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arXiv:2211.08860 · Physical Review A

Pairwise-measurement-induced synthesis of quantum coherence

Mariia Gumberidze, Michal Kolář, Radim Filip

Published Jan 3, 2022• 7 citations
arXivHTMLPDF

Abstract

Quantum coherent superpositions of states with different energies, i.e., states with coherence with respect to energy basis, are an important resource for modern quantum technologies. States with small coherence can be obtained either autonomously, due to the effect of a weak coherent drive, or, potentially, due to the presence of an environment. In this paper, we propose a measurement-based protocol for quantum coherence synthesis from individual systems (with low initial coherence) into a global (and higher) coherence of the joint system. As an input, it uses $N$ noninteracting copies of two-level systems (TLS), with low initial energy and coherence. These can be supplied by, e.g., a weak external drive or can result from an interaction with a bath. This protocol conditionally synthesizes an output state with higher energy and coherence than the initial state had, representing a universal process the rules of which have not been well studied, yet. In addition to energy and coherence, we study the quantity called mutual coherence, showing increase after the protocol application, as well. This approach is based on application of sequential pairwise projective measurements on TLS pairs (conditionally removing their ground states), that are diagonal in the TLS energy basis. The functionality of the coherence synthesis is robust with respect to dephasing effects of the TLS environment on the system. Our approach may show its benefits in quantum sensing, quantum batteries charging, or other applications where synthesis of a larger coherent system from smaller (weaker) resources is useful.

DOI
10.1103/physreva.105.012401

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Quantum coherent superpositions of states with different energies, i.e., states with coherence with respect to energy basis, are an important resource for modern quantum technologies. States with small coherence can be obtained either autonomously, due to the effect of a weak coherent drive, or, potentially, due to the presence of an environment. In this paper, we propose a measurement-based protocol for quantum coherence synthesis from individual systems (with low initial coherence) into a global (and higher) coherence of the joint system. As an input, it uses NNN noninteracting copies of two-level systems (TLS), with low initial energy and coherence. These can be supplied by, e.g., a weak external drive or can result from an interaction with a bath. This protocol conditionally synthesizes an output state with higher energy and coherence than the initial state had, representing a universal process the rules of which have not been well studied, yet. In addition to energy and coherence, we study the quantity called mutual coherence, showing increase after the protocol application, as well. This approach is based on application of sequential pairwise projective measurements on TLS pairs (conditionally removing their ground states), that are diagonal in the TLS energy basis. The functionality of the coherence synthesis is robust with respect to dephasing effects of the TLS environment on the system. Our approach may show its benefits in quantum sensing, quantum batteries charging, or other applications where synthesis of a larger coherent system from smaller (weaker) resources is useful.
Quantum coherence represented by a superposition of energy eigenstates is, together with energy, an important resource for quantum technology and thermodynamics. Energy and quantum coherence however, can be complementary. The increase of energy can reduce quantum coherence and vice versa. Recently, it was realized that steady-state quantum coherence could be autonomously harnessed from a cold environment. We propose a conditional synthesis of N independent two-level systems (TLS) with partial quantum coherence obtained from an environment to one coherent system using a measurement able to increase both energy and coherence simultaneously. The measurement process acts here as a Maxwell demon synthesizing the coherent energy of individual TLS to one large coherent quantum battery. The measurement process described by POVM elements is diagonal in energy representation and, therefore, it does not project on states with quantum coherence at all. We discuss various strategies and their efficiency to reach large coherent energy of the battery. After numerical optimization and proof-of-principle tests, it opens way to feasible repeat-until-success synthesis of coherent quantum batteries from steady-state autonomous coherence.
Abstract Quantum superposition of energy eigenstates can appear autonomously in a single quantum two-level system coupled to a low-temperature thermal bath, if such coupling has a proper composite nature. We propose here a principally different and more feasible approach employing engineered interactions between two-level systems being thermalized into a global Gibbs state by weakly coupled thermal bath at temperature T. Therefore, in such case quantum coherence appears by a different mechanism, whereas the system-bath coupling does not have to be engineered. We demonstrate such autonomous coherence generation reaching maximum values of coherence. Moreover, it can be alternatively built up by using weaker but collective interaction with several two-level systems. This approach surpasses the coherence generated by the engineered system-bath coupling for comparable interaction strengths and directly reduces phase estimation error in quantum sensing. This represents a necessary step towards the autonomous quantum sensing.
For a quantum system undergoing a unitary, process work is commonly defined based on the two projective measurement protocols, which measures the energies of the system before and after the process. However, it is well known that projective measurements disregard quantum coherences of the system with respect to the energy basis, thus removing potential quantum signatures in the work distribution. Here we consider weak measurements of the system's energy difference and establish corrections to work averages arising from initial system coherences. We discuss two weak measurement protocols that couple the system to a detector, prepared and measured either in the momentum or the position eigenstates. Work averages are derived for when the system starts in the proper thermal state versus when the initial system state is a pure state with thermal diagonal elements and coherences characterized by a set of phases. We show that by controlling only the phase differences between the energy eigenstate contributions in the system's initial pure state, the average work done during the same unitary process can be controlled. By changing the phases alone, one can toggle from regimes where the system absorbs energy, i.e., a work cost, to the ones where it emits energy, i.e., work can be drawn. This suggests that the coherences are additional resources that can be used to manipulate or store energy in a quantum system.
Quantum coherence is a crucial prerequisite for quantum technologies. Therefore, the robust generation, as autonomous as possible, of quantum coherence remains the essential problem for developing this field. We consider a method of synthesizing and multiplexing quantum coherence from spin systems without any direct drives only coupled to bosonic baths. The previous studies in this field have demonstrated that a back-action of the bath to the spin subsystem is important to generate it, however, it simultaneously gives significant limits to the generated coherence. We propose a viable approach with the bosonic bath that allows overcoming these limits by avoiding the destructive effect of the back-action processes. Using this approach, we suggest an advanced synthesis of the quantum coherence non-perturbatively in the spin-boson coupling parameters of multiple bosonic baths to increase and multiplex it for upcoming proof-of-principle experiments.
Beam splitters are optical elements widely used in modern technological applications to split the initial light beam into a required number of beams and they play a very promising role for generating entangled optical states. Here, a potential scheme is proposed to generate Bell coherent-states superpositions through the action of a beam splitter when a Glauber coherent state is injected on one input mode and vacuum state is incident on the other one. Different quantifiers are used to measure the quantumness in the output state such as concurrence entanglement, entropic quantum discord, quantum coherence, geometric measure of quantum discord, local quantum uncertainty (LQU) and local quantum Fisher information. Thereby, we derive their analytical formulas and focus more on the behavior and bounds of each measure. Besides, we have introduced the notion of "weak measurement-induced LQU" captured by weak measurements as the generalization of normal LQU defined for standard projective measurement, and we investigate the effect of the measurement strength on the estimated phase enhancement if the generated Bell cat states are the probe states in quantum metrology. Our results suggest that the sensitivity of the interferometric phase estimation depends on how strongly one perturbs the probe state and that a weak measurement does not necessarily capture more quantumness in composite system.
Fock states and their superpositions are exotic test beds for nonclassical physics and valuable resources for quantum technologies. We provide a simple protocol for the quantum measurement to generate an arbitrary Fock state and certain superposed Fock states from a coherent state of a target resonator, without any carefully tailored driving. This conditional protocol can be efficiently constructed by a sequence of joint free evolution of the resonator and an ancillary qubit, which are coupled via a Jaynes-Cummings interaction, and projective measurements on the qubit. By properly choosing the duration of each evolution-measurement cycle and the initial state of the resonator, we can generate a desired Fock state $|n\ensuremath{\rangle}$ and a superposed Fock state $(|0\ensuremath{\rangle}+|n\ensuremath{\rangle})/\sqrt{2}, n\ensuremath{\sim}10$, with a fidelity over 9999%99 in less than 30 measurements. Moreover, our protocol can be extended straightforwardly to the generation of a Bell-like state $(|00\ensuremath{\rangle}+|nn\ensuremath{\rangle})/\sqrt{2}$ with multiple excitations in a double-resonator system. We also calculate the outcome fidelity and the success probability of our protocol in the presence of decoherence.