INDRANIL

MAJOR RESEARCH DIRECTIONS

TOPOLOGY OF QUANTUM NETWORKS

With the advancement of quantum technologies, we are able to establish differerent quantum networks. This can either be established by free-space satellite based technologies or by repeater based technology in a ground to ground stations based scenario. In addition to theoretical understanding of the establishment of quantum networks, there are many experimental advancement in this direction. This will lead us to the establishment of quantum internet. It is interesting to see that whether the network topology will play a significant role in the efficacy of quantum network, when we move from simple scenarios to more complicated scenarios,.  

Our Achievements: Characterizing non n-local feature of quantum correlations in noisy network scenario, Generation of three party quantum network by cloning.

Some Publications: Phys. Rev. A 112, 032618 (2025), Phys. Rev. A 107, 032404 (2023), Mathematics, 11(11), 2440  (2023)

BROADCASTING OF CORRELATIONS IN QUANTUM WORLD

In quantum information theory, entanglement and other measures of correlation plays a significant role in the computation and communication. In a sense, purer the entanglement more valuable  it is. Therefore extraction of pure quantum entanglement from partially entangled states is considered to be an important task.  This process is called distillation of entanglement. The possibility of compression of quantum correlations naturally raises the question :   If the opposite, i.e decompression of quantum correlation is possible or not. This process of decompression of quantum correlations is known  as “Broadcasting of Quantum Correlations”.   This is The question becomes important when there   is exigency in increasing the number of available entangled pairs rather than purity of it.  Broadcasting helps us to create more number of entangled states with lesser entanglement between two quantum processors in a network. It is interesting to see to what extent we are able to broadcast correlations starting with different quantum systems.

Our Achievements: Broadcasting of entanglement, correlation, non locality and coherence for mixed states. Broadcasting with Asymmetric Cloning Machines.  Broadcasting of entanglement in qubit-qudit systems.

Some Publications: Pramana 98, 59 (2024), Phys. Rev. A 93, 042309 (2016), Phys. Rev. A 96, 052319 (2017), Phys. Rev. A 100 , 042319 (2019), Phys. Rev. A 99, 022315 (2019), Quantum Inf Process, 19, 15 (2020)

CHARACTERISATION OF RESOURCES FOR QUANTUM COMMUNICATION

One of the most important aspect of the quantum communication is to characterise  the useful resources for a quantum  communication. Quantum networks are made up of  entangled states. These states are like edges and are connected between the node and they can be used as a  resource for quantum communication. However the process of selection of resources are not straightforward and simple. There are in fact two possible ways of characterisation of resources in a broad sense.  The first case is the resources based on certain information processing tasks. These information processing tasks include 1) Teleportation 2) Super dense Coding 3) State merging and many others. It will not true if we say that any entangled state will be useful for any kind of tasks. As an example if we want built a network for teleportation, we know that not all entangled states will be useful for teleportation as long as we are expecting to have a quantum advantage. The second possible way is to select states which are not resource at the present moment but can be made useful for resource after quantum operations.  As an example there are separable states which can be converted into an entangled state after global unitary operations. Similarly there are non negative conditional entropy states which can be made useful by converting them to negative conditional entropy states. Hence charecterizing resources for quantum communication becomes all the more important.

Our Achievements: Characterising ACVENN  and CVENN Class, Characterising entangled states useful and not useful for teleportation

Some Publications:  Quantum 6, 641 (2022) , Eur. Phys. J. D 76, 127 (2022) , Phys. Rev. A 104, 012417 (2021) Phys. Rev. A 96, 062102 (2017), Quantum Inf Process 17, 3 (2018), Quant. Inf. Process, 10, 27 (2011), Eur. Phys. J. D, 57, 265 (2010). J. Phys. A: Math. Theor, 41 415302 (2008).

QUANTUM INFORMATION THEORY IN PRESENCE OF CLOSED TIME LIKE CURVES

In general theory of relativity we define closed  time like curves (CTC) by a world line which connects back on itself. However an important doubt always remains on  formulation of  a consistent theory of quantum mechanics that will allow the  presence of CTCs. Such a formalism was developed by Deutsch who proposed a model of quantum theory in the presence of CTCs.  The presence of closed time like curves can enhance the computational power. These include  tasks  like  factorisation of composite numbers,  solving NP-complete problems . It also improves  the performance of  quantum information processing tasks. One of these is  perfectly distinguishing non orthogonal quantum states. This have possible implications for the security of quantum cryptography . In the presence of CTCs ideas like purification of mixed states have also been addressed. In short closed time curve gives out a way of understanding as well as deconstructing the established results of quantum information theory in a framework beyond the causality respecting region.  

Our Achievements: Impossibility of Purification of Quantum states in presence of CTC, Addition of Two unknown Quantum States in presence of CTC, Cloning and Deletion in presence of CTC.

Some Publications: EPL 122 10007 (2018), Phys. Rev. A 84, 062325 (2011)., Mod. Phys. Lett. A, Vol. 31, No. 29 (2016) 1650170, Quantum Information and Computation, 14, 1251 (2014).

UNDERSTANDING COMPLIMENTARITY IN QUANTUM FOUNDATIONAL ISSUES

The problem of complementarity or mutually exclusive aspects of quantum phenomena is there to start with from the very beginning of the idea of quantum mechanics. It was Heisenberg who first coined the uncertainty principle for the momentum and the position.  Later  Bohr introduced the idea of complementarity.  Interestingly, it does not end there and also exists in different forms like the complementarity between the quantifiers of correlations, dual physical processes and in many other processes. 

Our Achievements: Complementarity between Dual operations like Cloning and Deletion, Complementarity between three qubit correlation and two qubit non locality, Complementarity in multi partite non locality .

Some Publications: Phys. Rev. A 91, 062311 (2015),Phys. Rev. A 94, 052126 (2016), Phys. Rev. A 96, 022121 (2017).

IMPOSSIBLE OPERATIONS AND NO-GO THEOREMS IN QUANTUM INFORMATION THEORY

Quantum superposition and entanglement is the key that makes quantum information processing radically different from classical counterpart. The same properties also stops us to do certain tasks which otherwise possible in the classical world . It  all started with the no-cloning theorem. According to  which there does not exist any quantum operation which can perfectly clone an arbitrary quantum  state . It was later showed that we cannot delete either of the two quantum states perfectly . There are many other no-go theorems like no-flipping , no-self replication, no-partial erasure  no-splitting  and no- partial swapping  which together tells us the indivisibility of the information content present in a quantum system.

Our Achievements: Impossibility of Cloning of Coherence, Impossibility Partial Swapping

Some Publications: Phys. Rev. A 103, 022422 (2021), Int. J. Theor. Phys, 46, 3281 (2007), Int. J. Theor. Phys, 46, 2513 (2007), Int. J. Quant Inf, 5, 605 (2007), Phys. Scr, 74, 555 (2006), Int. J. Theor. Phys, 46, 2829 (2007).

QUANTUM SECRET SHARING

The idea of secret sharing is nothing but to share a secret between people who can not reveal the secret unless all the parties collaborate. In a three party scenario,  the dealer shares secret with two parties in such a way that no body will be able to reveal the secret without  invoking the other parties. This is a very useful technique if one of the party is dishonest. Quantum secret sharing  generally deals with the problem of sharing of both classical as well as quantum secrets. 

Our Achievements: Differentiating Quantum secret sharing from Controlled State reconstruction, Retrieving and Routing of Quantum Secrets, Sequential Secret Sharing, Sequential Secret Sharing in Noisy Environment. Probabilistic Secret Sharing,  Quantum Advantage in Secret Sharing

Some Publications: Phys. Rev. A 109, 032406 (2024), Quant. Inf. Proc. Volume 14, Issue 12, pp 4651-4664 (2015), Quantum Information and Computation, 12, 0253 (2012), Eur. Phys. J. D 70: 114 (2016).