The coherent measurement cost of coherence distillation

Quantum coherence is an indispensable resource for quantum technological applications. It is known to be distillable from a noisy form using operations that cannot create coherence. However, distillation exacts a hidden coherent measurement cost, whose extent has not previously been estimated. Here we show that this cost (quantified by an equivalent number of Hadamard measurements) is related to what we call the irretrievable coherence: the difference between the coherence of formation and the distillable coherence. We conjecture (and make partial progress towards proving) that when distilling from many copies of a given noisy coherent state, the coherent measurement cost scales extensively in the number of copies, at an asymptotic rate exactly equalling the input's irretrievable coherence. This cost applies to any application whereof coherence distillation is an incidental outcome (e.g. incoherent randomness extraction), but the implications are more dramatic if pure coherence is the only desired outcome: the measurement cost may often be higher than the distilled yield, in which case coherence should rather be prepared afresh than distilled from a noisy input.Comment: 24+5 pages, 1 figur

Study of realistic devices for quantum key-distribution

Quantum key-distribution (QKD) is a scheme for establishing shared secret key between remote parties. In such a scheme, quantum preparation and measurement devices (sources and detectors) are used. In existing theoretical treatments of QKD, the device models used do not capture all the imperfections which might occur in realistic devices. This creates a gap between the practical implementations and theoretical descriptions of QKD. In the present work, we contribute in bridging this gap by three methods: 1) Advancing the study of squashing models of measurement devices, 2) Devising an alternative to squashing models using statistical estimation in optical QKD, and 3) Modifying the security proof formalism of QKD to account for imperfect devices

Quantifying memory capacity as a quantum thermodynamic resource

The information-carrying capacity of a memory is known to be a thermodynamic resource facilitating the conversion of heat to work. Szilard's engine explicates this connection through a toy example involving an energy-degenerate two-state memory. We devise a formalism to quantify the thermodynamic value of memory in general quantum systems with nontrivial energy landscapes. Calling this the thermal information capacity, we show that it converges to the non-equilibrium Helmholtz free energy in the thermodynamic limit. We compute the capacity exactly for a general two-state (qubit) memory away from the thermodynamic limit, and find it to be distinct from known free energies. We outline an explicit memory--bath coupling that can approximate the optimal qubit thermal information capacity arbitrarily well.Comment: 6 main + 7 appendix pages; 5 main + 2 appendix figure

Quantumness of correlations, quantumness of ensembles and quantum data hiding

We study the quantumness of correlations for ensembles of bi- and multi-partite systems and relate it to the task of quantum data hiding. Quantumness is here intended in the sense of minimum average disturbance under local measurements. We consider a very general framework, but focus on local complete von Neumann measurements as cause of the disturbance, and, later on, on the trace-distance as quantifier of the disturbance. We discuss connections with entanglement and previously defined notions of quantumness of correlations. We prove that a large class of quantifiers of the quantumness of correlations are entanglement monotones for pure bipartite states. In particular, we define an entanglement of disturbance for pure states, for which we give an analytical expression. Such a measure coincides with negativity and concurrence for the case of two qubits. We compute general bounds on disturbance for both single states and ensembles, and consider several examples, including the uniform Haar ensemble of pure states, and pairs of qubit states. Finally, we show that the notion of ensemble quantumness of correlations is most relevant in quantum data hiding. Indeed, while it is known that entanglement is not necessary for a good quantum data hiding scheme, we prove that ensemble quantumness of correlations is

Fisher information universally identifies quantum resources

We show that both the classical as well as the quantum definitions of the Fisher information faithfully identify resourceful quantum states in general quantum resource theories, in the sense that they can always distinguish between states with and without a given resource. This shows that all quantum resources confer an advantage in metrology, and establishes the Fisher information as a universal tool to probe the resourcefulness of quantum states. We provide bounds on the extent of this advantage, as well as a simple criterion to test whether different resources are useful for the estimation of unitarily encoded parameters. Finally, we extend the results to show that the Fisher information is also able to identify the dynamical resourcefulness of quantum operations.Comment: 5+6 page

The resource theory of informational nonequilibrium in thermodynamics

We review recent work on the foundations of thermodynamics in the light of quantum information theory. We adopt a resource-theoretic perspective, wherein thermodynamics is formulated as a theory of what agents can achieve under a particular restriction, namely, that the only state preparations and transformations that they can implement for free are those that are thermal at some fixed temperature. States that are out of thermal equilibrium are the resources. We consider the special case of this theory wherein all systems have trivial Hamiltonians (that is, all of their energy levels are degenerate). In this case, the only free operations are those that add noise to the system (or implement a reversible evolution) and the only nonequilibrium states are states of informational nonequilibrium, that is, states that deviate from the maximally mixed state. The degree of this deviation we call the state's nonuniformity; it is the resource of interest here, the fuel that is consumed, for instance, in an erasure operation. We consider the different types of state conversion: exact and approximate, single-shot and asymptotic, catalytic and noncatalytic. In each case, we present the necessary and sufficient conditions for the conversion to be possible for any pair of states, emphasizing a geometrical representation of the conditions in terms of Lorenz curves. We also review the problem of quantifying the nonuniformity of a state, in particular through the use of generalized entropies. Quantum state conversion problems in this resource theory can be shown to be always reducible to their classical counterparts, so that there are no inherently quantum-mechanical features arising in such problems. This body of work also demonstrates that the standard formulation of the second law of thermodynamics is inadequate as a criterion for deciding whether or not a given state transition is possible.Comment: 51 pages, 9 figures, Revised Versio