Communication cost for secret recovery in Quantum Secret Sharing

Quantum secret sharing, or QSS, is a quantum cryptographic primitive where a secret is encoded into quantum information and distributed among multiple parties. In QSS schemes, only authorized sets of parties are allowed to recover the information about the secret while unauthorized sets cannot recover any information on the secret. During my research work with Prof. Pradeep Sarvepalli at IIT Madras, we studied the communication cost for secret recovery in QSS schemes. We proposed the Communication Efficient Quantum Secret Sharing schemes which are QSS schemes with reduced comminication cost during secret recovery [1]. We derived the bound on communication cost for such schemes using a quantum information theoretic approach and provided two optimal constructions [2]. We later studied how concatenating extended CSS codes gives a general framework to construct such QSS schemes [3].

Storage cost - repair bandwith tradeoff in Regenerating codes

Regenerating codes are classical codes used for distributed storage which focus on two parameters.
1) How much memory space is needed to store the data reliably across multiple nodes?
2) How much bandwidth is needed while repairing one of the failed nodes?
There exists a tradeoff between these two parameters whose extreme points had been characterized earlier. However the interior points of the tradeoff are yet to be fully characterized. My work in Codes and Signal Design lab at IISc jointly with Birenjith Sasidharan and Prof. Vijay Kumar helped towards a better characterization of this tradeoff. Our work involved two approaches. First, we built upon an exisiting information-theoretic approach to tighten the outer bound of the tradeoff [4]. We also proposed a class of regenerating codes called improved layered codes with parameters very close to the tradeoff and even optimal under certain conditions [5].