210 research outputs found
A Quantum Broadcasting Problem in Classical Low Power Signal Processing
We pose a problem called ``broadcasting Holevo-information'': given an
unknown state taken from an ensemble, the task is to generate a bipartite state
transfering as much Holevo-information to each copy as possible.
We argue that upper bounds on the average information over both copies imply
lower bounds on the quantum capacity required to send the ensemble without
information loss. This is because a channel with zero quantum capacity has a
unitary extension transfering at least as much information to its environment
as it transfers to the output.
For an ensemble being the time orbit of a pure state under a Hamiltonian
evolution, we derive such a bound on the required quantum capacity in terms of
properties of the input and output energy distribution. Moreover, we discuss
relations between the broadcasting problem and entropy power inequalities.
The broadcasting problem arises when a signal should be transmitted by a
time-invariant device such that the outgoing signal has the same timing
information as the incoming signal had. Based on previous results we argue that
this establishes a link between quantum information theory and the theory of
low power computing because the loss of timing information implies loss of free
energy.Comment: 28 pages, late
Simulating Hamiltonians in Quantum Networks: Efficient Schemes and Complexity Bounds
We address the problem of simulating pair-interaction Hamiltonians in n node
quantum networks where the subsystems have arbitrary, possibly different,
dimensions. We show that any pair-interaction can be used to simulate any other
by applying sequences of appropriate local control sequences. Efficient schemes
for decoupling and time reversal can be constructed from orthogonal arrays.
Conditions on time optimal simulation are formulated in terms of spectral
majorization of matrices characterizing the coupling parameters. Moreover, we
consider a specific system of n harmonic oscillators with bilinear interaction.
In this case, decoupling can efficiently be achieved using the combinatorial
concept of difference schemes. For this type of interactions we present optimal
schemes for inversion.Comment: 19 pages, LaTeX2
Decomposition of time-covariant operations on quantum systems with continuous and/or discrete energy spectrum
Every completely positive map G that commutes which the Hamiltonian time
evolution is an integral or sum over (densely defined) CP-maps G_\sigma where
\sigma is the energy that is transferred to or taken from the environment. If
the spectrum is non-degenerated each G_\sigma is a dephasing channel followed
by an energy shift. The dephasing is given by the Hadamard product of the
density operator with a (formally defined) positive operator. The Kraus
operator of the energy shift is a partial isometry which defines a translation
on R with respect to a non-translation-invariant measure.
As an example, I calculate this decomposition explicitly for the rotation
invariant gaussian channel on a single mode.
I address the question under what conditions a covariant channel destroys
superpositions between mutually orthogonal states on the same orbit. For
channels which allow mutually orthogonal output states on the same orbit, a
lower bound on the quantum capacity is derived using the Fourier transform of
the CP-map-valued measure (G_\sigma).Comment: latex, 33 pages, domains of unbounded operators are now explicitly
specified. Presentation more detailed. Implementing the shift after the
dephasing is sometimes more convenien
Distinguishing n Hamiltonians on C^n by a single measurement
If an experimentalist wants to decide which one of n possible Hamiltonians
acting on an n dimensional Hilbert space is present, he can conjugate the time
evolution by an appropriate sequence of known unitary transformations in such a
way that the different Hamiltonians result in mutual orthogonal final states.
We present a general scheme providing such a sequence.Comment: 4 pages, Revte
Fragility of a class of highly entangled states of many quantum-bits
We consider a Quantum Computer with n quantum-bits (`qubits'), where each
qubit is coupled independently to an environment affecting the state in a
dephasing or depolarizing way. For mixed states we suggest a quantification for
the property of showing {\it quantum} uncertainty on the macroscopic level. We
illustrate in which sense a large parameter can be seen as an indicator for
large entanglement and give hypersurfaces enclosing the set of separable
states. Using methods of the classical theory of maximum likelihood estimation
we prove that this parameter is decreasing with 1/\sqrt{n} for all those states
which have been exposed to the environment.
Furthermore we consider a Quantum Computer with perfect 1-qubit gates and
2-qubit gates with depolarizing error and show that any state which can be
obtained from a separable initial state lies inbetween a family of pairs of
certain hypersurfaces parallel to those enclosing the separable ones.Comment: 9 Pages, RevTe
Fundamental limitations for quantum and nano thermodynamics
The relationship between thermodynamics and statistical physics is valid in
the thermodynamic limit - when the number of particles becomes very large.
Here, we study thermodynamics in the opposite regime - at both the nano scale,
and when quantum effects become important. Applying results from quantum
information theory we construct a theory of thermodynamics in these limits. We
derive general criteria for thermodynamical state transformations, and as
special cases, find two free energies: one that quantifies the
deterministically extractable work from a small system in contact with a heat
bath, and the other that quantifies the reverse process. We find that there are
fundamental limitations on work extraction from nonequilibrium states, owing to
finite size effects and quantum coherences. This implies that thermodynamical
transitions are generically irreversible at this scale. As one application of
these methods, we analyse the efficiency of small heat engines and find that
they are irreversible during the adiabatic stages of the cycle.Comment: Final, published versio
Thermodynamic efficiency of information and heat flow
A basic task of information processing is information transfer (flow). Here
we study a pair of Brownian particles each coupled to a thermal bath at
temperature and , respectively. The information flow in such a
system is defined via the time-shifted mutual information. The information flow
nullifies at equilibrium, and its efficiency is defined as the ratio of flow
over the total entropy production in the system. For a stationary state the
information flows from higher to lower temperatures, and its the efficiency is
bound from above by . This upper bound is
imposed by the second law and it quantifies the thermodynamic cost for
information flow in the present class of systems. It can be reached in the
adiabatic situation, where the particles have widely different characteristic
times. The efficiency of heat flow|defined as the heat flow over the total
amount of dissipated heat|is limited from above by the same factor. There is a
complementarity between heat- and information-flow: the setup which is most
efficient for the former is the least efficient for the latter and {\it vice
versa}. The above bound for the efficiency can be [transiently] overcome in
certain non-stationary situations, but the efficiency is still limited from
above. We study yet another measure of information-processing [transfer
entropy] proposed in literature. Though this measure does not require any
thermodynamic cost, the information flow and transfer entropy are shown to be
intimately related for stationary states.Comment: 19 pages, 1 figur
Complexity of decoupling and time-reversal for n spins with pair-interactions: Arrow of time in quantum control
Well-known Nuclear Magnetic Resonance experiments show that the time
evolution according to (truncated) dipole-dipole interactions between n spins
can be inverted by simple pulse sequences. Independent of n, the reversed
evolution is only two times slower than the original one. Here we consider more
general spin-spin couplings with long range. We prove that some are
considerably more complex to invert since the number of required time steps and
the slow-down of the reversed evolutions are necessarily of the order n.
Furthermore, the spins have to be addressed separately. We show for which
values of the coupling parameters the phase transition between simple and
complex time-reversal schemes occurs.Comment: Completely rewritten, new lower bounds on the number of time steps,
applications and references adde
On the entropy production of time series with unidirectional linearity
There are non-Gaussian time series that admit a causal linear autoregressive
moving average (ARMA) model when regressing the future on the past, but not
when regressing the past on the future. The reason is that, in the latter case,
the regression residuals are only uncorrelated but not statistically
independent of the future. In previous work, we have experimentally verified
that many empirical time series indeed show such a time inversion asymmetry.
For various physical systems, it is known that time-inversion asymmetries are
linked to the thermodynamic entropy production in non-equilibrium states. Here
we show that such a link also exists for the above unidirectional linearity.
We study the dynamical evolution of a physical toy system with linear
coupling to an infinite environment and show that the linearity of the dynamics
is inherited to the forward-time conditional probabilities, but not to the
backward-time conditionals. The reason for this asymmetry between past and
future is that the environment permanently provides particles that are in a
product state before they interact with the system, but show statistical
dependencies afterwards. From a coarse-grained perspective, the interaction
thus generates entropy. We quantitatively relate the strength of the
non-linearity of the backward conditionals to the minimal amount of entropy
generation.Comment: 16 page
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