arXiv subjects

Tapaswini Patro

Publications and source records attributed to Tapaswini Patro.

5 recordsLinked to original sources

arXiv2025

Fidelity of entanglement and quantum entropies: unveiling their relationship in quantum states and channels

Entanglement serves as a fundamental resource for various quantum information processing tasks. Fidelity of entanglement (which measures the proximity to a maximally entangled state) and various quantum entropies are key indicators for certifying entanglement in a quantum state. Quantum states with high fidelity are particularly useful for numerous information-theoretic applications. Similarly, states possessing negative conditional entropy provide significant advantages in several quantum information processing protocols. In this work, we examine the relationship between these two indicators of entanglement, both in state and channel regimes. First, we present a comprehensive analysis and characterization of channels that reduce fidelity of entanglement beyond a threshold limit of bipartite composite systems. In this context, we introduce the notion of fidelity annihilating channel and discuss its topological characterization, along with various information-theoretic properties. We then provide a comparison between channels that diminish the fidelity of entanglement and negative conditional entropies, using the depolarizing channel as an illustrative example. In particular, we determine the parameter regimes in which the depolarizing channel belongs to a given family and establish connections among these families of channels. Extending our analysis from channels to the state level, we further examine the relationship between the fidelity of entanglement and various quantum entropies for general two-qubit states. We derive the upper bound on R\'enyi 2-entropy, conditional R\'enyi 2-entropy, Tsallis 2-entropy, and conditional Tsallis 2-entropy, in terms of the fidelity of entanglement. Finally, we explore the relationship between relative entropy and the fidelity of entanglement of a two qudit quantum state.

quant-ph↗

arXiv2024

Quantum channels and some absolute properties of quantum states

Environmental interactions are ubiquitous in any real-world application of a quantum information processing protocol. Such interactions result in depletion of quantum resources. Two important figure of merits in the context of quantum information are the fully entangled fraction (FEF) and conditional entropy of a composite quantum system. FEF has a key role to play in tasks like teleportation. Conditional entropy on the other hand can be negative for certain quantum states and thus the negativity remains a resource for tasks like dense coding and state merging. FEF $ > 1/d $ for a $ d \otimes d $ quantum system is a significant threshold, however for some quantum states it remains less than the threshold even with global unitary operations, consequently being known as states having absolute fully entangled fraction (AFEF). Pertaining to conditional von Neumann entropy, there are some states which retains the nonnegativity of the conditional entropy under global unitary action, to be called as states with absolute conditional von Neumann entropy nonnegative (ACVENN) property. In the present submission, we probe the action of some quantum channels in two qubits and two qudits and find that some quantum states move from the non-absolute regime to the absolute regime under the action. Since, global unitary operations are unable to retrieve them back to the non-absolute regime, we provide a prescription for the retrieval using an entanglement swapping network. Furthermore, we extend the notion of absoluteness to conditional Rényi entropies and find the required condition for a state to have absolute conditional Rényi entropy non-negative (ACRENN) property. We then extend the work to include the marginals of a tripartite system and provide for their characterization with respect to the aforementioned absolute properties.

quant-ph↗

arXiv2023

Hidden Non n-locality In Linear Networks

We study hidden nonlocality in a linear network with independent sources. In the usual paradigm of Bell nonlocality, there are certain states which exhibit nonlocality only after the application of suitable local filtering operations, which, in turn, are some special stochastic local operations assisted with classical communication (SLOCC). In the present work, we introduce the notion of hidden non n-locality. The notion is detailed using a bilocal network. We provide instances of hidden nonbilocality and nontrilocality, where we notice quite intriguingly that nonbilocality is observed even when one of the sources distributes a mixed two-qubit separable state. Furthermore, a characterization of hidden nonbilocality is also provided in terms of the Bloch-Fano decomposition, wherein we conjecture that, to witness hidden nonbilocality, one of the two states (used by the sources) must have nonnull local Bloch vectors. Noise is inevitable in practical scenarios, which makes it imperative to study any possible method to enhance the possibility of detecting nonclassicality in the presence of noise in the network. We find that local filtering enhances the robustness to noise, which we demonstrate using bit-flip and amplitude-damping channels.

quant-ph↗

arXiv2022

Role of Steering Inequality In Quantum Key Distribution Protocol

Violation of Bell's inequality has been the mainspring for secure key generation in an entanglement assisted Quantum Key Distribution(QKD) protocol. Various contributions have relied on the violation of appropriate Bell inequalities to build an appropriate QKD protocol. Residing between Bell nonlocality and entanglement, there exists a hybrid trait of correlations, namely correlations exhibited through the violation of steering inequalities. However, such correlations have not been put to use in QKD protocols as much as their stronger counterpart, the Bell violations. In the present work, we show that the violations of the CJWR(E.G.Cavalcanti,S.J. Jones,H.M Wiseman and M.D. Reid, Phys.Rev.A 80,032112(2009))steering inequalities can act as key ingredients in an entanglement assisted QKD protocol. We work with arbitrary two qubit entangled states, characterize them in accordance with their utility in such protocols. The characterization is based on the quantum bit error rate and violation of a CJWR inequality. Furthermore, we show that subsequent applications of local filtering operations on initially entangled states exhibiting non violation, lead to violations necessary for the successful implementation of the protocol. An additional vindication of our protocol is provided by the use of absolutely Bell-CHSH local states, states which remain Bell-CHSH local even under global unitary operations.

quant-ph↗

arXiv2022

Absolute fully entangled fraction from spectrum

Fully entangled fraction (FEF) is a significant figure of merit for density matrices. In bipartite $ d \otimes d $ quantum systems, the threshold value FEF $ > 1/d $, carries significant implications for quantum information processing tasks. Like separability, the value of FEF is also related to the choice of global basis of the underlying Hilbert space. A state having its FEF $ \le 1/d $, might give a value $ > 1/d $ in another global basis. A change in the global basis corresponds to a global unitary action on the quantum state. In the present work, we find that there are quantum states whose FEF remains less than $ 1/d $, under the action of any global unitary i.e., any choice of global basis. We invoke the hyperplane separation theorem to demarcate the set from states whose FEF can be increased beyond $ 1/d $ through global unitary action. Consequent to this, we probe the marginals of a pure three party system in qubits. We observe that under some restrictions on the parameters, even if two parties collaborate (through unitary action on their combined system) they will not be able to breach the FEF threshold. The study is further extended to include some classes of mixed three qubit and three qutrit systems. Furthermore, the implications of our work pertaining to $ k- $copy nonlocality and teleportation are also investigated.

quant-ph↗