Uncovering the origin of the “arrow of time” remains a fundamental scientific challenge. Within the framework of statistical physics, this problem was inextricably associated with the Second Law of Thermodynamics, which declares that entropy growth proceeds from the system’s entanglement with the environment. This poses a question of whether it is possible to develop protocols for circumventing the irreversibility of time and if so to practically implement these protocols. Here we show that, while in nature the complex conjugation needed for time reversal may appear exponentially improbable, one can design a quantum algorithm that includes complex conjugation and thus reverses a given quantum state. Using this algorithm on an IBM quantum computer enables us to experimentally demonstrate a backward time dynamics for an electron scattered on a two-level impurity.
Making use of coherence and entanglement as metrological quantum resources allows to improve the measurement precision from the shot-noise-or quantum limit to the Heisenberg limit. Quantum metrology then relies on the availability of quantum engineered systems that involve controllable quantum degrees of freedom which are sensitive to the measured quantity. Sensors operating in the qubit mode and exploiting their coherence in a phase-sensitive measurement have been shown to approach the Heisenberg scaling in precision. Here, we show that this result can be further improved by operating the quantum sensor in the qudit mode, i.e., by exploiting d rather than 2 levels. Specifically, we describe the metrological algorithm for using a superconducting transmon device operating in a qutrit mode as a magnetometer. The algorithm is based on the base-3 semiquantum Fourier transformation and enhances the quantum theoretical performance of the sensor by a factor 2. Even more, the practical gain of our qutrit-implementation is found in a reduction of the number of iteration steps of the quantum Fourier transformation by a factor log 2/ log 3 ≈ 0.63 as compared to the qubit mode. We show, that a two-tone capacitively coupled rf-signal is sufficient for the implementation of the algorithm.
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.
We present a quantum algorithm to transform the cardinality of a set of charged particles flowing along a quantum wire into a binary number. The setup performing this task (for at most N particles) involves ∼ log 2 N quantum bits serving as counters and a sequential read out. Applications include a divisibility check to experimentally test the size of a finite train of particles in a quantum wire with a one-shot measurement and a scheme allowing to entangle multi-particle wave functions and generating Bell states, Greenberger-Horne-Zeilinger states, or Dicke states in a Mach-Zehnder interferometer.
We generalize the binary quantum counting algorithm of Lesovik, Suslov, and Blatter [Phys. Rev. A 82, 012316 (2010)] to higher counting bases. The algorithm makes use of qubits, qutrits, and qudits to count numbers in a base-2, base-3, or base-d representation. In operating the algorithm, the number n < N = d K is read into a K-qudit register through its interaction with a stream of n particles passing in a nearby wire; this step corresponds to a quantum Fourier transformation from the Hilbert space of particles to the Hilbert space of qudit states. An inverse quantum Fourier transformation provides the number n in the base-d representation; the inverse transformation is fully quantum at the level of individual qudits, while a simpler semiclassical version can be used on the level of qudit registers. Combining registers of qubits, qutrits, and qudits, where d is a prime number, with a simpler single-shot measurement allows us to find the powers of 2, 3, and other primes d in the number n. We show that the counting task naturally leads to the shift operation and an algorithm based on the quantum Fourier transformation. We discuss possible implementations of the algorithm using quantum spin-d systems, d-well systems, and their emulation with spin-1/2 or double-well systems. We establish the analogy between our counting algorithm and the phase estimation algorithm and make use of the latter's performance analysis in stabilizing our scheme. Applications embrace a quantum metrological scheme to measure voltage (an analog to digital converter) and a simple procedure to entangle multiparticle states.
Results of an investigation of galvanomagnetic properties of Bi_95Sb_5 block thin films on substrates with different coefficients of thermal expansion covered with polyimide are presented. The difference between thermal expansions of the film material and the substrate was found to have a strong effect on the films’ galvanomagnetic properties. Analysis of the properties of the films using the two-band model showed that the concentration and mobility of the charge carriers in the Bi_95Sb_5 films are related to the coefficient of thermal expansion of the substrate material.