7 research outputs found
Device-independent parallel self-testing of two singlets
Device-independent self-testing is the possibility of certifying the quantum
state and the measurements, up to local isometries, using only the statistics
observed by querying uncharacterized local devices. In this paper, we study
parallel self-testing of two maximally entangled pairs of qubits: in
particular, the local tensor product structure is not assumed but derived. We
prove two criteria that achieve the desired result: a double use of the
Clauser-Horne-Shimony-Holt inequality and the Magic Square game.
This demonstrate that the magic square game can only be perfectly won by
measureing a two-singlets state. The tolerance to noise is well within reach of
state-of-the-art experiments.Comment: 9 pages, 2 figure
Reliable quantum certification for photonic quantum technologies
A major roadblock for large-scale photonic quantum technologies is the lack
of practical reliable certification tools. We introduce an experimentally
friendly - yet mathematically rigorous - certification test for experimental
preparations of arbitrary m-mode pure Gaussian states, pure non-Gaussian states
generated by linear-optical circuits with n-boson Fock-basis states as inputs,
and states of these two classes subsequently post-selected with local
measurements on ancillary modes. The protocol is efficient in m and the inverse
post-selection success probability for all Gaussian states and all mentioned
non-Gaussian states with constant n. We follow the mindset of an untrusted
prover, who prepares the state, and a skeptic certifier, with classical
computing and single-mode homodyne-detection capabilities only. No assumptions
are made on the type of noise or capabilities of the prover. Our technique
exploits an extremality-based fidelity bound whose estimation relies on
non-Gaussian state nullifiers, which we introduce on the way as a byproduct
result. The certification of many-mode photonic networks, as those used for
photonic quantum simulations, boson samplers, and quantum metrology, is now
within reach.Comment: 8 pages + 20 pages appendix, 2 figures, results generalized to
scenarios with post-selection, presentation improve
An Application of Quantum Finite Automata to Interactive Proof Systems
Quantum finite automata have been studied intensively since their
introduction in late 1990s as a natural model of a quantum computer with
finite-dimensional quantum memory space. This paper seeks their direct
application to interactive proof systems in which a mighty quantum prover
communicates with a quantum-automaton verifier through a common communication
cell. Our quantum interactive proof systems are juxtaposed to
Dwork-Stockmeyer's classical interactive proof systems whose verifiers are
two-way probabilistic automata. We demonstrate strengths and weaknesses of our
systems and further study how various restrictions on the behaviors of
quantum-automaton verifiers affect the power of quantum interactive proof
systems.Comment: This is an extended version of the conference paper in the
Proceedings of the 9th International Conference on Implementation and
Application of Automata, Lecture Notes in Computer Science, Springer-Verlag,
Kingston, Canada, July 22-24, 200
Nonlocality under Computational Assumptions
Nonlocality and its connections to entanglement are fundamental features of
quantum mechanics that have found numerous applications in quantum information
science. A set of correlations is said to be nonlocal if it cannot be
reproduced by spacelike-separated parties sharing randomness and performing
local operations. An important practical consideration is that the runtime of
the parties has to be shorter than the time it takes light to travel between
them. One way to model this restriction is to assume that the parties are
computationally bounded. We therefore initiate the study of nonlocality under
computational assumptions and derive the following results:
(a) We define the set (not-efficiently-local) as consisting of
all bipartite states whose correlations arising from local measurements cannot
be reproduced with shared randomness and \emph{polynomial-time} local
operations.
(b) Under the assumption that the Learning With Errors problem cannot be
solved in \emph{quantum} polynomial-time, we show that
, where is the set of \emph{all}
bipartite entangled states (pure and mixed). This is in contrast to the
standard notion of nonlocality where it is known that some entangled states,
e.g. Werner states, are local. In essence, we show that there exist (efficient)
local measurements producing correlations that cannot be reproduced through
shared randomness and quantum polynomial-time computation.
(c) We prove that if unconditionally, then
. In other words, the ability to certify all
bipartite entangled states against computationally bounded adversaries gives a
non-trivial separation of complexity classes.
(d) Using (c), we show that a certain natural class of 1-round delegated
quantum computation protocols that are sound against provers
cannot exist.Comment: 65 page