142 research outputs found
Quantum thermodynamics with missing reference frames: Decompositions of free energy into non-increasing components
If an absolute reference frame with respect to time, position, or orientation
is missing one can only implement quantum operations which are covariant with
respect to the corresponding unitary symmetry group G. Extending observations
of Vaccaro et al., I argue that the free energy of a quantum system with
G-invariant Hamiltonian then splits up into the Holevo information of the orbit
of the state under the action of G and the free energy of its orbit average.
These two kinds of free energy cannot be converted into each other. The first
component is subadditive and the second superadditive; in the limit of
infinitely many copies only the usual free energy matters.
Refined splittings of free energy into more than two independent
(non-increasing) terms can be defined by averaging over probability measures on
G that differ from the Haar measure.
Even in the presence of a reference frame, these results provide lower bounds
on the amount of free energy that is lost after applying a covariant channel.
If the channel properly decreases one of these quantities, it decreases the
free energy necessarily at least by the same amount, since it is unable to
convert the different forms of free energies into each other.Comment: 17 pages, latex, 1 figur
A Complexity Measure for Continuous Time Quantum Algorithms
We consider unitary dynamical evolutions on n qubits caused by time dependent
pair-interaction Hamiltonians and show that the running time of a parallelized
two-qubit gate network simulating the evolution is given by the time integral
over the chromatic index of the interaction graph. This defines a complexity
measure of continuous and discrete quantum algorithms which are in exact
one-to-one correspondence. Furthermore we prove a lower bound on the growth of
large-scale entanglement depending on the chromatic index.Comment: 6 pages, Revte
Spin-1/2 particles moving on a 2D lattice with nearest-neighbor interactions can realize an autonomous quantum computer
What is the simplest Hamiltonian which can implement quantum computation
without requiring any control operations during the computation process? In a
previous paper we have constructed a 10-local finite-range interaction among
qubits on a 2D lattice having this property. Here we show that
pair-interactions among qutrits on a 2D lattice are sufficient, too, and can
also implement an ergodic computer where the result can be read out from the
time average state after some post-selection with high success probability.
Two of the 3 qutrit states are given by the two levels of a spin-1/2 particle
located at a specific lattice site, the third state is its absence. Usual
hopping terms together with an attractive force among adjacent particles induce
a coupled quantum walk where the particle spins are subjected to spatially
inhomogeneous interactions implementing holonomic quantum computing. The
holonomic method ensures that the implemented circuit does not depend on the
time needed for the walk.
Even though the implementation of the required type of spin-spin interactions
is currently unclear, the model shows that quite simple Hamiltonians are
powerful enough to allow for universal quantum computing in a closed physical
system.Comment: More detailed explanations including description of a programmable
version. 44 pages, 12 figures, latex. To appear in PR
Quantum control without access to the controlling interaction
In our model a fixed Hamiltonian acts on the joint Hilbert space of a quantum
system and its controller. We show under which conditions measurements, state
preparations, and unitary implementations on the system can be performed by
quantum operations on the controller only.
It turns out that a measurement of the observable A and an implementation of
the one-parameter group exp(iAr) can be performed by almost the same sequence
of control operations. Furthermore measurement procedures for A+B, for (AB+BA),
and for i[A,B] can be constructed from measurements of A and B. This shows that
the algebraic structure of the set of observables can be explained by the Lie
group structure of the unitary evolutions on the joint Hilbert space of the
measuring device and the measured system.
A spin chain model with nearest neighborhood coupling shows that the border
line between controller and system can be shifted consistently.Comment: 10 pages, Revte
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
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
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
Relating the thermodynamic arrow of time to the causal arrow
Consider a Hamiltonian system that consists of a slow subsystem S and a fast
subsystem F. The autonomous dynamics of S is driven by an effective
Hamiltonian, but its thermodynamics is unexpected. We show that a well-defined
thermodynamic arrow of time (second law) emerges for S whenever there is a
well-defined causal arrow from S to F and the back-action is negligible. This
is because the back-action of F on S is described by a non-globally Hamiltonian
Born-Oppenheimer term that violates the Liouville theorem, and makes the second
law inapplicable to S. If S and F are mixing, under the causal arrow condition
they are described by microcanonic distributions P(S) and P(S|F). Their
structure supports a causal inference principle proposed recently in machine
learning.Comment: 10 page
Universal quantum interfaces
To observe or control a quantum system, one must interact with it via an
interface. This letter exhibits simple universal quantum interfaces--quantum
input/output ports consisting of a single two-state system or quantum bit that
interacts with the system to be observed or controlled. It is shown that under
very general conditions the ability to observe and control the quantum bit on
its own implies the ability to observe and control the system itself. The
interface can also be used as a quantum communication channel, and multiple
quantum systems can be connected by interfaces to become an efficient universal
quantum computer. Experimental realizations are proposed, and implications for
controllability, observability, and quantum information processing are
explored.Comment: 4 pages, 3 figures, RevTe
A measure of majorisation emerging from single-shot statistical mechanics
The use of the von Neumann entropy in formulating the laws of thermodynamics
has recently been challenged. It is associated with the average work whereas
the work guaranteed to be extracted in any single run of an experiment is the
more interesting quantity in general. We show that an expression that
quantifies majorisation determines the optimal guaranteed work. We argue it
should therefore be the central quantity of statistical mechanics, rather than
the von Neumann entropy. In the limit of many identical and independent
subsystems (asymptotic i.i.d) the von Neumann entropy expressions are recovered
but in the non-equilbrium regime the optimal guaranteed work can be radically
different to the optimal average. Moreover our measure of majorisation governs
which evolutions can be realized via thermal interactions, whereas the
nondecrease of the von Neumann entropy is not sufficiently restrictive. Our
results are inspired by single-shot information theory.Comment: 54 pages (15+39), 9 figures. Changed title / changed presentation,
same main results / added minor result on pure bipartite state entanglement
(appendix G) / near to published versio
- …