arXiv subjects

Bivas Mallick

Publications and source records attributed to Bivas Mallick.

15 recordsLinked to original sources

arXiv2026

Operational certification of nonclassicality in arbitrary quantum states from few copies

States with negative Wigner functions constitute a fundamental nonclassical resource underlying quantum advantage. However, their experimental certification typically relies on reconstructing the full phase-space distribution, resulting in a prohibitive measurement overhead for arbitrary quantum states. In this letter, we overcome this limitation by introducing Wigner moments, a family of global phase-space quantities that admit an exact multicopy realization as parity expectation values, and are therefore directly measurable from only a modest number of state copies. This operational correspondence enables systematic hierarchies of detection criteria together with experimentally accessible lower bounds on the logarithmic Wigner negativity, and constitutes a genuine measure of nonclassicality. Numerical benchmarking of our protocol reveals a substantial reduction in copy budget relative to conventional Wigner tomography, establishing Wigner moments as an efficient framework for certifying continuous-variable quantum resources such as genuine multipartite entanglement.

quant-ph↗

arXiv2026

Absolute Schmidt number: characterization, detection and resource-theoretic quantification

The dimensionality of entanglement, quantified by the Schmidt number, is a valuable resource for a wide range of quantum information processing tasks. In this work, we introduce the notion of the absolute Schmidt number, referring to states whose Schmidt number cannot be increased by any global unitary transformation. We provide a characterization of the set of arbitrary-dimensional states whose Schmidt number is invariant under all global unitaries. Our approach enables us to develop both witness-based and moment-based techniques to detect nonabsolute Schmidt number states which could provide significant operational advantages through Schmidt number enhancement by global unitaries. We next formulate two resource-theoretic measures of nonabsolute Schmidt number states, based respectively on Schmidt number witness and robustness, and demonstrate an operational utility of the latter in a channel discrimination task. Finally, we extend our analysis to quantum channels by introducing a new class of channels that possess the absolute Schmidt number property. We derive a necessary and sufficient condition for identifying when a channel has the absolute Schmidt number property, confining our analysis to the class of covariant channels.

quant-ph↗

arXiv2026

Detection of quantum imaginarity using moments and its interferometric realization

Complex numbers, intrinsic to the formulation of quantum theory, play a pivotal role in enabling advantages across a broad range of quantum information-processing tasks. Despite their fundamental importance, practical and scalable criteria for detecting quantum imaginarity remain relatively underexplored, particularly methods that enable its identification with reduced experimental overhead. In this work, we propose a realistic and experimentally feasible method to detect quantum imaginarity using moment-based approach. Our framework relies on experimentally accessible moments of the Kirkwood-Dirac quasiprobability distribution, enabling scalable detection in many-body and high-dimensional systems without requiring full state tomography. We then present an illustrative example to support our detection scheme. Finally, we present an interferometric scheme for measuring these moments, paving the way for experimental implementation of our detection protocol.

quant-ph↗

arXiv2025

Certifying the dimensionality of any quantum channel with minimal assumptions

High-dimensional entanglement offers significant advantages over its low-dimensional counterpart in various information-processing tasks. However, to harness these advantages, it is crucial that the quantum channels used to store or transmit the subsystems of an entangled system not only preserve entanglement but also maintain its dimensionality above a certain threshold. The maximum entanglement dimension that a channel can preserve is referred to as its effective dimensionality, since the channel cannot be used to transmit information of dimension greater than that in a single use. In this work, we present a method to certify whether a quantum channel can preserve entanglement dimension above a given threshold. Unlike existing approaches, our method is faithful, i.e., it can be applied to any channel, and avoids common assumptions such as preparation of entangled states, auxiliary side channels, or perfect measurement devices. Moreover, the method can be extended to faithfully certify other classes of non-resource-breaking channels, such as non-nonpositive-partial-transpose-breaking channels (non-NPT-breaking channels). Finally, we discuss possible experimental realizations of our certification scheme through explicit examples.

quant-ph↗

arXiv2025

Detection of nonabsolute separability in quantum states and channels through moments

In quantum information and computation, the generation of entanglement through unitary gates remains a significant and active area of research. However, there are states termed as absolutely separable, from which entanglement cannot be created through any non-local unitary action. Thus, from a resource-theoretic perspective, non-absolutely separable states are useful as they can be turned into entangled states using some appropriate unitary gates. In this work, we propose an efficient method to detect non-absolutely separable states. Our approach relies on evaluating moments that can bypass the need for full state tomography, thereby enhancing its practical applicability. We then present several examples in support of our detection scheme. We also address a closely related problem concerning states whose partial transpose remains positive under any arbitrary non-local unitary action. Furthermore, we examine the effectiveness of our moment-based approach in the detection of quantum channels that are not absolutely separating, which entails the detection of resource preserving channels. Finally, we demonstrate the operational significance of non-absolutely separable states by proving that every such state can provide an advantage in a quantum-channel discrimination task.

quant-ph↗

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↗

arXiv2025

Probing Kirkwood-Dirac nonpositivity and its operational implications via moments

The Kirkwood-Dirac (KD) distribution has recently emerged as a powerful quasiprobability framework with wide-ranging applications in quantum information processing tasks. In this work, we introduce an experimentally motivated criterion for detecting nonclassical signatures of the KD distribution using its statistical moments and demonstrate its effectiveness through explicit examples. We further show that this approach extends naturally to identifying other quantum resources, such as quantum coherence and nonclassical extractable work -- that are intrinsically connected to the KD distribution. Our criteria involves the evaluation of simple functionals, making it well-suited for efficient experimental implementation.

quant-ph↗

arXiv2025

Detecting genuine multipartite entanglement using moments of positive maps

Genuine multipartite entanglement (GME) represents the strongest form of entanglement in multipartite systems, providing significant advantages in various quantum information processing tasks. In this work, we propose an experimentally feasible scheme for detecting GME, based on the truncated moments of positive maps. Our method avoids the need for full state tomography, making it scalable for larger systems. We provide illustrative examples of both pure and mixed states to demonstrate the efficacy of our formalism in detecting inequivalent classes of tripartite genuine entanglement. We further demonstrate the detection of quadripartite genuine entanglement, underscoring the effectiveness of our method in identifying entanglement beyond the tripartite case. Finally, we present a proposal for realising these moments in real experiments.

quant-ph↗

arXiv2025

Higher-dimensional entanglement detection and quantum channel characterization using moments of generalized positive maps

Higher-dimensional entanglement is a valuable resource for several quantum information processing tasks, and is often characterized by the Schmidt number and specific classes of entangled states beyond qubit-qubit and qubit-qutrit systems. We propose a criterion to detect higher-dimensional entanglement, focusing on determining the Schmidt number of quantum states and identifying significant classes of positive partial transposition and negative partial transposition entangled states. Our approach relies on evaluating moments of generalized positive maps which can be efficiently simulated in real experiments without the requirement of full-state tomography. We demonstrate the effectiveness of our detection scheme through various illustrative examples. As a direct application, we explore the implications of our moment-based detection schemes in identifying useful quantum channels such as non-Schmidt-number breaking channels and non-entanglement breaking channels. Finally, we present an operational implication of our proposed moment criterion through its manifestation in channel discrimination tasks.

quant-ph↗

arXiv2025

Measurement-device-independent Schmidt number certification of all entangled states

Bipartite quantum states with higher Schmidt numbers have been shown to outperform those with lower Schmidt numbers in various quantum information processing tasks, highlighting the operational advantage of entanglement dimensionality. Certifying the Schmidt number of such states is therefore crucial for efficient resource utilisation. Ideally, this certification should rely as little as possible on the certifying devices to ensure robustness against their potential imperfections. Fully device-independent certification via Bell-nonlocal games offers strong robustness but suffers from fundamental limitations: it cannot certify the Schmidt number of all entangled states. We demonstrate that this insufficiency of Bell-nonlocal games is not limited to entangled states that do not exhibit Bell-nonlocality. Specifically, we prove the existence of Bell-nonlocal states whose Schmidt number cannot be certified by any Bell-nonlocal game when the parties are restricted to local projective measurements. To overcome this, we develop a measurement-device-independent certification method based on semiquantum nonlocal games, which assume trusted preparation devices but treat measurement devices as black boxes. We prove that for any bipartite state with Schmidt number exceeding $r$, there exists a semiquantum nonlocal game that can certify its Schmidt number. Finally, we provide an explicit construction of such a semiquantum nonlocal game based on an optimal Schmidt number witness operator.

quant-ph↗

arXiv2024

On the characterization of partially entanglement breaking and annihilating channels

Transmission of high dimensional entanglement through quantum channels is a significant area of interest in quantum information science. The certification of high dimensional entanglement is usually done through Schmidt numbers, which quantify the entanglement dimensionality of quantum states. States with high Schmidt numbers provide a larger advantage in various quantum information processing tasks compared to quantum states with low Schmidt numbers. However, the action of quantum channels may reduce the Schmidt number of transmitted states, thereby degrading their resourcefulness. Here we present a comprehensive analysis of partially entanglement breaking channels which reduce the Schmidt number of bipartite composite systems. From a resource theoretic perspective, it becomes imperative to identify channels that preserve the Schmidt number. Based on our characterization we lay down prescriptions to identify such channels which are non-resource breaking, i.e., preserve the Schmidt number. Additionally, we introduce a new class of quantum channels, termed partially entanglement annihilating channels which reduce the Schmidt number of a quantum state that is a part of a larger composite system. Finally, we study the connection between entanglement breaking, partially entanglement breaking, and partially entanglement annihilating channels.

quant-ph↗

arXiv2024

Efficient detection of nonclassicality using moments of the Wigner function

States with a negative Wigner function, a significant subclass of nonclassical states, serve as a valuable resource for various quantum information processing tasks. Here, we provide a criterion for detecting such quantum states characterized by a negative Wigner function. Our method relies on evaluating moments of the Wigner function, which involves computing simple functionals and can be implemented in a real experiment without the need for full state tomography or Wigner function reconstruction. We provide explicit examples to support our detection scheme. Further, we propose an experimental method utilizing the mode SWAP operator to realize these moments in a real experiment.

quant-ph↗

arXiv2024

Genuine entanglement detection via projection map in multipartite systems

We present a formalism to detect genuine multipartite entanglement by considering projection map which is a positive but not completely positive map. Projection map has been motivated by the no-pancake theorem which repudiates the existence of a quantum operation that maps the Bloch sphere onto a disk along its equator. The not complete positivity feature of projection map is explored to investigate genuine multipartite entanglement in arbitrary N-qubit quantum systems. Our proposed framework can detect some important classes of genuinely entangled states in tripartite and quadripartite scenarios. We provide illustrative example to show the efficacy of our formalism to detect a class of tripartite PPT bound entangled states. Finally, we construct a suitable witness operator based on projection map to certify genuine tripartite entanglement, which is likely to be feasible experimentally.

quant-ph↗

arXiv2023

Interplay between the Hilbert-space dimension of a control system and the memory induced by a quantum SWITCH

Several recent studies have demonstrated the utility of the quantum SWITCH as an important resource for enhancing the performance of various information processing tasks. In a quantum SWITCH, the advantages appear significantly due to the coherent superposition of alternative configurations of the quantum components which are controlled by an additional control system. Here we explore the impact of increasing the Hilbert-space dimension of the control system on the performance of the quantum SWITCH. In particular, we focus on a quantifier of the quantum SWITCH through the emergence of non-Markovianity and explicitly study their behavior when we increase the Hilbert-space dimension of the control system. We observe that increasing the Hilbert-space dimension of the control system leads to the corresponding enhancement of the non-Markovian memory induced by it. Our study demonstrates how the dimension of the control system can be harnessed to improve the quantum SWITCH-based information processing or communication tasks.

quant-ph↗

arXiv2023

Assessing non-Markovian dynamics through moments of the Choi state

Non-Markovian effects in open quantum system dynamics usually manifest backflow of information from the environment to the system, indicating complete-positive divisibility breaking of the dynamics. We provide a criterion for witnessing such non-Markovian dynamics exhibiting information backflow, based on the moments of Choi-matrices. The moment condition determined by the positive semi-definiteness of a matrix, does not hold for a Choi-state describing non-Markovian dynamics. We then present some explicit examples in support of our proposed non-Markovianity detection scheme. Finally, a moment based measure of non-Markovianity for unital dynamics is formulated.

quant-ph↗