We study the relationship between the number of rounds needed to repeatedly perform a private computation (i.e., where there are many sets of inputs sequentially given to the players on which the players must compute a function privately) and the overall randomness needed for this task. For the XOR function we show that, by re-using the same $\ell$ random bits, we can significantly speed up the round-complexity of each computation compared to what is achieved by the naive strategy of partitioning the $\ell$ random bits between the computations. Moreover, we prove that our protocols are optimal in the amount of randomness they require.We study the relationship between the number of rounds needed to repeatedly perform a private computation (i.e., where there are many sets of inputs sequentially given to the players on which the players must compute a function privately) and the overall randomness needed for this task. For the XOR function we show that, by re-using the same $\ell$ random bits, we can significantly speed up the round-complexity of each computation compared to what is achieved by the naive strategy of partitioning the $\ell$ random bits between the computations. Moreover, we prove that our protocols are optimal in the amount of randomness they require.

SIAM Journal on Discrete MathematicsJan 1, 20037 citations

Stateless Virtual Quantum Acceleration (vQPU) and Spatiotemporal Lattice Materialization for Post-Quantum Blockchain Sovereignty

Min Ho Jung

This technical report introduces the HSKG Virtual Quantum Processing Unit (vQPU), a software-defined acceleration layer achieving O(1) computational complexity for spatiotemporal lattice quantization. It presents a stateless data materialization protocol that eliminates persistent private key storage in blockchain infrastructures, providing an immediate defense against quantum threats. Verified by the Google DeepMind Antigravity audit, this work establishes a new paradigm in post-quantum data sovereignty.This technical report introduces the HSKG Virtual Quantum Processing Unit (vQPU), a software-defined acceleration layer achieving O(1) computational complexity for spatiotemporal lattice quantization. It presents a stateless data materialization protocol that eliminates persistent private key storage in blockchain infrastructures, providing an immediate defense against quantum threats. Verified by the Google DeepMind Antigravity audit, this work establishes a new paradigm in post-quantum data sovereignty.

May 12, 20260 citations

Randomness in distribution protocols

Carlo Blundo, Alfredo De Santis, Ugo Vaccaro

Lecture notes in computer scienceJan 1, 199422 citations

Composing Protocols with Randomized Actions

Matthew S. Bauer, Rohit Chadha, Mahesh Viswanathan

Lecture notes in computer scienceJan 1, 20168 citations

Quantum waste management: Utilizing residual states in quantum information processing

Karol Horodecki, Chirag Srivastava, Leonard Sikorski +1 more

Quantum resource theories use distillation protocols to convert less resourceful states into fully resourceful ones. However, these protocols often also generate an additional, unused output-referred to as a residual. We propose a framework for the quantum residual management, in which states discarded after a resource distillation protocol are repurposed as inputs for subsequent quantum information tasks. This approach extends conventional quantum resource theories by incorporating secondary resource extraction from residual states, thereby enhancing overall resource utility. As a concrete example, we investigate the distillation of private randomness from the residual states remaining after quantum key distribution (QKD). More specifically, we quantitatively show that after performing a well-known coherent Devetak-Winter protocol, one can locally extract private randomness from its residual. We further consider the Gottesman-Lo QKD protocol and provide the achievable rate of private randomness from the discarded states that are left after its performance. We also provide a formal framework that highlights a general principle for improving quantum resource utilization across sequential information processing tasks.Quantum resource theories use distillation protocols to convert less resourceful states into fully resourceful ones. However, these protocols often also generate an additional, unused output-referred to as a residual. We propose a framework for the quantum residual management, in which states discarded after a resource distillation protocol are repurposed as inputs for subsequent quantum information tasks. This approach extends conventional quantum resource theories by incorporating secondary resource extraction from residual states, thereby enhancing overall resource utility. As a concrete example, we investigate the distillation of private randomness from the residual states remaining after quantum key distribution (QKD). More specifically, we quantitatively show that after performing a well-known coherent Devetak-Winter protocol, one can locally extract private randomness from its residual. We further consider the Gottesman-Lo QKD protocol and provide the achievable rate of private randomness from the discarded states that are left after its performance. We also provide a formal framework that highlights a general principle for improving quantum resource utilization across sequential information processing tasks.

arXiv:2510.27687Oct 31, 20250 citations

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random bits, we can significantly speed up the round-complexity of each computation compared to what is achieved by the naive strategy of partitioning the

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random bits between the computations. Moreover, we prove that our protocols are optimal in the amount of randomness they require.