Hello!

Robust quantum metrology using disordered probes

Vishnupriya K., Harikrishnan K. J., and A. K. Pal

Disorder is ubiquitous in quantum devices including quantum probes designed and fabricated for quantum parameter estimation and sensing. We investigate the robustness of a quantum probe against the presence of glassy disorder. We define a disorder marker quantifying the effect of the disorder by expanding the quantum Fisher information in terms of different orders of the standardized central moments of the disorder-distributions. We classify the quantum probes in terms of the possible values of the disorder marker, and analytically show, for a disorder-sensitive probe with identical and weak disorder on all or a subset of the parameters of the probe-Hamiltonian, that the absolute value of the disorder marker exhibits a quadratic dependence on the disorder strength. We derive a robustness scale intrinsic to the probe that competes with the disorder, and provide a prescription for estimating the maximum disorder strength that the probe can withstand from the disorder-free probe-Hamiltonian for a given initial state of the probe, which can be computed without the disorder averaging. We demonstrate our results in the case of a single-qubit probe under disordered magnetic field, and a multi-qubit probe described by a disordered one-dimensional Kitaev model with nearest-neighbor interactions.

A graph-aware bounded distance decoder for all stabilizer codes

Harikrishnan K. J., and A. K. Pal

We formulate a bounded distance decoding strategy applicable to all stabilizer codes including both CSS and non-CSS code-families. The framework emerges out of the local Clifford equivalence between arbitrary stabilizer states and graph states. Using the graphical representation of the stabilizers and the syndromes, we constitute the bounded distance decoding as an adaptable generalization of maximum likelihood decoding, ensuring correction of all errors with weights upper bounded by a target weight. We show that strategic pruning associated with a feed-forward network structure of the graph can reduce the search space and subsequently the runtime of the designed decoder. We demonstrate satisfactory performance of the bounded distance decoder in the case of the optimal non-CSS codes up to distance d = 11 subjected to the depolarizing error on all qubits, and near-optimal decoding for the color and the surface codes, both belonging to the CSS family, under the bit-flip errors on the qubits. We also develop an open-source library, QGDecoder, enabling the graph-aware bounded distance decoding of arbitrary stabilizer codes.

Bridging the daemonic gap en route to charge multi-mode batteries via a single auxiliary

C. B. Pushpan and A. K. Pal

Physical Review A

We show that harnessing daemonic advantage is possible while charging a quantum battery by first time-evolving the battery collectively with an auxiliary charger, followed by an energy extraction via tracing out the charger. We define the difference between the minimum daemonic ergotropy and the maximum ergotropy of the battery as the daemonic gap at the time where the ergotropy of the battery is maximum. Considering a harmonic mode as the battery and a qubit as the auxiliary charger interacting via Jaynes-Cummings interaction, we show that the daemonic gap can be closed for specific initial passive states of the battery, including the ground state, truncated mixtures of low-lying states, and canonical thermal states. We further define the daemonic band as the difference between the maximum and the minimum daemonic ergotropy, and show that starting from the ground state of the single-mode battery, the daemonic band collapses. We also show that achieving a complete charging, along with accessing the full daemonic band, is possible for the single-mode battery using all of the other initial states by repeating the charging cycle and maximizing ergotropy in every round. We extend the battery-charger design to a multi-mode resonator battery and a qudit charger, and demonstrate, for a double-mode battery and a qutrit charger, that repeating the charging cycle is vital for simultaneously charging individual modes of the collective battery.

Block entanglement bounds distribution of regionally localized entanglement

J. G. Krishnan, A. Sen(De), and A. K. Pal

Physics Letters A

In quantum networks, eliminating connections between nodes is crucial to mitigate the effects of decoherence, often achieved by performing measurements on nodes that are idle, or vulnerable to noise. To characterize the entanglement content of the resulting smaller network, we introduce the notion of regionally localized entanglement, defined as the average entanglement concentrated over a two-qubit region in a multi-qubit system. Hence, the total regionally localized entanglement can be obtained by considering all two-qubit regions sharing a common qubit, referred to as the hub. We prove that the total regionally localized entanglement corresponding to a specific hub is bounded above and below via the localizable block entanglement shared between the hub and the rest of the multi-qubit system for a number of paradigmatic pure quantum states, including permutation-symmetric states and arbitrary superposition of states from a specific magnetization sector. Numerical simulations confirm that the bounds for permutation-symmetric pure states remain valid even for Haar-uniformly generated pure states, and when each of the qubits is sent through local phase-flip channels of Markovian and non-Markovian types, except when the system-size is small. On the other hand, arbitrary states from a particular magnetization sector yield bounds on total regionally localized entanglement that are distinct from the permutation-symmetric states, highlighting the structurally unique entanglement properties of the former.

Scaling of entanglement entropy and correlations in the variable-range extended Ising model

Harikrishnan K. J., D. Sadhukhan, and A. K. Pal

Physical Review A

We study the two-point correlation functions and the bipartite entanglement in the ground state of the exactly-solvable variable-range extended Ising model of qubits in the presence of a transverse field on a one-dimensional lattice. We introduce the variation in the range of interaction by varying the coordination number, z, of each qubit, where the interaction strength between a pair of qubits at a distance r varies as ∼ r^(−α). We show that the algebraic nature of the correlation functions is present only up to r = z/2, above which it exhibits short-range exponential scaling. We also show that at the critical point, the bipartite entanglement exhibits a power-law decrease (∼ z^(−γ)) with increasing coordination number irrespective of the partition size and the value of α for α > 1. We further consider a sudden quench of the system starting from the ground state of the infinite-field limit of the system Hamiltonian via turning on the critical Hamiltonian, and demonstrate that the long-time averaged bipartite entanglement exhibits a qualitatively similar variation (∼ z^(−γ)) with z.

Developing a universal logical state-purification strategy

C. B. Pushpan, T. K. Konar, A. Sen(De), and A. K. Pal

Physical Review A

We develop a measurement-based protocol for simultaneously purifying arbitrary logical states in multiple quantum error correcting codes with unit fidelity and finite probability, starting from arbitrary thermal states of each code. The protocol entails a time evolution caused by an engineered Hamiltonian, which results in transitions between the logical and error subspaces of the quantum error correcting code mediated by the auxiliary qubit, followed by a projective measurement in an optimum basis on the auxiliary qubit and an appropriate post-selection of the measurement outcomes. We illustrate the results with the three-qubit repetition code and the logical qubit used in quantum state transfer protocol. We further demonstrate that when the measurement base is not optimal, it is possible to achieve both classical fidelity, and fidelity as high as 90% through several iterations of the purifying procedure, thereby establishing its robustness against variations in the measurement basis. By repeating the purification rounds, we show that purifying the cardinal states of the logical Bloch sphere corresponding to logical qubits in quantum state transfer is feasible utilizing paradigmatic quantum spin models as the generator of the time evolution.

Scalable and deterministic Greenberger-Horne-Zeilinger state generation via graph states-assisted measurements

Harikrishnan K. J. and A. K. Pal

Physical Review A

We propose a scalable and deterministic protocol for growing large multi-qubit states starting from two-qubit non-maximally entangled pure states, where the bipartite entanglement in the resultant state is higher than the maximum of the available entangled qubit-pairs. This is achieved via a truncation of the Hilbert space corresponding to a subsystem of qubits to a space that hosts a single qubit, brought about by a multi-qubit measurement assisted by the graph basis. We prove its equivalence to a repetitive two-qubit measurement-based protocol, and demonstrate realization of the required two-qubit measurement via a two-qubit parity measurement, thereby establishing the implementability of the protocol. We derive lower and upper bounds of the bipartite entanglement concentrated after a given number of rounds of measurements, where the entanglement of the available qubit-pairs are not-necessarily equal. We further discuss the effect of possible imperfections that may arise in the protocol, and its robustness towards such imperfections. We demonstrate the usefulness of our proposal by applying it to create generalized GHZ states on arbitrary number of qubits, thereby underlining the possibility of creating maximally entangled qubit pairs via qubit-local projection measurements.

Simultaneous cooling of qubits via a quantum absorption refrigerator and beyond

J. G. Krishnan, C. B. Pushpan, and A. K. Pal

Physics Letters A

We design a quantum thermal device that can simultaneously and dynamically cool multiple target qubits. Using a setup with three bosonic heat baths, we propose an engineering of interaction Hamiltonian using operators on different subspaces of the full Hilbert space of the system labelled by different magnetizations. We demonstrate, using the local as well as global quantum master equations, that a set of target qubits can be cooled simultaneously using these interaction Hamiltonians, while equal cooling of all target qubits is possible only when the local quantum master equation is used. However, the amount of cooling obtained from different magnetization subspaces, as quantified by a distance-based measure of qubit-local steady-state temperatures, may vary. We also investigate cooling of a set of target qubits when the interaction Hamiltonian has different magnetization components, and when the design of the quantum thermal device involves two heat baths instead of three. Further, we demonstrate, using local quantum master equation, that during providing cooling to the target qubits, the designed device operates only as a quantum absorption refrigerator. In contrast, use of the global quantum master equation indicates cooling of the target qubits even when the device works outside the operation regime of a quantum absorption refrigerator. We also extend the design to a star network of qubits interacting via Heisenberg interaction among each other, kept in contact with either three, or two heat baths, and discuss cooling of a set of target qubits using this device.

Quantum error correction via purification using a single auxiliary

C. B. Pushpan, T. K. Konar, A. Sen(De), and A. K. Pal

We propose a single auxiliary-assisted purification-based framework for quantum error correction, capable of correcting errors that drive a system from its ground-state subspace into excited-state sectors. The protocol consists of a joint time evolution of the system-auxiliary duo under a specially engineered interaction Hamiltonian, followed by a single measurement of the auxiliary in its energy eigenbasis and a subsequent post-selection of one of the measurement outcomes. We show that the resulting purified state always achieves unit fidelity, while the probability of obtaining any energy of the auxiliary other than its ground state energy yields the success rate of the protocol. We demonstrate the power of this proposed method for several low-distance quantum codes, including the three-, four-, and five-qubit codes, and for the one-dimensional isotropic Heisenberg model, subjected to bit-flip, phase-flip, and amplitude-damping noises acting on all qubits. Notably, the protocol expands the class of correctable errors for a given code, particularly in the presence of amplitude-damping noise. We further analyze the impact of replacing the auxiliary qudit with a single auxiliary qubit, and the changes in the performance of the protocol under the realistic scenario where noise remains active during the correction cycle.

Quantum advantage unlocked: Charging quantum batteries with K-regular graph stabilizers

D. Ghosh, T. K. Konar, G. Francica, A. K. Pal, and A. Sen(De)

Regular graphs find broad applications ranging from quantum communication to quantum computation. Motivated by this, we investigate the design of a quantum battery based on a K-regular graph, where K denotes the number of edges incident on each vertex. We show that a 0-regular graph battery exhibits extractable work that scales linearly with the system-size when charged using a K-regular graph. This linear scaling is shown to persist even when the charging is implemented via a collective K-regular charger with power-law decaying interactions. Interestingly, we prove that both the maximum average power and instantaneous power scale super-linearly in the thermodynamic limit when the connectivity of the charging graph is of the order of the system size, thereby exhibiting it quantum advantage. Furthermore, by introducing the notion of the fraction of extractable work when only subsystems are accessible, we identify this fraction to be independent of system-size if the battery is prepared in the down-polarized product state. This independence breaks down when the battery is oriented along the x- and y-directions of the Bloch sphere.