The duration, strength and structure of memory effects are crucial properties of physical evolution. Due to the invasive nature of quantum measurement, such properties must be defined with respect to the probing instruments employed. Here, using a photonic platform, we experimentally demonstrate this necessity via two paradigmatic processes: future-history correlations in the first process can be erased by an intermediate quantum measurement; for the second process, a noisy classical measurement blocks the effect of history. We then apply memory truncation techniques to recover an efficient description that approximates expectation values for multi-time observables. Our proof-of-principle analysis paves the way for experiments concerning more general non-Markovian quantum processes and highlights where standard open systems techniques break down.
We investigate the problem of reversing quantum dynamics, specifically via optimal Petz recovery maps. We focus on typical decoherence channels, such as dephasing, depolarizing and amplitude damping. We illustrate how well a physically implementable recovery map simulates an inverse evolution. We extend this idea to explore the use of recovery maps as an approximation of inverse maps, and apply it in the context of non-Markovian dynamics. We show how this strategy attenuates non-Markovian effects, such as the backflow of information.
In the scale-up of quantum computers, the framework underpinning fault-tolerance generally relies on the strong assumption that environmental noise affecting qubit logic is uncorrelated (Markovian). However, as physical devices progress well into the complex multi-qubit regime, attention is turning to understanding the appearance and mitigation of correlated -- or non-Markovian -- noise, which poses a serious challenge to the progression of quantum technology. This error type has previously remained elusive to characterisation techniques. Here, we develop a framework for characterising non-Mar…
We assess non-Markovianity of a quantum open-system dynamics through the violation of temporal bell-like inequalities in a controllable Nuclear Magnetic Resonance system. We investigate experimentally the connections between the violation of the addressed temporal Bell-like inequality and the non-divisibility of the effective evolution of our system, which we fully characterize in a broad range of experimentally controllable regimes. Finally, we investigate the link between our approach and Leggett-Garg-like inequalities based on time-translational two-time correlation functions. These results…
In many applications entanglement must be distributed through noisy communication channels that unavoidably degrade it. Entanglement cannot be generated by local operations and classical communication (LOCC), implying that once it has been distributed it is not possible to recreate it by LOCC. Recovery of entanglement by purely local control is however not forbidden in the presence of non-Markovian dynamics, and here we demonstrate in two all-optical experiments that such entanglement restoration can even be achieved on-demand. First, we implement an open-loop control scheme based on a purely …
Generic non-Markovian quantum processes have infinitely long memory, implying an exact description that grows exponentially in complexity with observation time. Here, we present a finite memory ansatz that approximates (or recovers) the true process with errors bounded by the strength of the non-Markovian memory. The introduced memory strength is an operational quantity and depends on the way the process is probed. Remarkably, the recovery error is bounded by the smallest memory strength over all possible probing methods. This allows for an unambiguous and efficient description of non-Markovia…
We show that measurement can recover the quantum coherence of a qubit in a non-Markovian environment. The experimental demonstration in an optical system is provided by comparing the visibilities (and fidelities) of the final states with and without measurement. This method can be extended to other two-level quantum systems and entangled states in a non-Markovian evolution environment. It may also be used to implement other quantum information processing.
The promise of quantum computing with imperfect qubits relies on the ability of a quantum computing system to scale cheaply through error correction and fault-tolerance. While fault-tolerance requires relatively mild assumptions about the nature of qubit errors, the overhead associated with coherent and non-Markovian errors can be orders of magnitude larger than the overhead associated with purely stochastic Markovian errors. One proposal to address this challenge is to randomize the circuits of interest, shaping the errors to be stochastic Pauli errors but leaving the aggregate computation un…
We propose a method for the dynamical control in three-level open systems and realize it in the experiment with a superconducting qutrit. Our work demonstrates that in the Markovian environment for a relatively long time (3 us), the systemic populations or coherence can still strictly follow the preset evolution paths. This is the first experiment for precisely controlling the Markovian dynamics of three-level open systems, providing a solid foundation for the future realization of dynamical control in multiple open systems. An instant application of the techniques demonstrated in this experim…
Recently remarkable progress in quantum technology has been witnessed. In view of this it is important to investigate an open quantum system as a model of such quantum devices. Quantum devices often require extreme conditions such as very low temperature for the devices to operate. Dynamics can be non-Markovian in such a situation in contrast with Markovian dynamics in high temperature regime. This observation necessitates us to investigate a non-Markovian open quantum system, both theoretically and experimentally. In this paper, we report two important results: 1) Exact solution of a simple b…
Recent developments in practical quantum engineering and control techniques have allowed significant developments for experimental studies of open quantum systems and decoherence engineering. Indeed, it has become possible to test experimentally various theoretical, mathematical, and physical concepts related to non-Markovian quantum dynamics. This includes experimental characterization and quantification of non-Markovian memory effects and proof-of-principle demonstrations how to use them for certain quantum communication and information tasks. We describe here recent experimental advances fo…
We explore in a rigorous manner the intuitive connection between the non-Markovianity of the evolution of an open quantum system and the performance of the system as a quantum memory. Using the paradigmatic case of a two-level open quantum system coupled to a bosonic bath, we compute the recovery fidelity, which measures the best possible performance of the system to store a qubit of information. We deduce that this quantity is connected, but not uniquely determined, by the non-Markovianity, for which we adopt the BLP measure proposed in \cite{breuer2009}. We illustrate our findings with expli…
In this paper, we study measures of quantum non-Markovianity based on the conditional mutual information. We obtain such measures by considering multiple parts of the total environment such that the conditional mutual information can be defined in this multipartite setup. The benefit of this approach is that the conditional mutual information is closely related to recovery maps and Markov chains; we also point out its relations with the change of distinguishability. We study along the way the properties of leaked information which is the conditional mutual information that can be back flowed, …
In order to analyze non-Markovianity of tripartite quantum states from a resource theoretical viewpoint, we introduce a class of quantum operations performed by three distant parties, and investigate an operational resource theory (ORT) induced it. A tripartite state is a free state if and only if it is a quantum Markov chain. We prove monotonicity of functions such as the conditional quantum mutual information, intrinsic information, squashed entanglement, a generalization of entanglement of purification, and the relative entropy of recovery. The ORT has five bound sets, each of which corresp…
It is widely spread in the literature that non-Markovianity (NM) may be regarded as a resource in quantum mechanics. However, it is still unclear how and when this alleged resource may be exploited. Here, we study the relationship between NM and quantum optimal control under the objective of generating entanglement within M non-interacting subsystems, each one coupled to the same non-Markovian environment. Thus, we design a variety of entangling protocols that are only achievable due to the existence of the environment. We show that NM plays a crucial role in all the entangling protocols consi…
The non-Markovian nature of quantum systems recently turned to be a key subject for investigations on open quantum system dynamics. Many studies, from its theoretical grounding to its usefulness as a resource for quantum information processing and experimental demonstrations, have been reported in the literature. Typically, in these studies, a structured reservoir is required to make non-Markovian dynamics to emerge. Here, we investigate the dynamics of a qubit interacting with a bosonic bath and under the injection of a classical stochastic colored noise. A canonical Lindblad-like master equa…
Heisenberg-limited metrology in the presence of non-Markovian noise with finite control rates
Center for Quantum Information and Control, University of New Mexico（新墨西哥大学量子信息与控制中心）；Department of Physics and Astronomy, University of New Mexico（新墨西哥大学物理与天文学系）
Sparse Non-Markovian Noise Modeling of Transmon-Based Multi-Qubit Operations
Johns Hopkins University（约翰斯·霍普金斯大学）；Johns Hopkins University Applied Physics Laboratory（约翰斯·霍普金斯大学应用物理实验室）；IBM Quantum, IBM Thomas J Watson Research Center（IBM量子，IBM托马斯·J·沃森研究中心）
In this paper, we investigate the dynamics behaviors of genuine multipartite Einstein-Podolsky-Rosen steering (GMS) and genuine multipartite nonlocality (GMN), and explore how to recover the lost GMS and GMN under a mixed decoherence system. Explicitly, the decoherence system can be modeled by that a tripartite Werner-type state suffers from the non-Markovian regimes and one subsystem of the tripartite is under a non-inertial frame. The conditions for steerable and nonlocal states can be obtained with respect to the tripartite Werner-type state established initially. GMS and GMN are very fragi…
Quantum metrology is supposed to significantly improve the precision of parameter estimation by utilizing suitable quantum resources. However, the predicted precision can be severely distorted by realistic noises. Here, we propose a control-enhanced quantum metrology scheme to defend against these noises for improving the metrology performance. Our scheme can automatically alter the parameter encoding dynamics with adjustable controls, thus leading to optimal resultant states that are less sensitive to the noises under consideration. As a demonstration, we numerically apply it to the problem o…
We experimentally demonstrate, for the first time, noise diagnostics by repeated quantum measurements. Specifically, we establish the ability of a single photon, subjected to random polarisation noise, to diagnose non-Markovian temporal correlations of such a noise process. In the frequency domain, these noise correlations correspond to colored noise spectra, as opposed to the ones related to Markovian, white noise. Both the noise spectrum and its corresponding temporal correlations are diagnosed by probing the photon by means of frequent, (partially-)selective polarisation measurements. Our m…
Simulating the Dynamics of Markovian Quantum Processes by Quantum Collision Models on Quantum Computers
RIKEN Center for Computational Science（理化学研究所计算科学中心）；Q-CTRL；RIKEN Center for Quantum Computing（理化学研究所量子计算中心）；RIKEN Pioneering Research Institute（理化学研究所先导研究本部）；RIKEN Center for Emergent Matter Science（理化学研究所新兴物质科学中心）
Open quantum systems and study of decoherence are important for our fundamental understanding of quantum physical phenomena. For practical purposes, there exists a large number of quantum protocols exploiting quantum resources, e.g. entanglement, which allows to go beyond what is possible to achieve by classical means. We combine concepts from open quantum systems and quantum information science, and give a proof-of-principle experimental demonstration -- with teleportation -- that it is possible to implement efficiently a quantum protocol via non-Markovian open system. The results show that, …
We present a theory of frequency-dependent counting statistics of electron transport through nanostructures within the framework of Markovian quantum master equations. Our method allows the calculation of finite-frequency current cumulants of arbitrary order, as we explicitly show for the second- and third-order cumulants. Our formulae generalize previous zero-frequency expressions in the literature and can be viewed as an extension of MacDonald's formula beyond shot noise. When combined with an appropriate treatment of tunneling, using, e.g. Liouvillian perturbation theory in Laplace space, o…
Quantum no-Hiding theorem, first proposed by Braunstein and Pati [Phys. Rev. Lett. 98, 080502 (2007)], was verified experimentally by Samal et al. [Phys. Rev. Lett. 186, 080401 (2011)] using NMR quantum processor. Till then, this fundamental test has not been explored in any of the experimental architecture. Here, we demonstrate the above no-hiding theorem using the IBM 5Q quantum processor. Categorical algebra developed by Coecke and Duncan [New J. Phys. 13, 043016 (2011)] has been used for better visualization of the no-hiding theorem by analyzing the quantum circuit using the ZX calculus. T…
We present a technique for recovering the spectrum of a non-Markovian bosonic bath and/or non-Markovian noises coupled to an harmonic oscillator. The treatment is valid under the conditions that the environment is large and hot compared to the oscillator, and that its temporal auto-correlation functions are symmetric with respect to time translation and reflection -- criteria which we consider fairly minimal. We model a demonstration of the technique as deployed in the experimental scenario of a nanosphere levitated in a Paul trap, and show that it would effectively probe the spectrum of an el…
Markovian master equations (formally known as quantum dynamical semigroups) can be used to describe the evolution of a quantum state $ρ$ when in contact with a memoryless thermal bath. This approach has had much success in describing the dynamics of real-life open quantum systems in the lab. Such dynamics increase the entropy of the state $ρ$ and the bath until both systems reach thermal equilibrium, at which point entropy production stops. Our main result is to show that the entropy production at time $t$ is bounded by the relative entropy between the original state and the state at time $2t$…
The intrinsic probabilistic nature of quantum systems makes error correction or mitigation indispensable for quantum computation. While current error-correcting strategies focus on correcting errors in quantum states or quantum gates, these fine-grained error-correction methods can incur significant overhead for quantum algorithms of increasing complexity. We present a first step in achieving error correction at the level of quantum algorithms by combining a unified perspective on modern quantum algorithms via quantum signal processing (QSP). An error model of under- or over-rotation of the si…
Most matter-wave interferometry (MWI) schemes for quantum sensing are so far evaluated in ideal situations without noises. In this work, we provide assessments of generic multiqubit MWI schemes under Markovian dephasing noises. We find that for certain classes of the MWI schemes with scale factors that are nonlinearly dependent on the interrogation time, the optimal precision of maximally entangled probes \emph{decreases} with increasing the particle number $N$, for both independent and collective dephasing situations. This result challenges the conventional wisdom found in dephasing Ramsey-ty…
We develop a generalized theory of quantum error correction (QEC) that applies to any linear map, in particular maps that are not completely positive (CP). This theory describes entanglement-assisted QEC for invertible noise maps, which we use to provides an example of the physical implementation of non-CP recovery maps. We argue that a consistent map-based theory of fault-tolerant QEC (whether Markovian or not) requires linear, non-CP maps, and that this impacts the value of the fault-tolerance threshold.
The sensitivity of classical and quantum sensing is impaired in a noisy environment. Thus, one of the main challenges facing sensing protocols is to reduce the noise while preserving the signal. State of the art quantum sensing protocols that rely on dynamical decoupling achieve this goal under the restriction of long noise correlation times. We implement a proof-of-principle experiment of a protocol to recover sensitivity by using an error correction for photonic systems that does not have this restriction. The protocol uses a protected entangled qubit to correct a single error. Our results s…
Trapped atomic ions enable a precise quantification of the flow of information between internal and external degrees of freedom by employing a non-Markovianity measure [H.-P. Breuer et al., Phys. Rev. Lett. 103, 210401 (2009)]. We reveal that the nature of projective measurements in quantum mechanics leads to a fundamental, nontrivial bias in this measure. We observe and study the functional dependence of this bias to permit a demonstration of applications of local quantum probing. An extension of our approach can act as a versatile reference, relevant for understanding complex systems.
Correlated memory effect of environment in radical-pair magnetoreception
University of Science and Technology of China（中国科学技术大学）；State Key Laboratory of Precision and Intelligent Chemistry（精密与智能化学国家重点实验室）；Hefei National Research Center for Physical Sciences at the Microscale（合肥微尺度物质科学国家研究中心）
A big open question in the quantum information theory concerns feasibility of a self-correcting quantum memory. A quantum state recorded in such memory can be stored reliably for a macroscopic time without need for active error correction if the memory is put in contact with a cold enough thermal bath. In this paper we derive a rigorous lower bound on the memory time $T_{mem}$ of the 3D Cubic Code model which was recently conjectured to have a self-correcting behavior. Assuming that dynamics of the memory system can be described by a Markovian master equation of Davies form, we prove that $T_{…
The fluctuation theorem, where the central quantity is the work distribution, is an important characterization of nonequilibrium thermodynamics. In this work, based on the dissipaton-equation-of-motion theory, we develop an exact method to evaluate the work distributions in quantum impurity system-bath mixing processes, in the presence of non-Markovian and strong couplings. Our results not only precisely reproduce the Jarzynski equality and Crooks relation, but also reveal rich information on large deviation. The numerical demonstrations are carried out with a spin-boson model system.
