16 research outputs found
Gibbs-Preserving Maps outperform Thermal Operations in the quantum regime
In this brief note, we compare two frameworks for characterizing possible
operations in quantum thermodynamics. One framework considers Thermal
Operations---unitaries which conserve energy. The other framework considers all
maps which preserve the Gibbs state at a given temperature. Thermal Operations
preserve the Gibbs state; hence a natural question which arises is whether the
two frameworks are equivalent. Classically, this is true---Gibbs-Preserving
Maps are no more powerful than Thermal Operations. Here, we show that this no
longer holds in the quantum regime: a Gibbs-Preserving Map can generate
coherent superpositions of energy levels while Thermal Operations cannot. This
gap has an impact on clarifying a mathematical framework for quantum
thermodynamics.Comment: 4 pages, 1 figur
A single-shot measurement of the energy of product states in a translation invariant spin chain can replace any quantum computation
In measurement-based quantum computation, quantum algorithms are implemented
via sequences of measurements. We describe a translationally invariant
finite-range interaction on a one-dimensional qudit chain and prove that a
single-shot measurement of the energy of an appropriate computational basis
state with respect to this Hamiltonian provides the output of any quantum
circuit. The required measurement accuracy scales inverse polynomially with the
size of the simulated quantum circuit. This shows that the implementation of
energy measurements on generic qudit chains is as hard as the realization of
quantum computation. Here a ''measurement'' is any procedure that samples from
the spectral measure induced by the observable and the state under
consideration. As opposed to measurement-based quantum computation, the
post-measurement state is irrelevant.Comment: 19 pages, transition rules for the CA correcte
Is there a physically universal cellular automaton or Hamiltonian?
It is known that both quantum and classical cellular automata (CA) exist that
are computationally universal in the sense that they can simulate, after
appropriate initialization, any quantum or classical computation, respectively.
Here we introduce a different notion of universality: a CA is called physically
universal if every transformation on any finite region can be (approximately)
implemented by the autonomous time evolution of the system after the complement
of the region has been initialized in an appropriate way. We pose the question
of whether physically universal CAs exist. Such CAs would provide a model of
the world where the boundary between a physical system and its controller can
be consistently shifted, in analogy to the Heisenberg cut for the quantum
measurement problem. We propose to study the thermodynamic cost of computation
and control within such a model because implementing a cyclic process on a
microsystem may require a non-cyclic process for its controller, whereas
implementing a cyclic process on system and controller may require the
implementation of a non-cyclic process on a "meta"-controller, and so on.
Physically universal CAs avoid this infinite hierarchy of controllers and the
cost of implementing cycles on a subsystem can be described by mixing
properties of the CA dynamics. We define a physical prior on the CA
configurations by applying the dynamics to an initial state where half of the
CA is in the maximum entropy state and half of it is in the all-zero state
(thus reflecting the fact that life requires non-equilibrium states like the
boundary between a hold and a cold reservoir). As opposed to Solomonoff's
prior, our prior does not only account for the Kolmogorov complexity but also
for the cost of isolating the system during the state preparation if the
preparation process is not robust.Comment: 27 pages, 1 figur
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