@inproceedings{bib_Quan_2024, AUTHOR = {P V Srinidhi, Indranil Chakrabarty, Samyadeb Bhattacharya, Nirman Ganguly}, TITLE = {Quantum channels that destroy negative conditional entropy}, BOOKTITLE = {Physical Review A}. YEAR = {2024}}

Counter-intuitive to classical notions, quantum conditional entropy can be negative, playing a pivotal role in information-processing tasks. This article delves deeply into quantum channels, em- phasizing negative conditional entropy breaking channels (NCEB) and introducing negative condi- tional entropy annihilating channels (NCEA). We characterize these channels from both topological and information-theoretic perspectives, examining their properties when combined serially and in parallel. Our exploration extends to complimentary channels associated with NCEB, leading to the introduction of information-leaking channels. Utilizing the parameters of the standard depolarizing channel, we provide tangible examples and further characterization. We demonstrate the relation- ship of NCEB and NCEA with newly introduced channels like coherent information breaking (CIB) and mutual information breaking (MIB), along with standard channels like zero capacity channels. Preservation of quantum resources is an integral constituent of quantum information theory. Rec- ognizing this, we lay prescriptions to detect channels that do not break the negativity of conditional entropy, ensuring the conservation of this quantum resource

@inproceedings{bib_Cont_2024, AUTHOR = {Pahulpreet Singh, Indranil Chakrabarty}, TITLE = {Controlled State Reconstruction and Quantum Secret Sharing}, BOOKTITLE = {Physical Review A}. YEAR = {2024}}

In this article we present a benchmark for resource characterization in the process of controlled quantum state reconstruction and secret sharing for general three-qubit states. This is achieved by providing a closed expression for the reconstruction fidelity, which relies on the genuine tripartite correlation and the bipartite channel between the dealer and the reconstructor characterized by the respective correlation parameters. We formulate the idea of quantum advantage in approximate state reconstruction as surpassing the classical limit set at 2/3. This article introduces new interoperability between teleportation and state reconstruction. This is detailed through a case-by-case analysis of relevant correlation matrices. We reformulate the idea of quantum secret sharing by setting up additional constraints on the teleportation capacity of the bipartite channels between dealer and shareholders by ensuring that, individually, the shareholders cannot reconstruct the secret. We believe that this will give us an ideal picture of how quantum secret sharing should be.

@inproceedings{bib_Tele_2023, AUTHOR = {Sohail, Arun K Pati, Vijeth Aradhya, Indranil Chakrabarty, Subhasree Patro}, TITLE = {Teleportation of Quantum Coherence}, BOOKTITLE = {Physical Review A}. YEAR = {2023}}

We investigate whether it is possible to teleport the coherence of an unknown quantum state from Alice to Bob by communicating lesser number of classical bits in comparison to what is required in teleporting an unknown quantum state. We find that we cannot do perfect teleportation of coherence with one bit of classical communication for an arbitrary qubit. However, we find that if the qubit is chosen from equatorial and polar circles, then teleportation of coherence will be possible with transfer of one cbit of information if we have maximally entangled states as a shared resource. In the case of resource being a non maximally entangled state, we can teleport quantum coherence with a certain probability of success. In a general teleportation protocol for coherence, we derive a compact formula for the final state at Bob’s lab in terms of composition of the completely positive maps corresponding to the shared resource state and joint POVM performed by Alice on her qubit and the unknown state. With the help of this formula, we investigate the amount of coherence teleported when the resource shared state is the maximally entangled mixed state and Werner state for the unknown pure as well as mixed states state at Alice’s lab. In particular, we show that when the Werner state becomes separable then also the amount of teleported coherence is non-zero, implying the possibility of teleportation of coherence without entanglement. We have also shown that teleportation of coherence of an arbitrary state with real matrix elements is exactly possible with the help of maximally entangled state as a resource.

@inproceedings{bib_Pers_2023, AUTHOR = {Kaushiki Mukherjee, Indranil Chakrabarty, Ganesh Mylavarapu}, TITLE = {Persistency of non--local correlations in noisy linear network}, BOOKTITLE = {Physical Review A}. YEAR = {2023}}

Linear n-local networks are compatible with quantum-repeater-based entanglement distribution protocols. Different sources of imperfections such as error in entanglement generation, communication over noisy quantum channels, and imperfections in measurements result in decay of quantumness across such networks. From practical perspectives it becomes imperative to analyze the nonclassicality of quantum network correlations in the presence of different types of noise. The present discussion provides a formal characterization of non-n-local features of quantum correlations in a noisy network scenario. In this context, persistency of non-n-locality has been introduced. Such a notion helps in analyzing decay of non-n-local features of network correlations with increasing length of the linear network in the presence of one or more causes of imperfections.

@inproceedings{bib_A-un_2022, AUTHOR = {MAHATHI VEMPATI, Shah Saumya Mihirkumar, Nirman Ganguly, Indranil Chakrabarty}, TITLE = {A-unital Operations and Quantum Conditional Entropy}, BOOKTITLE = {Quantum Journal}. YEAR = {2022}}

The significance of negative quantum conditional entropy is underscored by its ubiquity in information processing tasks like dense coding, state merging and one-way entanglement distillation. Mere presence of entanglement is not sufficient for these tasks, a fact underpinned by the existence of entangled quantum states with non-negative conditional entropy. This stimulates one to go beyond the paradigm of entanglement theory and probe the hitherto unexplored area of operations influencing quantum conditional entropy. To this end, we introduce the class of A-unital channels. We characterize them and demonstrate that A-unital channels are to states having non-negative conditional entropy what separable channels are to separable states. We also show that A-unital channels form the largest class of channels that do not decrease the conditional entropy of any state, a relation analogous to unital channels and entropy. A comparative study between A-unital and other channels crucial to the resource theory of entanglement is done to further exemplify the distinction with entanglement theory. Non-local unitary operations can decrease conditional entropy to sub-zero levels. However, there exist states whose conditional entropy remains non-negative even under this action. Termed as states having absolute conditional entropy, they prove to be robust against non-local unitary action. In this work, the completely free operations for such states are also characterized. Finally, since von Neumann entropy is the mainspring of these discussions, the bounds on the conditional entropy of states having a given entropy are derived. The definition of A-unital channels naturally lends itself to a procedure for determining membership of channels in this class. Thus, we not only characterize completely free channels for quantum conditional entropy, but also show how resourceful channels can be detected.

@inproceedings{bib_Witn_2021, AUTHOR = {MAHATHI VEMPATI, Nirman Ganguly, Indranil Chakrabarty, Arun K Pati}, TITLE = {Witnessing Negative Conditional Entropy}, BOOKTITLE = {Physical Review A}. YEAR = {2021}}

Quantum states that possess negative conditional von Neumann entropy provide quantum advantage in several information-theoretic protocols including superdense coding, state merging, distributed private randomness distillation and one-way entanglement distillation. While entanglement is an important resource, only a subset of entangled states have negative conditional von Neumann entropy. In this work, we characterize the class of density matrices having non-negative conditional von Neumann entropy as convex and compact. This allows us to prove the existence of a Hermitian operator (a witness) for the detection of states having negative conditional entropy for bipartite systems in arbitrary dimensions. We show two constructions of such witnesses. For one of the constructions, the expectation value of the witness in a state is an upper bound to the conditional entropy of the state. We pose the problem of obtaining a tight upper bound to the set of conditional entropies of states in which an operator gives the same expectation value. We solve this convex optimization problem numerically for a two qubit case and find that this enhances the usefulness of our witnesses. We also find that for a particular witness, the estimated tight upper bound matches the value of conditional entropy for Werner states. We explicate the utility of our work in the detection of useful states in several protocols.

@inproceedings{bib_Broa_2019, AUTHOR = {ROUNAK MUNDRA, DHRUMIL PATEL, Indranil Chakrabarty, Nirman Ganguly, SOURAV CHATTERJEE}, TITLE = {Broadcasting of quantum correlations in qubit-qudit systems}, BOOKTITLE = {Physical Review A}. YEAR = {2019}}

Quantum mechanical properties like entanglement, discord and coherence act as fundamental resources in various quantum information processing tasks. Consequently, generating more resources from a few, typically termed as broadcasting is a task of utmost significance. One such strategy of broadcasting is through the application of cloning machines. In this article, broadcasting of quantum resources beyond 2 ⊗ 2 systems is investigated. In particular, in 2 ⊗ 3 dimension, a class of states not useful for broadcasting of entanglement is characterized for a choice of optimal universal Heisenberg cloning machine. The broadcasting ranges for maximally entangled mixed states (MEMS) and two parameter class of states (TPCS) are obtained to exemplify our protocol. A significant derivative of the protocol is the generation of entangled states with positive partial transpose in 3 ⊗ 3 dimension and states which are absolutely separable in 2 ⊗ 2 dimension. Moving beyond entanglement, in 2 ⊗ d dimension, the impossibility to optimally broadcast quantum correlations beyond entanglement (QCsbE) (discord) and quantum coherence(l1-norm) is established. However, some significant illustrations are provided to highlight that non-optimalbroadcasting of QCsbE and coherence are still possible

@inproceedings{bib_Asym_2019, AUTHOR = {Aditya Jain, Indranil Chakrabarty, SOURAV CHATTERJEE}, TITLE = {Asymmetric broadcasting of quantum correlations}, BOOKTITLE = {Physical Review A}. YEAR = {2019}}

In this work, we exhaustively investigate 1 → 2 local and nonlocal broadcasting of entanglement as well as correlations beyond entanglement (geometric discord) using asymmetric Pauli cloners with most general two qubit state as the resource. We exemplify asymmetric broadcasting of entanglement using 'Maximally Entangled Mixed States'. We demonstrate the variation of broadcasting range with the amount of entanglement present in the resource state as well as with the asymmetry in the cloner. We show that it is impossible to optimally broadcast geometric discord with the help of these asymmetric Pauli cloning machines. We also study the problem of 1 → 3 broadcasting of entanglement using non-maximally entangled state (NME) as the resource. For this task, we introduce a method we call successive broadcasting which involves application of 1 → 2 optimal cloning machines multiple times. We compare and contrast the performance of this method with the application of direct 1 → 3 optimal cloning machines. We show that 1 → 3 optimal cloner does a better job at broadcasting than the successive application of 1 → 2 cloners and the successive method can be beneficial in the absence of 1 → 3 cloners. We also bring out the fundamental difference between the tasks of cloning and broadcasting in the final part of the manuscript. We create examples to show that there exist local unitaries which can be employed to give a better range for broadcasting. Such unitary operations are not only economical, but also surpass the best possible range obtained using existing cloning machines enabling broadcasting of lesser entangled states. This result opens up a new direction in exploration of methods to facilitate broadcasting which may outperform the standard strategies implemented through cloning transformations

@inproceedings{bib_Impo_2018, AUTHOR = {DHRUMIL PATEL, SUBHASREE PATRO, V CHIRANJEEVI, Indranil Chakrabarty, Arun Kumar Pati}, TITLE = {Impossibility of cloning of quantum coherence}, BOOKTITLE = {Physical Review A}. YEAR = {2018}}

It is well known that it is impossible to clone an arbitrary quantum state. However, this inability does not lead directly to no-cloning of quantum coherence. Here, we show that it is impossible to clone the coherence of an arbitrary quantum state which is a stronger statement than the ’no-cloning of quantum state’. In particular, with ancillary system as machine state, we show that it is impossible to clone the coherence of states whose coherence is greater than the coherence of the known states on which the transformations are defined. Also, we characterize the class of states for which coherence cloning will be possible for a given choice of machine. Furthermore, we find the maximum range of states whose coherence can be cloned perfectly. The impossibility proof also holds when we do not include machine states.

@inproceedings{bib_Non-_2018, AUTHOR = {SUBHASREE PATRO, Indranil Chakrabarty}, TITLE = {Non-negativity of conditional von Neumann entropy and global unitary operations}, BOOKTITLE = {Physical Review A}. YEAR = {2018}}

Conditional von Neumann entropy is an intriguing concept in quantum information theory. In the present work, we examine the effect of global unitary operations on the conditional entropy of the system. We start with the set containing states with non-negative conditional entropy and find that some states preserve the non-negativity under unitary operations on the composite system. We call this class of states as Absolute Conditional von Neumann entropy Non Negative class (ACVENN). We are able to characterize such states for 2 ⊗ 2 dimensional systems. On a different perspective the characterization accentuates the detection of states whose conditional entropy becomes negative after the global unitary action. Interestingly, we show that this ACVENN class of states forms a set which is convex and compact. This feature enables the existence of hermitian witness operators. With these we can distinguish the unknown states which will have negative conditional entropy after the global unitary operation. We also show that this has immediate application in super dense coding and state merging as negativity of conditional entropy plays a key role in both these information processing tasks. Some illustrations followed by analysis are also provided to probe the connection of such states with absolutely separable (AS) states and absolutely local (AL) states.