1,876 research outputs found
Distillation protocols for Fourier states in quantum computing
Fourier states are multi-qubit registers that facilitate phase rotations in
fault-tolerant quantum computing. We propose distillation protocols for
constructing the fundamental, -qubit Fourier state with error at
a cost of Toffoli gates and Clifford gates, or any arbitrary
Fourier state using gates. We analyze these protocols with methods
from digital signal processing. These results suggest that phase kickback,
which uses Fourier states, could be the current lowest-overhead method for
generating arbitrary phase rotations.Comment: 18 pages, 4 figure
Distillation Protocols for Mixed States of Multilevel Qubits and the Quantum Renormalization Group
We study several properties of distillation protocols to purify multilevel
qubit states (qudits) when applied to a certain family of initial mixed
bipartite states. We find that it is possible to use qudits states to increase
the stability region obtained with the flow equations to distill qubits. In
particular, for qutrits we get the phase diagram of the distillation process
with a rich structure of fixed points. We investigate the large- limit of
qudits protocols and find an analytical solution in the continuum limit. The
general solution of the distillation recursion relations is presented in an
appendix. We stress the notion of weight amplification for distillation
protocols as opposed to the quantum amplitude amplification that appears in the
Grover algorithm. Likewise, we investigate the relations between quantum
distillation and quantum renormalization processes.Comment: REVTEX4 file, 12 pages, 3 tables, color figure
Private states, quantum data hiding and the swapping of perfect secrecy
We derive a formal connection between quantum data hiding and quantum
privacy, confirming the intuition behind the construction of bound entangled
states from which secret bits can be extracted. We present three main results.
First, we show how to simplify the class of private states and related states
via reversible local operation and one-way communication. Second, we obtain a
bound on the one-way distillable entanglement of private states in terms of
restricted relative entropy measures, which is tight in many cases and shows
that protocols for one-way distillation of key out of states with low
distillable entanglement lead to the distillation of data hiding states. Third,
we consider the problem of extending the distance of quantum key distribution
with help of intermediate stations. In analogy to the quantum repeater, this
paradigm has been called the quantum key repeater. We show that when extending
private states with one-way communication, the resulting rate is bounded by the
one-way distillable entanglement. In order to swap perfect secrecy it is thus
essentially optimal to use entanglement swapping.Comment: v3 published version, some details of the main proofs have been moved
to the appendix, 21 pages. v2 claims changed from LOCC to one-way LOCC in the
process of correcting a mistake found in v1 (in proof of Lemma 3). v1: 15
pages, 9 figure
- …