47 research outputs found
Self-testing graph states
We give a construction for a self-test for any connected graph state. In
other words, for each connected graph state we give a set of non-local
correlations that can only be achieved (quantumly) by that particular graph
state and certain local measurements. The number of correlations considered is
small, being linear in the number of vertices in the graph. We also prove
robustness for the test.Comment: 21 page
Self-testing in parallel
Self-testing allows us to determine, through classical interaction only,
whether some players in a non-local game share particular quantum states. Most
work on self-testing has concentrated on developing tests for small states like
one pair of maximally entangled qubits, or on tests where there is a separate
player for each qubit, as in a graph state. Here we consider the case of
testing many maximally entangled pairs of qubits shared between two players.
Previously such a test was shown where testing is sequential, i.e., one pair is
tested at a time. Here we consider the parallel case where all pairs are tested
simultaneously, giving considerably more power to dishonest players. We derive
sufficient conditions for a self-test for many maximally entangled pairs of
qubits shared between two players and also two constructions for self-tests
where all pairs are tested simultaneously.Comment: 22 page
Insider-proof encryption with applications for quantum key distribution
It has been pointed out that current protocols for device independent quantum
key distribution can leak key to the adversary when devices are used repeatedly
and that this issue has not been addressed. We introduce the notion of an
insider-proof channel. This allows us to propose a means by which devices with
memories could be reused from one run of a device independent quantum key
distribution protocol to the next while bounding the leakage to Eve, under the
assumption that one run of the protocol could be completed securely using
devices with memories.Comment: 20 pages, version 2: new presentation introducing the insider-proof
channel as a cryptographic elemen
On the power quantum computation over real Hilbert spaces
We consider the power of various quantum complexity classes with the
restriction that states and operators are defined over a real, rather than
complex, Hilbert space. It is well know that a quantum circuit over the complex
numbers can be transformed into a quantum circuit over the real numbers with
the addition of a single qubit. This implies that BQP retains its power when
restricted to using states and operations over the reals. We show that the same
is true for QMA(k), QIP(k), QMIP, and QSZK.Comment: Significant improvements from previous version, in particular showing
both containments (eg. QMA_R is in QMA and vice versa
Interactive proofs for BQP via self-tested graph states
Using the measurement-based quantum computation model, we construct
interactive proofs with non-communicating quantum provers and a classical
verifier. Our construction gives interactive proofs for all languages in BQP
with a polynomial number of quantum provers, each of which, in the honest case,
performs only a single measurement.
Our techniques use self-tested graph states. In this regard we introduce two
important improvements over previous work. Specifically, we derive new error
bounds which scale polynomially with the size of the graph compared with
exponential dependence on the size of the graph in previous work. We also
extend the self-testing error bounds on measurements to a very general set
which includes the adaptive measurements used for measurement-based quantum
computation as a special case.Comment: 53 page
Simulating quantum systems using real Hilbert spaces
We develop a means of simulating the evolution and measurement of a
multipartite quantum state under discrete or continuous evolution using another
quantum system with states and operators lying in a real Hilbert space. This
extends previous results which were unable to simulate local evolution and
measurements with local operators and was limited to discrete evolution. We
also detail applications to Bell inequalities and self-testing of quantum
apparatus.Comment: 4 page
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
Design and Analysis of RC4-like Stream Ciphers
RC4 is one of the most widely used ciphers in practical software applications. In this thesis we examine security and design aspects of RC4. First we describe the functioning of RC4 and present previously published analyses. We then present a new cipher, Chameleon which uses a similar internal organization to RC4 but uses different methods. The remainder of the thesis uses ideas from both Chameleon and RC4 to develop design strategies for new ciphers. In particular, we develop a new cipher, RC4B, with the goal of greater security with an algorithm comparable in simplicity to RC4. We also present design strategies for ciphers and two new ciphers for 32-bit processors. Finally we present versions of Chameleon and RC4B that are implemented using playing-cards