Heating without heat: thermodynamics of passive energy filters between finite systems

Passive filters allowing the exchange of particles in a narrow band of energy are currently used in micro-refrigerators and energy transducers. In this letter, we analyze their thermal properties using linear irreversible thermodynamics and kinetic theory, and discuss a striking phenomenon: the possibility of increasing or decreasing simultaneously the temperatures of two systems without any supply of energy. This occurs when the filter induces a flow of particles whose energy is between the average energies of the two systems. Here we show that this selective transfer of particles does not need the action of any sort of Maxwell demon and can be carried out by passive filters without compromising the second law of thermodynamics. The phenomenon allows us to design cycles between two reservoirs at temperatures $T_1<T_2$ that are able to reach temperatures below $T_1$ or above $T_2$.Comment: 5 pages, 3 figure

Measuring the purity of a qubit state: entanglement estimation with fully separable measurements

Given a finite number $N$ of copies of a qubit state we compute the maximum fidelity that can be attained using joint-measurement protocols for estimating its purity. We prove that in the asymptotic $N\to\infty$ limit, separable-measurement protocols can be as efficient as the optimal joint-measurement one if classical communication is used. This in turn shows that the optimal estimation of the entanglement of a two-qubit state can also be achieved asymptotically with fully separable measurements. The relationship between our global Bayesian approach and the quantum Cramer-Rao bound is also discussed.Comment: 5 pages, 1 figure, RevTeX, improved versio

Quantum reverse-engineering and reference frame alignment without non-local correlations

Estimation of unknown qubit elementary gates and alignment of reference frames are formally the same problem. Using quantum states made out of $N$ qubits, we show that the theoretical precision limit for both problems, which behaves as $1/N^{2}$, can be asymptotically attained with a covariant protocol that exploits the quantum correlation of internal degrees of freedom instead of the more fragile entanglement between distant parties. This cuts by half the number of qubits needed to achieve the precision of the dense covariant coding protocol

Phase-Covariant Quantum Benchmarks

We give a quantum benchmark for teleportation and quantum storage experiments suited for pure and mixed test states. The benchmark is based on the average fidelity over a family of phase-covariant states and certifies that an experiment can not be emulated by a classical setup, i.e., by a measure-and-prepare scheme. We give an analytical solution for qubits, which shows important differences with standard state estimation approach, and compute the value of the benchmark for coherent and squeezed states, both pure and mixed.Comment: 4 pages, 2 figure

Recycling of quantum information: Multiple observations of quantum systems

Given a finite number of copies of an unknown qubit state that have already been measured optimally, can one still extract any information about the original unknown state? We give a positive answer to this question and quantify the information obtainable by a given observer as a function of the number of copies in the ensemble, and of the number of independent observers that, one after the other, have independently measured the same ensemble of qubits before him. The optimality of the protocol is proven and extensions to other states and encodings are also studied. According to the general lore, the state after a measurement has no information about the state before the measurement. Our results manifestly show that this statement has to be taken with a grain of salt, specially in situations where the quantum states encode confidential information.Comment: 4 page

Multi-copy programmable discrimination of general qubit states

Quantum state discrimination is a fundamental primitive in quantum statistics where one has to correctly identify the state of a system that is in one of two possible known states. A programmable discrimination machine performs this task when the pair of possible states is not a priori known, but instead the two possible states are provided through two respective program ports. We study optimal programmable discrimination machines for general qubit states when several copies of states are available in the data or program ports. Two scenarios are considered: one in which the purity of the possible states is a priori known, and the fully universal one where the machine operates over generic mixed states of unknown purity. We find analytical results for both, the unambiguous and minimum error, discrimination strategies. This allows us to calculate the asymptotic performance of programmable discrimination machines when a large number of copies is provided, and to recover the standard state discrimination and state comparison values as different limiting cases.Comment: Based on version published in Physical Review A, some errors in appendix A corrected. 13 pages, 4 figure

Separable Measurement Estimation of Density Matrices and its Fidelity Gap with Collective Protocols

We show that there exists a gap between the performance of separable and collective measurements in qubit mixed-state estimation that persists in the large sample limit. We characterize such gap in terms of the corresponding bounds on the mean fidelity. We present an adaptive protocol that attains the separable-measurement bound. This (optimal separable) protocol uses von Neumann measurements and can be easily implemented with current technology.Comment: version published in PR