Towards a unified approach to information-disturbance tradeoffs in quantum measurements

We show that the global balance of information dynamics for general quantum measurements given in [F. Buscemi, M. Hayashi, and M. Horodecki, Phys.Rev.Lett. 100, 210504 (2008)] makes it possible to unify various and generally inequivalent approaches adopted in order to derive information-disturbance tradeoffs in quantum theory. We focus in particular on those tradeoffs, constituting the vast majority of the literature on the subject, where disturbance is defined either in terms of average output fidelity or of entanglement fidelity

Approximate reversibility in the context of entropy gain, information gain, and complete positivity

There are several inequalities in physics which limit how well we can process physical systems to achieve some intended goal, including the second law of thermodynamics, entropy bounds in quantum information theory, and the uncertainty principle of quantum mechanics. Recent results provide physically meaningful enhancements of these limiting statements, determining how well one can attempt to reverse an irreversible process. In this paper, we apply and extend these results to give strong enhancements to several entropy inequalities, having to do with entropy gain, information gain, entropic disturbance, and complete positivity of open quantum systems dynamics. Our first result is a remainder term for the entropy gain of a quantum channel. This result implies that a small increase in entropy under the action of a subunital channel is a witness to the fact that the channel's adjoint can be used as a recovery map to undo the action of the original channel. Our second result regards the information gain of a quantum measurement, both without and with quantum side information. We find here that a small information gain implies that it is possible to undo the action of the original measurement if it is efficient. The result also has operational ramifications for the information-theoretic tasks known as measurement compression without and with quantum side information. Our third result shows that the loss of Holevo information caused by the action of a noisy channel on an input ensemble of quantum states is small if and only if the noise can be approximately corrected on average. We finally establish that the reduced dynamics of a system-environment interaction are approximately completely positive and trace-preserving if and only if the data processing inequality holds approximately.Comment: v3: 12 pages, accepted for publication in Physical Review

Jarzynski-like Equality of Nonequilibrium Information Production Based on Quantum Cross Entropy

The two-time measurement scheme is well studied in the context of quantum fluctuation theorem. However, it becomes infeasible when the random variable determined by a single measurement trajectory is associated with the von-Neumann entropy of the quantum states. We employ the one-time measurement scheme to derive a Jarzynski-like equality of nonequilibrium information production by proposing an information production distribution based on the quantum cross entropy. The derived equality further enables one to explore the roles of the quantum cross entropy in quantum communications, quantum machine learning and quantum thermodynamics.Comment: v2: We removed the results of two-time measurement scheme, and added the relations of our main result of the one-time measurement scheme to the cost function of quantum autoencoder and maximum available work theore

Functional traits and resource-use strategies of native and invasive plants in Eastern North American forests

Despite the presumption that native species are well adapted to their local environment, non-native invaders seem to outperform native plants. Intuitively, it appears paradoxical that non-native species, with no opportunity for local adaptation, can exhibit greater fitness than native plants with this advantage. Here, I compared traits of native and invasive shrub and liana species in Eastern North American (ENA) forests to test the overarching hypothesis that non-native understory species invasive to this region have superior resource-use strategies, or alternatively, they share the same metabolic tradeoffs as the native flora. First, at a global scale, I addressed the largely untested hypothesis that biogeography places significant constraints on trait evolution. Reanalyzing a large functional trait database, along with species\u27 native distribution data, I found that regional floras with different evolutionary histories exhibit different tradeoffs in resource capture strategies. Second, using a common garden to control for environment, I measured leaf physiological traits relating to resource investments, carbon returns, and resource-use efficiencies in 14 native and 18 non-native invasive species of common genera found in ENA understories, where growth is presumably constrained by light and nutrient limitation. I tested whether native and invasive plants have similar metabolic constraints or if these invasive species (predominantly from East Asia) are more productive per unit resource cost. Despite greater resource costs (leaf construction, leaf N), invaders exhibited greater energy- and nitrogen-use efficiencies, particularly when integrated over leaf lifespan. Efficiency differences were primarily driven by greater mean photosynthetic abilities (20% higher daily C gain) and leaf lifespans (24 days longer) in invasive species. Third, motivated by common garden results, I conducted a resource addition experiment in a central NY deciduous forest to investigate the role of resource limitation on invasion success in the field. I manipulated understory light environments (overstory tree removal) and N availabilities (ammonium-nitrate fertilization) to create a resource gradient across plots each containing 3 invasive and 6 native woody species. Invasive species generally exhibited greater aboveground productivity and photosynthetic gains. After two treatment years, invasive species displayed more pronounced trait responses to the resource gradients, primarily light, relative to the weaker responses of native species. Lastly, I asked whether species exhibit similar resource-use strategies in their native and invasive ranges. I measured leaf functional traits of Rhamnus cathartica (native to Europe, invasive in ENA) and Prunus serotina (native to ENA, invasive in Europe) in populations across central NY and northern France. Notably, I found invasive US populations of R. cathartica had markedly greater photosynthetic rates (50% higher) and reduced leaf N resorption rates in autumn (30% lower) than native French populations. Contrastingly, I found minimal leaf trait differences in P. serotina between native (US) and invasive (French) populations. Collectively, my results highlight the utility of functional trait perspectives and support a mechanistic explanation for invasion success based on differential abilities of species to convert limiting resources to biomass

Quantum-Classical Hybrid Systems and their Quasifree Transformations

We study continuous variable systems, in which quantum and classical degrees of freedom are combined and treated on the same footing. Thus all systems, including the inputs or outputs to a channel, may be quantum-classical hybrids. This allows a unified treatment of a large variety of quantum operations involving measurements or dependence on classical parameters. The basic variables are given by canonical operators with scalar commutators. Some variables may commute with all others and hence generate a classical subsystem. We systematically study the class of "quasifree" operations, which are characterized equivalently either by an intertwining condition for phase-space translations or by the requirement that, in the Heisenberg picture, Weyl operators are mapped to multiples of Weyl operators. This includes the well-known Gaussian operations, evolutions with quadratic Hamiltonians, and "linear Bosonic channels", but allows for much more general kinds of noise. For example, all states are quasifree. We sketch the analysis of quasifree preparation, measurement, repeated observation, cloning, teleportation, dense coding, the setup for the classical limit, and some aspects of irreversible dynamics, together with the precise salient tradeoffs of uncertainty, error, and disturbance. Although the spaces of observables and states are infinite dimensional for every non-trivial system that we consider, we treat the technicalities related to this in a uniform and conclusive way, providing a calculus that is both easy to use and fully rigorous.Comment: 63 pages, 6 figure

Quantum-Classical Hybrid Systems and their Quasifree Transformations

We study continuous variable systems, in which quantum and classical degrees of freedom are combined and treated on the same footing. Thus all systems, including the inputs or outputs to a channel, may be quantum-classical hybrids. This allows a unified treatment of a large variety of quantum operations involving measurements or dependence on classical parameters. The basic variables are given by canonical operators with scalar commutators. Some variables may commute with all others and hence generate a classical subsystem. We systematically study the class of "quasifree" operations, which are characterized equivalently either by an intertwining condition for phase-space translations or by the requirement that, in the Heisenberg picture, Weyl operators are mapped to multiples of Weyl operators. This includes the well-known Gaussian operations, evolutions with quadratic Hamiltonians, and "linear Bosonic channels", but allows for much more general kinds of noise. For example, all states are quasifree. We sketch the analysis of quasifree preparation, measurement, repeated observation, cloning, teleportation, dense coding, the setup for the classical limit, and some aspects of irreversible dynamics, together with the precise salient tradeoffs of uncertainty, error, and disturbance. Although the spaces of observables and states are infinite dimensional for every non-trivial system that we consider, we treat the technicalities related to this in a uniform and conclusive way, providing a calculus that is both easy to use and fully rigorous