arXiv subjects

Anindita Bera

Publications and source records attributed to Anindita Bera.

At least 19 recordsLinked to original sources

arXiv2026

Estimation of trace distance between two arbitrary quantum states

When it comes to discriminating between two quantum states, trace distance is one of the well-known metrics used in quantum computation and quantum information theory. While there are several quantum algorithms for calculating the trace distance between two quantum states, computing it for any two general density matrices remains computationally demanding. In this paper, we propose a quantum algorithm based on the exponentiation of the density matrix and the improved quantum phase estimation (IQPE) to determine the trace distance for both pure and mixed states, with a time complexity of $O(N^2/\varepsilon^6)$ where $N$ is the number of qubits of the given states and $\varepsilon$ is the simulation or estimation precision error. We demonstrate its ability to predict the quantity with proof-of-principle simulations and also quantum hardware computations on the IBM quantum computers, confirming its promise for near-term quantum devices.

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arXiv2026

Detecting Entanglement by State Preparation and Local Measurements

Entanglement witnesses (EWs) are a collection of observables that can characterize separable states and, experimentally, estimating EWs can verify entangled states. In this work, we show that a fixed measurement setting on a multipartite entangled state, which we introduce as a network state for the purpose, can estimate EWs. Namely, entangled states can be fully verified in a measurement-based manner, in which experimenters do not necessarily change measurement settings. We present a fixed measurement setting and network states for estimating decomposable EWs, equivalent to the partial transpose criteria. We also consider non-decomposable EWs that detect bound entangled states beyond the partial transpose criteria. The results can be extended to multipartite states such as graph states, a resource for measurement-based quantum computing, and readily applied to distributed settings such as quantum metrology or sensor networks where multipartite entangled states are resourceful.

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arXiv2026

Practical and Efficient Verification of Entanglement with Incomplete Measurement Settings

In this work, we present a practical and efficient framework for verifying entangled states when only a tomographically incomplete measurement setting is available-specifically, when access to observables is severely limited. We show how the experimental estimation of a small number of observables can be directly exploited to construct a large family of entanglement witnesses, enabling the efficient identification of entangled states. Moreover, we introduce an optimization approach, formulated as a semidefinite program, that systematically searches for those witnesses best suited to reveal entanglement under the given measurement constraints. We demonstrate the practicality of the approach in a proof-of-principle experiment with photon-polarization qubits, where entanglement is certified using only a fraction of the full measurement data. These results reveal the maximal usefulness of incomplete measurement settings for entanglement verification in realistic scenarios.

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arXiv2026

Tomiyama-type maps with a diagonal perturbation

We investigate a two-parameter family of linear maps on matrix algebras, constructed as diagonal perturbations of classical Tomiyama maps. Employing the Choi matrix method alongside block-positivity techniques, we derive explicit necessary and sufficient conditions for positivity, complete positivity, and k-positivity across arbitrary dimensions. These conditions provide a transparent geometric characterization of the positivity regions within the parameter space.

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arXiv2026

Mirrored Entanglement Witnesses for Multipartite and High-Dimensional Quantum Systems

Entanglement witnesses (EWs) are a versatile tool to detect entangled states and characterize related properties of entanglement in quantum information theory. A witness $W$ corresponds to an observable satisfying $\mathrm{tr}[Wσ_{\mathrm{sep}}]\geq 0$ for all separable states $σ_{\mathrm{sep}}$; entangled states are detected once the inequality is violated. Recently, mirrored EWs have been introduced by showing that there exist non-trivial upper bounds to EWs, \begin{eqnarray} u_W\geq \mathrm{tr}[Wσ_{\mathrm{sep}}]\geq 0. \nonumber \end{eqnarray} An upper bound to a witness $W$ signifies the existence of the other one $M$, called a mirrored EW, such that $W+M = u_W I \otimes I$. The framework of mirrored EWs shows that a single EW can be even more useful, as it can detect a larger set of entangled states by lower and upper bounds. In this work, we develop and investigate mirrored EWs for multipartite qubit states and also for high-dimensional systems, to find the efficiency and effectiveness of mirrored EWs in detecting entangled states. We provide mirrored EWs for $n$-partite GHZ states, graph states such as two-colorable states, and tripartite bound entangled states. We also show that optimal EWs can be reflected with each other. For bipartite systems, we present mirrored EWs for existing optimal EWs and also construct a mirrored pair of optimal EWs in dimension three. Finally, we generalize mirrored EWs such that a pair of EWs can be connected by another EW, i.e., $W+M =K$ is also an EW. Our results enhance the capability of EWs to detect a larger set of entangled states in multipartite and high-dimensional quantum systems.

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arXiv2025

Entanglement detection via third-order local invariants from randomized measurements

We compute all third-order local invariants accessible via randomised measurements and employ them to derive separability criteria. The reconstruction of the invariants yields experimentally accessible entanglement criteria for multipartite states with arbitrary local dimensions. The results show that third-order invariants capture inter-subsystem correlations beyond second-order spectral criteria within more feasible entanglement detection protocols than full tomography. As an example, Werner states in $d=3$ the entanglement is detected for $p>\frac 12$ at the second-order correlations, and it is improved to $p>\frac 1{\sqrt[3]{10}}$ at the third-order.

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arXiv2025

A mirrored pair of optimal non-decomposable entanglement witnesses for two qudits does exist

Two approaches can be utilized to handle the separability problem, finding out whether a given bipartite qudit state is separable or not: a direct procedure on the state space or the effective tool of entanglement witnesses (EWs). This contribution studies the structure of EWs. Exploiting the very concept of mirrored EWs, increasing the detection power, we show, in contrast to the conjecture in a recent paper (Sci. Rep. {\bf 13}, 10733 (2023)), there exist pairs of optimal EWs, which are both non-decomposible, i.e. can detect bound/PPT-entangled states in an optimal way. Since we show that the structure also extends to higher dimensions, our results reveal a further structure of entanglement witnesses.

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arXiv2023

Optimality of generalized Choi maps in $M_3$

A family of linear positive maps in the algebra of $3 \times 3$ complex matrices proposed recently in Bera et al. arXiv:2212.03807 is further analyzed. It provides a generalization of a seminal Choi nondecomposable extremal map in $M_3$. We investigate when generalized Choi maps are optimal, i.e. cannot be represented as a sum of positive and completely positive maps. This property is weaker than extremality, however, it turns out that it plays a key role in detecting quantum entanglement.

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arXiv2023

Optimizing positive maps in the matrix algebra $M_n$

We present an optimization procedure for a seminal class of positive maps $τ_{n,k}$ in the algebra of $n \times n$ complex matrices introduced and studied by Tanahasi and Tomiyama, Ando, Nakamura and Osaka. Recently, these maps were proved to be optimal whenever the greatest common divisor $GCD(n,k)=1$. We attain a general conjecture how to optimize a map $τ_{n,k}$ when $GCD(n,k)=2$ or 3. For $GCD(n,k)=2$, a series of analytical results are derived and for $GCD(n,k)=3$, we provide a suitable numerical analysis.

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arXiv2023

A class of optimal positive maps in $M_n$

It is proven that a certain class of positive maps in the matrix algebra $M_n$ consists of optimal maps, i.e. maps from which one cannot subtract any completely positive map without loosing positivity. This class provides a generalization of a seminal Choi positive map in $M_3$.

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arXiv2023

How many mutually unbiased bases are needed to detect bound entangled states?

From a practical perspective it is advantageous to develop methods that verify entanglement in quantum states with as few measurements as possible. In this paper we investigate the minimal number of mutually unbiased bases (MUBs) needed to detect bound entanglement in bipartite $(d\times d)$-dimensional states, i.e. entangled states that are positive under partial transposition. In particular, we show that a class of entanglement witnesses composed of mutually unbiased bases can detect bound entanglement if the number of measurements is greater than $d/2+1$. This is a substantial improvement over other detection methods, requiring significantly fewer resources than either full quantum state tomography or measuring a complete set of $d+1$ MUBs. Our approach is based on a partial characterisation of the (non-)decomposability of entanglement witnesses. We show that non-decomposability is a universal property of MUBs, which holds regardless of the choice of complementary observables, and we find that both the number of measurements and the structure of the witness play an important role in the detection of bound entanglement.

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arXiv2022

On the structure of mirrored operators obtained from optimal entanglement witnesses

Entanglement witnesses (EWs) are a versatile tool in the verification of entangled states. The framework of mirrored EW doubles the power of a given EW by introducing its twin -- a mirrored EW -- whereby two EWs related by mirroring can bound the set of separable states more efficiently. In this work, we investigate the relation between the EWs and its mirrored ones, and present a conjecture which claims that the mirrored operator obtained from an optimal EW is either a positive operator or a decomposable EW, which implies that positive-partial-transpose entangled states, also known as the bound entangled states, cannot be detected. This conjecture is reached by studying numerous known examples of optimal EWs. However, the mirrored EWs obtained from the non-optimal ones can be non-decomposable as well. We also show that mirrored operators obtained from the extremal decomposable witnesses are positive semi-definite. Interestingly, the witnesses that violate the well known conjecture of Structural Physical Approximation, do satisfy our conjecture. The intricate relation between these two conjectures is discussed and it reveals a novel structure of the separability problem.

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arXiv2022

Generalizing Choi map in $M_3$ beyond circulant scenario

We present a generalization of the family of linear positive maps in $M_3$ proposed thirty years ago by Cho et al. (Linear Algebra Appl. ${\bf 171}$, 213 (1992)) as a generalization of the seminal Choi non-decomposable map. The necessary and sufficient conditions for decomposability are provided.

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arXiv2022

Memory effects displayed in the evolution of continuous variable system

We analyze non-Markovian memory effects displayed by the quantum Brownian motion modelled as quantum harmonic oscillators coupled to a bath consisting of harmonic oscillators. We study the time evolution of fidelity, Petz-Rényi relative entropy and quantum entanglement for a family of 1-, 2- and 3-mode Gaussian states.

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arXiv2022

Simulating violation of causality using a topological phase transition

We consider a topological Hamiltonian and establish a correspondence between its eigenstates and the resource for a causal order game introduced in Ref. [1] known as process matrix. We show that quantum correlations generated in the quantum many-body energy eigenstates of the model can mimic the statistics that can be obtained by exploiting different quantum measurements on the process matrix of the game. This provides an interpretation of the expectation values of the observables computed for the quantum many-body states in terms of the success probabilities of the game. As a result, we show that the ground state (GS) of the model can be related to the optimal strategy of the causal order game. Subsequently, we observe that at the point of maximum violation of the classical bound in the causal order game, corresponding quantum many-body model undergoes a second-order quantum phase transition (QPT). The correspondence equally holds even when we generalize the game for a higher number of parties.

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arXiv2022

Recycling the resource: Sequential usage of shared state in quantum teleportation with weak measurements

Complete measurements, while providing maximal information gain, results in destruction of the shared entanglement. In the standard teleportation scheme, the sender's measurement on the shared entangled state between the sender and the receiver has that consequence. We propose here a teleportation scheme involving weak measurements which can sustain entanglement upto a certain level so that the reusability of the shared resource state is possible. The measurements are chosen in such a way that it is weak enough to retain entanglement and hence can be reused for quantum tasks, yet adequately strong to ensure quantum advantage in the protocol. In this scenario, we report that at most six sender-receiver duos can reuse the state, when the initial shared state is entangled in a finite neighborhood of the maximally entangled state and for a suitable choice of weak measurements. However, we observe that the reusability number decreases with the decrease in the entanglement of the initial shared state. Among the weakening strategies studied, Bell measurement admixed with white noise performs better than any other low-rank weak measurements in this situation.

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arXiv2021

A class of Bell diagonal entanglement witnesses in $\mathbb{C}^4 \otimes \mathbb{C}^4$: optimization and the spanning property

Two classes of Bell diagonal indecomposable entanglement witnesses in $\mathbb{C}^4 \otimes \mathbb{C}^4$ are considered. Within the first class, we find a generalization of the well-known Choi witness from $\mathbb{C}^3 \otimes \mathbb{C}^3$, while the second one contains the reduction map. Interestingly, contrary to $\mathbb{C}^3 \otimes \mathbb{C}^3$ case, the generalized Choi witnesses are no longer optimal. We perform an optimization procedure of finding spanning vectors, that eventually gives rise to optimal witnesses. Operators from the second class turn out to be optimal, however, without the spanning property. This analysis sheds a new light into the intricate structure of optimal entanglement witnesses.

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arXiv2021

Thermodynamics and the quantum speed limit in the non-Markovian regime

Quantum speed limit (QSL) for open quantum systems in the non-Markovian regime is analyzed. We provide a the lower bound for the time required to transform an initial state to a final state in terms of thermodynamic quantities such as the energy fluctuation, entropy production rate and dynamical activity. Such bound was already analyzed for Markovian evolution satisfying detailed balance condition. Here we generalize this approach to deal with arbitrary evolution governed by time-local generator. Our analysis is illustrated by three paradigmatic examples of qubit evolution: amplitude damping, pure dephasing, and the eternally non-Markovian evolution.

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