Quantum theory is based on few postulates, yet it has a very rich structure
and amazing predictive power. Whatever is allowed by the rules of
quantum mechanics
that is going to happen sooner or later (it is a matter of technological
development). Below you will find that some of our quantum predictions
have been experimentally tested.
- We have proved the no-deletion theorem in quantum information
theory. This is also known as the Pati-Braunstein theorem in the literature.
Like the no-cloning theorem this is another fundamental limitation on
quantum information. This says that given two identical copies of an unknown
quantum state we cannot delete a copy against the other. This has opened up a
new direction of research. It has gone into text books of quantum
information theory and is part of regular course at many Universities
(eg Stanford University).
- Along with other collaborators (E. Sjoqvist, A. Ekert, J. S. Anandan,
M. Ericsson, D. K. L. Oi and V.Vedral) we have introduced the concept of
geometric phase for mixed states undergoing unitary time evolution.
This has opened up another direction of research. Recently, several groups have
experimentally tested our geometric phase for mixed quantum states.
These ideas may play an important role in geometric quantum computation.
- We have proposed the exact remote state preparation (RSP) protocol
for special class of qubits. Using this protocol one can prepare a known
qubit with the help of one EPR state and communication of one classical bit.
Also, we have shown that any single qubit measurement statistics can be
simulated for any arbitrary qubit at a remote location using one EPR pair and
one classical bit. This is called remote state measurement (RSM). Like
quantum teleportation,
RSP has become another quantum communication protocol.
Recently, several groups have verified our RSP protocol for special class of
qubit states.
- We have shown the necessity of quantum
entanglement in Grover's algorithm in pure state and pseudo-pure state
implementations. Earlier there have been doubts whether one needs
entanglement or just linear superposition would be enough to achieve
the speed-up.
- In collaboration with S. L. Braunstein we have proved the
no-hiding theorem for quantum information and its
robustness to imperfect hiding process. Accordingly, if the original
quantum information is missing from one subsystem then it must be found in
the reminder of the subsystem and moreover this cannot be hidden in the
correlations. This has several applications that includes quantum
teleportation, any physical process leading to thermalization and black
hole information loss paradox.
- Recently, Anil Kumar and his group has experimentally tested the
no-hiding theorem in state randomization of an arbitrary qubit. When a qubit in
a pure state is randomized it is transformed to a completely random mixture.
In this process the original information is completely lost from the system.
However, in accordance with the no-hiding theorem the lost information is
indeed recovered from the ancilla qubits using NMR setup. This experiment
constitute the first experimental test of conservation of quantum information.
- Heisenberg-Robertson's uncertainty relation expresses a limitation in
the possible preparations of the system by giving a lower bound to the
product of the variances of two observables in terms of their
commutator. However, it does not capture the concept of incompatible
observables because it can be trivial, i.e., the lower bound can be null
even for two non-compatible observables. ALong with L. Maccone we have
proved two stronger
uncertainty relations, relating to the sum of variances, whose lower bound
is guaranteed to be nontrivial whenever the two observables are
incompatible on the state of the system. Recently, the new uncertainty
relations have been tested in experiment. This is also highlighted in
NATURE ASIA.