arXiv subjects

Jatin Ghai

Publications and source records attributed to Jatin Ghai.

8 recordsLinked to original sources

arXiv2026

Informational completeness of qubit measurements and IC preservability of qubit channels: Characterization and Quantification

Informationally complete (IC) measurements are a useful class of measurements, as their outcome statistics uniquely determine an unknown quantum state. Hence, they are important for certain tasks such as quantum state tomography, quantum process tomography, etc. In this work, we study the quantification of informational completeness for arbitrary quantum measurements by introducing and characterizing a faithful measure for it. We explicitly evaluate the informational completeness of qubit symmetric informationally complete (SIC) measurements and show that it is an upper bound for all qubit minimal informationally complete measurements. Furthermore, by introducing a faithful measure, we try to quantify and characterize the ability of an arbitrary quantum channel to preserve the informational completeness of any IC measurement when the channel acts on it in the Heisenberg picture. We call this measure informational completeness-preservability (IC preservability) of quantum channels. After studying its properties, we establish its relation to another quantity, namely, the absolute output coherence of a quantum channel, which quantifies the minimum amount of coherence (w.r.t. an arbitrary incoherent basis) that can always be obtained from the output of that channel. Finally, we illustrate our results with an example from light-matter interaction scenarios. Thus, in this work, not only do we try to provide a quantitative framework for studying both the informational completeness of quantum measurements and the ability of quantum channels to preserve it, but we also try to offer key insight into the conceptual relation between informational completeness and quantum coherence.

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arXiv2025

Comparing quantum channels using Hermitian-preserving trace-preserving linear maps: A physically meaningful approach

In quantum technologies, quantum channels are essential elements for the transmission of quantum states. The action of a quantum channel usually introduces noise in the quantum state and thereby reduces the information contained in it. These are mathematically described by completely positive trace-preserving linear maps that represent the generic evolution of quantum systems and are also special cases of Hermitian-preserving trace-preserving (HPTP) linear maps. Concatenating a quantum channel with another quantum channel makes it noisier and degrades its information and resource preservability. In this work, we demonstrate a physically meaningful way to compare a pair of quantum channels using Hermitian-preserving trace-preserving linear maps. More precisely, given a pair of quantum channels and an arbitrary unknown input state, we show that if the output state of one quantum channel from the pair can be uniquely identified from the output statistics of the other channel from the pair using some quantum measurement, then the former channel from the pair can be obtained from the latter channel by concatenating it with a Hermitian-preserving trace-preserving linear map that is not necessarily positive. In such cases, the former channel may not always be obtained from the latter through post-processing. This relation between these two channels is a preorder, and we try to study its characterization in this work. Furthermore, we try to characterize the difficulty of implementing the former channel given that the latter channel has already been implemented via a quantifier, namely, physical implementability. We also illustrate the implications of our results for the incompatibility of quantum devices through an example. In short, we try to provide valuable insights about the relevance of Hermitian-preserving trace-preserving linear maps in physically motivated settings.

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arXiv2025

Convex Optimization Approaches to Optimal Teleportation Fidelity in Linear Three-Party Networks

We study the maximum achievable quantum teleportation fidelity between two distant parties, Alice and Charlie, where each of them share a bipartite quantum state only with a common intermediary, Bob, and all parties are allowed to perform {\it Local Operations and Classical Communication} (LOCC). As the structure of LOCC is complicated, we relax the set of free operations to separable (SEP) operations and formulate a convex optimization problem that provides upper bounds on the LOCC achievable fidelity value. We observe that the complexity of such optimization problem reduces significantly if we restrict ourselves to a subclass of SEP operations, where the Kraus operators of either Alice or Charlie are proportional to unitary operators, leading to a simplified convex optimization that matches the general LOCC limit for certain two-qubit states. Through explicit examples, we show that protocols initiated by Bob by performing measurements in a maximally entangled basis are not necessarily optimal, and alternative strategies can outperform them. Finally, we extend our analysis to linear networks and demonstrate that different LOCC strategies can achieve the same optimal fidelity while consuming different amounts of entanglement content.

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arXiv2025

Instrument-based quantum resources: quantification, hierarchies and constructing resource theories

Quantum resources are certain features of the quantum world that provide advantages in certain information-theoretic, thermodynamic, or other useful operational tasks that are outside the realm of what classical theories can achieve. Quantum resource theories provide us with an elegant framework for studying these resources quantitatively and rigorously. While numerous state-based quantum resource theories have already been investigated, and to some extent, measurement-based resource theories have also been explored, instrument-based resource theories remain largely unexplored, with only a few notable exceptions. As quantum instruments are devices that provide both the classical outcomes of induced measurements and the post-measurement quantum states, they are quite important, especially for scenarios where multiple parties sequentially act on a quantum system. In this work, we study several instrument-based resource theories, namely (1) the resource theory of information preservability, (2) the resource theory of (strong) entanglement preservability, (3) the resource theory of (strong) incompatibility preservability, (4) the resource theory of traditional incompatibility, and (5) the resource theory of parallel incompatibility. Furthermore, we outline the hierarchies of these instrument-based resources and provide measures to quantify them. We then also established a relationship between our resource measure and the advantage in an information-theoretic task. In short, we provide a detailed framework for a wide variety of instrument-based quantum resource theories.

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arXiv2025

Repeater-Based Quantum Communication Protocol: Maximizing Teleportation Fidelity with Minimal Entanglement

Transmitting unknown quantum states to distant locations is crucial for distributed quantum information protocols. The seminal quantum teleportation scheme achieves this feat while requiring prior maximal entanglement between the sender and receiver. In scenarios with noisy entangled states, optimal teleportation fidelity characterizes the efficacy of transmitting the state, demanding the proper selection of local operations at the sender's and receiver's ends. The complexity escalates further in long-range communication setups, prompting the consideration of a repeater-based approach, which incorporates arrays of nodes with multiple segments to facilitate the efficient transmission of quantum information. The fidelity of the communication line gets degraded even if a single segment is affected by noise. In such cases, the general wisdom employs the standard entanglement swapping protocol involving maximally entangled states across the noiseless segments and applying maximally entangled basis measurement at the corresponding nodes to achieve optimal fidelity. In this Letter, we propose a more efficient protocol for a certain class of noisy states in any intermediary segment, achieving the same fidelity as the standard protocol while consuming less amount of entanglement. Our approach ensures enhanced teleportation fidelity even when the end-to-end state gets noisier, and thus promises efficient utility of quantum resources in repeater-based distributed quantum protocols.

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arXiv2024

Linear optics and the problem of Bell-like state discrimination

A linear optics-based scheme to implement various quantum information processing tasks is of paramount importance due to ease of implementation and low noise. Many information-theoretic tasks depend on the successful discrimination of Bell states. A no-go theorem has been proved in literature which tells that it is not possible to perfectly discriminate among the four Bell states by restricting measurement apparatus to linear optical elements. The success probability is only $50\%$. Through using extra resources such as hyper entanglement, ancillary entanglement, and even a minimum amount of non-linearity complete Bell-state discrimination can be achieved. The success probability for Bell-like state discrimination is only $25\%$. We find that this can be boosted up to $50\%$ using hyperentanglement in polarization, momentum, or OAM degrees of freedom of the photons which is in contrast to the Bell-state discrimination scenario where $100\%$ can be achieved. Furthermore, we find that by using correlation in time of the photons all four Bell states can be distinguished with $100\%$ success probability while for the Bell-like state discrimination, it strictly lies between $25\%$ and $50\%$ depending on the state parameter with only three Bell-like states being distinguishable. We also observe a similar contrast when we use ancillary entangled photons. While the success probability for all four Bell-state discrimination increases as $1-\frac{1}{2^N}$ where N is the number of ancillary photons for Bell-like states it depends again on the state parameters and can be less than $25\%$ in some cases. Also adding further ancillary photons decreases the success probability. We then show that using non-linear gadgets namely SFG $100\%$ success probability can be achieved even for Bell-like state discrimination.

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arXiv2023

Negativity of Wigner distribution function as a measure of incompatibility

Measurement incompatibility and the negativity of quasiprobability distribution functions are well-known non-classical aspects of quantum systems. Both of them are widely accepted resources in quantum information processing. We acquaint an approach to establish a connection between the negativity of the Wigner function, a well-known phase-space quasiprobability distribution, of finite-dimensional Hermitian operators and incompatibility among them. We calculate the negativity of the Wigner distribution function for noisy eigenprojectors of qubit Pauli operators as a function of the noise and observe that the amount of negativity increases with the decrease in noise vis-à-vis the increase in the incompatibility. It becomes maximum for the set of maximally unbiased operators. Our results, although qualitatively, provide a direct comparison between relative degrees of incompatibility among a set of operators for different amounts of noise. We generalize our treatment for higher dimensional qudits for specific finite-dimensional Gell-Mann operators to observe that with an increase in the dimension of the operators, the negativity of their Wigner distribution, and hence incompatibility, decreases.

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arXiv2020

Unified trade-off optimization of a three-level quantum refrigerator

We study the optimal performance of a three-level quantum refrigerator using a trade-off objective function, $Ω$ function, which represents a compromise between the energy benefits and the energy losses of a thermal device. First, we optimize the performance of our refrigerator by employing a two-parameter optimization scheme and show that the first two-terms in the series expansion of the obtained coefficient of performance (COP) match with those of some classical models of refrigerator. Then, in the high-temperature limit, optimizing with respect to one parameter while constraining the other one, we obtain the lower and upper bounds on the COP for both strong as well as weak (intermediate) matter-field coupling conditions. In the strong matter-field coupling regime, the obtained bounds on the COP exactly match with the bounds already known for some models of classical refrigerators. Further for weak matter-field coupling, we derive some new bounds on the the COP of the refrigerator which lie beyond the range covered by bounds obtained for strong matter-field coupling. Finally, in the parameter regime where both cooling power and $Ω$ function can be maximized, we compare the cooling power of the quantum refrigerator at maximum $Ω$ function with the maximum cooling power.

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