36 research outputs found
Improved quantum metrology using quantum error-correction
We consider quantum metrology in noisy environments, where the effect of
noise and decoherence limits the achievable gain in precision by quantum
entanglement. We show that by using tools from quantum error-correction this
limitation can be overcome. This is demonstrated in two scenarios, including a
many-body Hamiltonian with single-qubit dephasing or depolarizing noise, and a
single-body Hamiltonian with transversal noise. In both cases we show that
Heisenberg scaling, and hence a quadratic improvement over the classical case,
can be retained. Moreover, for the case of frequency estimation we find that
the inclusion of error-correction allows, in certain instances, for a finite
optimal interrogation time even in the asymptotic limit.Comment: Version 2 is the published version. Appendices contain Supplemental
materia
Macroscopic superpositions require tremendous measurement devices
We consider fundamental limits on the detectable size of macroscopic quantum
superpositions. We argue that a full quantum mechanical treatment of system
plus measurement device is required, and that a (classical) reference frame for
phase or direction needs to be established to certify the quantum state. When
taking the size of such a classical reference frame into account, we show that
to reliably distinguish a quantum superposition state from an incoherent
mixture requires a measurement device that is quadratically bigger than the
superposition state. Whereas for moderate system sizes such as generated in
previous experiments this is not a stringent restriction, for macroscopic
superpositions of the size of a cat the required effort quickly becomes
intractable, requiring measurement devices of the size of the Earth. We
illustrate our results using macroscopic superposition states of photons,
spins, and position. Finally, we also show how this limitation can be
circumvented by dealing with superpositions in relative degrees of freedom.Comment: 20 pages (including appendices), 1 Figur
On the epistemic view of quantum states
We investigate the strengths and limitations of the Spekkens toy model, which
is a local hidden variable model that replicates many important properties of
quantum dynamics. First, we present a set of five axioms that fully encapsulate
Spekkens' toy model. We then test whether these axioms can be extended to
capture more quantum phenomena, by allowing operations on epistemic as well as
ontic states. We discover that the resulting group of operations is isomorphic
to the projective extended Clifford Group for two qubits. This larger group of
operations results in a physically unreasonable model; consequently, we claim
that a relaxed definition of valid operations in Spekkens' toy model cannot
produce an equivalence with the Clifford Group for two qubits. However, the new
operations do serve as tests for correlation in a two toy bit model, analogous
to the well known Horodecki criterion for the separability of quantum states.Comment: 16 pages, 9 figure
Accessible coherence in open quantum system dynamics
Quantum coherence generated in a physical process can only be cast as a potentially useful resource if its effects can be detected at a later time. Recently, the notion of non-coherence-generating-and-detecting (NCGD) dynamics has been introduced and related to the classicality of the statistics associated with sequential measurements at different times. However, in order for a dynamics to be NCGD, its propagators need to satisfy a given set of conditions for all triples of consecutive times. We reduce this to a finite set of d(d 121) conditions, where d is the dimension of the quantum system, provided that the generator is time-independent. Further conditions are derived for the more general time-dependent case. The application of this result to the case of a qubit dynamics allows us to elucidate which kind of noise gives rise to non-coherence-generation-and-detection