Alladi Ramakrishnan Hall

Tighter and Stronger Quantum Speed Limits for General Quantum States

Shrobona Bagchi

Center for Quantum Information, Korea Institute of Science and Technology, Seoul, South Korea

The quantum speed limit provides a fundamental bound on how fast a quantum
system can evolve between the initial and the final states under any
physical operation. The celebrated Mandelstam-Tamm (MT) bound has been
widely studied for various quantum systems undergoing unitary time
evolution. Not only of fundamental importance, but motivated by the immense
potential for it to be useful in quantum metrology and practical quantum
technology, we find out newer quantum speed limit bounds from time energy
uncertainty relations. Specifically, here we derive a tighter uncertainty
relation for general mixed quantum states and then derive a new quantum
speed limit for general quantum states from it such that it reduces to that
of the pure quantum states derived from tighter uncertainty relations. We
show that the MT bound is a special case of the tighter quantum speed limit
derived here. We also show that this bound can be improved when optimized
over many different sets of basis vectors. We illustrate the tighter speed
limit for pure states with examples using random Hamiltonians and show that
the new quantum speed limit outperforms the MT bound. Thereafter, we derive
a quantum speed limit for mixed quantum states using the stronger
uncertainty relation for mixed quantum states and unitary evolution. We
also show that this bound can be optimized over different choices of
operators for obtaining a better bound. We illustrate this bound with some
examples and show its better performance with respect to some important
earlier and recent bounds. Our work will thus be useful in various areas of
quantum metrology and quantum control.