5 research outputs found
Purifying and Reversible Physical Processes
Starting from the observation that reversible processes cannot increase the
purity of any input state, we study deterministic physical processes, which map
a set of states to a set of pure states. Such a process must map any state to
the same pure output, if purity is demanded for the input set of all states.
But otherwise, when the input set is restricted, it is possible to find
non-trivial purifying processes. For the most restricted case of only two input
states, we completely characterize the output of any such map. We furthermore
consider maps, which combine the property of purity and reversibility on a set
of states, and we derive necessary and sufficient conditions on sets, which
permit such processes.Comment: 5 pages, no figures, v2: only minimal change
Quantum-secure message authentication via blind-unforgeability
Formulating and designing unforgeable authentication of classical messages in
the presence of quantum adversaries has been a challenge, as the familiar
classical notions of unforgeability do not directly translate into meaningful
notions in the quantum setting. A particular difficulty is how to fairly
capture the notion of "predicting an unqueried value" when the adversary can
query in quantum superposition. In this work, we uncover serious shortcomings
in existing approaches, and propose a new definition. We then support its
viability by a number of constructions and characterizations. Specifically, we
demonstrate a function which is secure according to the existing definition by
Boneh and Zhandry, but is clearly vulnerable to a quantum forgery attack,
whereby a query supported only on inputs that start with 0 divulges the value
of the function on an input that starts with 1. We then propose a new
definition, which we call "blind-unforgeability" (or BU.) This notion matches
"intuitive unpredictability" in all examples studied thus far. It defines a
function to be predictable if there exists an adversary which can use
"partially blinded" oracle access to predict values in the blinded region. Our
definition (BU) coincides with standard unpredictability (EUF-CMA) in the
classical-query setting. We show that quantum-secure pseudorandom functions are
BU-secure MACs. In addition, we show that BU satisfies a composition property
(Hash-and-MAC) using "Bernoulli-preserving" hash functions, a new notion which
may be of independent interest. Finally, we show that BU is amenable to
security reductions by giving a precise bound on the extent to which quantum
algorithms can deviate from their usual behavior due to the blinding in the BU
security experiment.Comment: 23+9 pages, v3: published version, with one theorem statement in the
summary of results correcte
Two-sided bounds on minimum-error quantum measurement, on the reversibility of quantum dynamics, and on the maximum overlap problem using directional iterates
In a unified framework, we obtain two-sided estimates of the following
quantities of interest in quantum information theory:
1.The minimum-error distinguishability of arbitrary ensembles of mixed
quantum states.
2.The approximate reversibility of quantum dynamics in terms of entanglement
fidelity. (This is also referred to as "channel-adapted quantum error recovery"
when the reversed channel is the composition of an encoding operation and a
noise channel.)
3.The maximum overlap between a bipartite pure quantum state and a bipartite
mixed state that may be achieved by applying a local quantum operation to one
part of the mixed state.
4. The conditional min-entropy of bipartite quantum states.
A refined version of the author's techniques [J. Math. Phys. 50, 032016] for
bounding the first quantity is employed to give two-sided estimates of the
remaining three quantities. Our primary tool is "small angle" initialization of
an abstract generalization of the iterative schemes for computing optimal
measurements and quantum error recoveries introduced by Jezek-Rehacek-Fiurasek
[Phys. Rev. A 65, 060301], Jezek-Fiurasek-Hradil [Phys. Rev. A 68, 012305], and
Reimpell-Werner [Phys. Rev. Lett 94, 080501].Comment: Extensively revised & new content added. Improved min-entropy bounds.
Notation made more accessible. Minimax theorem used to clarify relationship
between "worst case" bounds and "single instance" bounds. Improved motivation
of the choice of "small angle" guess. Eliminated spurious factor appearing
when overlap bounds are applied to state distinction. Work connected to that
of Beny and Oreshko