8 research outputs found
Quantum Stopwatch: How To Store Time in a Quantum Memory
Quantum mechanics imposes a fundamental tradeoff between the accuracy of time
measurements and the size of the systems used as clocks. When the measurements
of different time intervals are combined, the errors due to the finite clock
size accumulate, resulting in an overall inaccuracy that grows with the
complexity of the setup. Here we introduce a method that in principle eludes
the accumulation of errors by coherently transferring information from a
quantum clock to a quantum memory of the smallest possible size. Our method
could be used to measure the total duration of a sequence of events with
enhanced accuracy, and to reduce the amount of quantum communication needed to
stabilize clocks in a quantum network.Comment: 10 + 5 pages, 3 figure
Compression for quantum population coding
We study the compression of n quantum systems, each prepared in the same
state belonging to a given parametric family of quantum states. For a family of
states with f independent parameters, we devise an asymptotically faithful
protocol that requires a hybrid memory of size (f/2)log(n), including both
quantum and classical bits. Our construction uses a quantum version of local
asymptotic normality and, as an intermediate step, solves the problem of
compressing displaced thermal states of n identically prepared modes. In both
cases, we show that (f/2)log(n) is the minimum amount of memory needed to
achieve asymptotic faithfulness. In addition, we analyze how much of the memory
needs to be quantum. We find that the ratio between quantum and classical bits
can be made arbitrarily small, but cannot reach zero: unless all the quantum
states in the family commute, no protocol using only classical bits can be
faithful, even if it uses an arbitrarily large number of classical bits.Comment: 14 Pages, 4 Figures + Appendi
An efficient high dimensional quantum Schur transform
The Schur transform is a unitary operator that block diagonalizes the action
of the symmetric and unitary groups on an fold tensor product of a vector space of dimension . Bacon, Chuang and Harrow
\cite{BCH07} gave a quantum algorithm for this transform that is polynomial in
, and , where is the precision. In a
footnote in Harrow's thesis \cite{H05}, a brief description of how to make the
algorithm of \cite{BCH07} polynomial in is given using the unitary
group representation theory (however, this has not been explained in detail
anywhere. In this article, we present a quantum algorithm for the Schur
transform that is polynomial in , and using a
different approach. Specifically, we build this transform using the
representation theory of the symmetric group and in this sense our technique
can be considered a "dual" algorithm to \cite{BCH07}. A novel feature of our
algorithm is that we construct the quantum Fourier transform over the so called
\emph{permutation modules}, which could have other applications.Comment: 21 page
Optimal Compression for Identically Prepared Qubit States
accepted for oral presentationWe establish the ultimate limits to the compression of sequences of identically prepared qubits. The limits are determined by Holevo’s information quantity and are attained through use of the optimal universal cloning machine, which finds here a novel application to quantum Shannon theory