Following are our interests in this direction:

• Quantum Protocols Under Energy Constraints: Quantum communication and information processing protocols often operate under physical constraints, such as limits on energy, coherence, or entanglement resources. Energy constraints, in particular, are significant in continuous-variable systems where operations involve states with finite energy, such as Gaussian states or photon-number-restricted states. Key questions include:
  1. How do energy constraints affect the fidelity, efficiency, or security of quantum communication protocols such as quantum key distribution, teleportation, or state transfer?
  2. What trade-offs exist between energy consumption and the achievable performance of quantum tasks, and how can these trade-offs be optimized?
  3. Are there new resource-efficient protocols specifically tailored to low-energy states or systems with restricted energy budgets?
  We aim to systematically analyze these issues, providing a deeper understanding of how resource constraints shape quantum communication and computation strategies.
• Quantum Tasks with Unknown Input States: Many practical and foundational tasks in quantum information involve scenarios where the quantum state of the input system is unknown. This raises significant challenges, as unknown states cannot be directly copied due to the no-cloning theorem, and measurement inherently disturbs the state. Our interest lies in designing efficient protocols for such tasks, particularly in the context of:
  1. State-Agnostic Quantum Communication: Can quantum communication protocols, such as those for transferring information or sharing entanglement, be designed to operate effectively even when the sender does not know the precise quantum state being communicated?
  2. Estimation of Thermodynamic Quantities: In scenarios where the quantum state is unknown, can one devise protocols for estimating thermodynamic quantities such as energy, entropy, or free energy? This could have implications for quantum thermodynamics, where practical implementations often involve limited knowledge of the underlying states.
  3. Generalized State Estimation Protocols: Beyond thermodynamic quantities, are there efficient strategies for extracting relevant information or performing computations on unknown quantum states, particularly when resources such as measurement or processing time are constrained?

By exploring these two directions—quantum protocols under energy constraints and efficient handling of unknown quantum states—we seek to advance both theoretical insights and practical methodologies in quantum information science. These investigations not only address foundational questions but also have direct implications for developing scalable, resource-efficient quantum technologies.