3,598 research outputs found
Improving Einstein-Podolsky-Rosen Steering Inequalities with State Information
We discuss the relationship between entropic Einstein-Podolsky-Rosen
(EPR)-steering inequalities and their underlying uncertainty relations, along
with the hypothesis that improved uncertainty relations lead to tighter
EPR-steering inequalities. In particular, we discuss how the intrinsic
uncertainty in a mixed quantum state is used to improve existing uncertainty
relations and how this information affects one's ability to witness
EPR-steering. As an example, we consider the recent improvement (using a
quantum memory) to the entropic uncertainty relation between pairs of discrete
observables (Nat. Phys. 6, 659 (2010)) and show that a trivial substitution of
the tighter bound in the steering inequality leads to contradictions, due in
part to the fact that the improved bound depends explicitly on the state being
measured. By considering the assumptions that enter into the development of a
steering inequality, we derive correct steering inequalities from these
improved uncertainty relations and find that they are identical to ones already
developed (Phys. Rev. A, 87, 062103 (2013)). In addition, we consider how one
can use the information about the quantum state to improve our ability to
witness EPR-steering, and develop a new symmetric EPR-steering inequality as a
result.Comment: 6 page
Uncertainty Relation for Mutual Information
We postulate the existence of a universal uncertainty relation between the
quantum and classical mutual informations between pairs of quantum systems.
Specifically, we propose that the sum of the classical mutual information,
determined by two mutually unbiased pairs of observables, never exceeds the
quantum mutual information. We call this the complementary-quantum correlation
(CQC) relation and prove its validity for pure states, for states with one
maximally mixed subsystem, and for all states when one measurement is minimally
disturbing. We provide results of a Monte Carlo simulation suggesting the CQC
relation is generally valid. Importantly, we also show that the CQC relation
represents an improvement to an entropic uncertainty principle in the presence
of a quantum memory, and that it can be used to verify an achievable secret key
rate in the quantum one-time pad cryptographic protocol.Comment: 6 pages, 2 figure
Experimental Violation of Two-Party Leggett-Garg Inequalities with Semi-weak Measurements
We generalize the derivation of Leggett-Garg inequalities to systematically
treat a larger class of experimental situations by allowing multi-particle
correlations, invasive detection, and ambiguous detector results. Furthermore,
we show how many such inequalities may be tested simultaneously with a single
setup. As a proof of principle, we violate several such two-particle
inequalities with data obtained from a polarization-entangled biphoton state
and a semi-weak polarization measurement based on Fresnel reflection. We also
point out a non- trivial connection between specific two-party Leggett-Garg
inequality violations and convex sums of strange weak values.Comment: 4 pages, 6 figure
Unconditionally verifiable blind computation
Blind Quantum Computing (BQC) allows a client to have a server carry out a
quantum computation for them such that the client's input, output and
computation remain private. A desirable property for any BQC protocol is
verification, whereby the client can verify with high probability whether the
server has followed the instructions of the protocol, or if there has been some
deviation resulting in a corrupted output state. A verifiable BQC protocol can
be viewed as an interactive proof system leading to consequences for complexity
theory. The authors, together with Broadbent, previously proposed a universal
and unconditionally secure BQC scheme where the client only needs to be able to
prepare single qubits in separable states randomly chosen from a finite set and
send them to the server, who has the balance of the required quantum
computational resources. In this paper we extend that protocol with new
functionality allowing blind computational basis measurements, which we use to
construct a new verifiable BQC protocol based on a new class of resource
states. We rigorously prove that the probability of failing to detect an
incorrect output is exponentially small in a security parameter, while resource
overhead remains polynomial in this parameter. The new resource state allows
entangling gates to be performed between arbitrary pairs of logical qubits with
only constant overhead. This is a significant improvement on the original
scheme, which required that all computations to be performed must first be put
into a nearest neighbour form, incurring linear overhead in the number of
qubits. Such an improvement has important consequences for efficiency and
fault-tolerance thresholds.Comment: 46 pages, 10 figures. Additional protocol added which allows
arbitrary circuits to be verified with polynomial securit
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