675 research outputs found
Quantum state targeting
We introduce a new primitive for quantum communication that we term "state
targeting" wherein the goal is to pass a test for a target state even though
the system upon which the test is performed is submitted prior to learning the
target state's identity. Success in state targeting can be described as having
some control over the outcome of the test. We show that increasing one's
control above a minimum amount implies an unavoidable increase in the
probability of failing the test. This is analogous to the unavoidable
disturbance to a quantum state that results from gaining information about its
identity, and can be shown to be a purely quantum effect. We provide some
applications of the results to the security analysis of cryptographic tasks
implemented between remote antagonistic parties. Although we focus on weak coin
flipping, the results are significant for other two-party protocols, such as
strong coin flipping, partially binding and concealing bit commitment, and bit
escrow. Furthermore, the results have significance not only for the traditional
notion of security in cryptography, that of restricting a cheater's ability to
bias the outcome of the protocol, but also on a novel notion of security that
arises only in the quantum context, that of cheat-sensitivity. Finally, our
analysis of state targeting leads to some interesting secondary results, for
instance, a generalization of Uhlmann's theorem and an operational
interpretation of the fidelity between two mixed states
An Entanglement-Based Protocol For Strong Coin Tossing With Bias 1/4
In the literature, strong coin tossing protocols based on bit commitment have
been proposed. Here we examine a protocol that instead tries to achieve the
task by sharing entanglement securely. The protocol uses only qubits, and has
bias 1/4. This is equal to the best known bias for bit commitment based
schemes.Comment: 4 pages, no figures. Title changed, and paragraph "Additional Notes"
adde
Pooling quantum states obtained by indirect measurements
We consider the pooling of quantum states when Alice and Bob both have one
part of a tripartite system and, on the basis of measurements on their
respective parts, each infers a quantum state for the third part S. We denote
the conditioned states which Alice and Bob assign to S by alpha and beta
respectively, while the unconditioned state of S is rho. The state assigned by
an overseer, who has all the data available to Alice and Bob, is omega. The
pooler is told only alpha, beta, and rho. We show that for certain classes of
tripartite states, this information is enough for her to reconstruct omega by
the formula omega \propto alpha rho^{-1} beta. Specifically, we identify two
classes of states for which this pooling formula works: (i) all pure states for
which the rank of rho is equal to the product of the ranks of the states of
Alice's and Bob's subsystems; (ii) all mixtures of tripartite product states
that are mutually orthogonal on S.Comment: Corrected a mistake regarding the scope of our original result. This
version to be published in Phys. Rev. A. 6 pages, 1 figur
Contextual advantage for state discrimination
Finding quantitative aspects of quantum phenomena which cannot be explained
by any classical model has foundational importance for understanding the
boundary between classical and quantum theory. It also has practical
significance for identifying information processing tasks for which those
phenomena provide a quantum advantage. Using the framework of generalized
noncontextuality as our notion of classicality, we find one such nonclassical
feature within the phenomenology of quantum minimum error state discrimination.
Namely, we identify quantitative limits on the success probability for minimum
error state discrimination in any experiment described by a noncontextual
ontological model. These constraints constitute noncontextuality inequalities
that are violated by quantum theory, and this violation implies a quantum
advantage for state discrimination relative to noncontextual models.
Furthermore, our noncontextuality inequalities are robust to noise and are
operationally formulated, so that any experimental violation of the
inequalities is a witness of contextuality, independently of the validity of
quantum theory. Along the way, we introduce new methods for analyzing
noncontextuality scenarios, and demonstrate a tight connection between our
minimum error state discrimination scenario and a Bell scenario.Comment: 18 pages, 9 figure
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