposition. We use a non-Hermitian $\mathcal{PT}$-symmetric quantum walk as a toy model to study this metric dependency, where we use the internal (coin state) as the subsystem of interest and study the coin-position entanglement and non-Markovianity of the coin dynamics.

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arXiv2023

Improvement in quantum communication using quantum switch

Applications of the quantum switch on quantum channels have recently become a topic of intense discussion. In the present work, we show that some useless (for communication) channels may provide useful communication under the action of quantum switch for several information-theoretic tasks: quantum random access codes, quantum steering, etc. We demonstrate that the quantum switch can also be useful in preventing the loss of coherence in a system when only coherence-breaking channels are the available channels for communication. We also show that if a useless quantum channel does not provide useful communication even after using a quantum switch, concatenating the channel with another suitable quantum channel, and subsequently using the switch, one may achieve useful communication. Finally, we discuss how the introduction of noise in the quantum switch can reduce the advantage that the switch provides.

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arXiv2021

Gravitationally induced entanglement dynamics between two quantum walkers

Quantum walk is a synonym for multi-path interference and faster spread of a particle in a superposition of position space. We study the effects of a quantum mechanical interaction modeled to mimic quantum mechanical gravitational interaction between the two states of the walkers. The study has been carried out to investigate the entanglement generation between the two quantum walkers that do not otherwise interact. We see that the states do in fact get entangled more and more as the quantum walks unfold, and there is an interesting dependence of entanglement generation on the mass of the two particles performing the walks. We also show the sensitivity of entanglement between the two walkers on the noise introduced in one of the walks. The signature of quantum effects due to gravitational interactions highlights the potential role of quantum systems in probing the nature of gravity.

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