4 research outputs found
All Real Projective Measurements Can be Self-tested
Self-testing is the strongest form of quantum functionality verification
which allows a classical user to deduce the quantum state and measurements used
to produce measurement statistics. While self-testing of quantum states is
well-understood, self-testing of measurements, especially in high dimensions,
has remained more elusive. We demonstrate the first general result in this
direction by showing that every real projective measurement can be self-tested.
The standard definition of self-testing only allows for the certification of
real measurements. Therefore, our work effectively broadens the scope of
self-testable projective measurements to their full potential. To reach this
result, we employ the idea that existing self-tests can be extended to verify
additional untrusted measurements. This is known as `post-hoc self-testing'. We
formalize the method of post-hoc self-testing and establish a sufficient
condition for its application. Using this condition we construct self-tests for
all real projective measurements. Inspired by our construction, we develop a
new technique of iterative self-testing, which involves using post-hoc
self-testing in a sequential manner. Starting from any established self-test,
we fully characterize the set of measurements that can be verified via
iterative self-testing. This provides a clear methodology for constructing new
self-tests from pre-existing ones.Comment: 25 pages, 2 figures. Authors in alphabetical order. More
comprehensive abstract and introduction. Minor typos fixe
A mathematical foundation for self-testing: Lifting common assumptions
In this work we study the phenomenon of self-testing from the first
principles, aiming to place this versatile concept on a rigorous mathematical
footing. Self-testing allows a classical verifier to infer a quantum mechanical
description of untrusted quantum devices that she interacts with in a black-box
manner. Somewhat contrary to the black-box paradigm, existing self-testing
results tend to presuppose conditions that constrain the operation of the
untrusted devices. A common assumption is that these devices perform a
projective measurement of a pure quantum state. Naturally, in the absence of
any prior knowledge it would be appropriate to model these devices as measuring
a mixed state using POVM measurements, since the purifying/dilating spaces
could be held by the environment or an adversary.
We prove a general theorem allowing to remove these assumptions, thereby
promoting most existing self-testing results to their assumption-free variants.
On the other hand, we pin-point situations where assumptions cannot be lifted
without loss of generality. As a key (counter)example we identify a quantum
correlation which is a self-test only if certain assumptions are made.
Remarkably, this is also the first example of a correlation that cannot be
implemented using projective measurements on a bipartite state of full Schmidt
rank. Finally, we compare existing self-testing definitions, establishing many
equivalences as well as identifying subtle differences.Comment: 43 pages, 2 figure