Exact dimension estimation of interacting qubit systems assisted by a single quantum probe

Estimating the dimension of an Hilbert space is an important component of quantum system identification. In quantum technologies, the dimension of a quantum system (or its corresponding accessible Hilbert space) is an important resource, as larger dimensions determine e.g. the performance of quantum computation protocols or the sensitivity of quantum sensors. Despite being a critical task in quantum system identification, estimating the Hilbert space dimension is experimentally challenging. While there have been proposals for various dimension witnesses capable of putting a lower bound on the dimension from measuring collective observables that encode correlations, in many practical scenarios, especially for multiqubit systems, the experimental control might not be able to engineer the required initialization, dynamics and observables. Here we propose a more practical strategy, that relies not on directly measuring an unknown multiqubit target system, but on the indirect interaction with a local quantum probe under the experimenter's control. Assuming only that the interaction model is given and the evolution correlates all the qubits with the probe, we combine a graph-theoretical approach and realization theory to demonstrate that the dimension of the Hilbert space can be exactly estimated from the model order of the system. We further analyze the robustness in the presence of background noise of the proposed estimation method based on realization theory, finding that despite stringent constrains on the allowed noise level, exact dimension estimation can still be achieved.Comment: v3: accepted version. We would like to offer our gratitudes to the editors and referees for their helpful and insightful opinions and feedback

Quantifying precision loss in local quantum thermometry via diagonal discord

When quantum information is spread over a system through nonclassical correlation, it makes retrieving information by local measurements difficult---making global measurement necessary for optimal parameter estimation. In this paper, we consider temperature estimation of a system in a Gibbs state and quantify the separation between the estimation performance of the global optimal measurement scheme and a greedy local measurement scheme by diagonal quantum discord. In a greedy local scheme, instead of global measurements, one performs sequential local measurement on subsystems, which is potentially enhanced by feed-forward communication. We show that, for finite-dimensional systems, diagonal discord quantifies the difference in the quantum Fisher information quantifying the precision limits for temperature estimation of these two schemes, and we analytically obtain the relation in the high-temperature limit. We further verify this result by employing the examples of spins with Heisenberg's interaction.Comment: 5+4 pages, 4 figures, We thank the referees and editors for helpful opinions. Accepted by Phys. Rev. A (accepted version

Hamiltonian identifiability assisted by a single-probe measurement

We study the Hamiltonian identifiability of a many-body spin-1/2 system assisted by the measurement on a single quantum probe based on the eigensystem realization algorithm approach employed in Zhang and Sarovar, Phys. Rev. Lett. 113, 080401 (2014). We demonstrate a potential application of Gröbner basis to the identifiability test of the Hamiltonian, and provide the necessary experimental resources, such as the lower bound in the number of the required sampling points, the upper bound in total required evolution time, and thus the total measurement time. Focusing on the examples of the identifiability in the spin-chain model with nearest-neighbor interaction, we classify the spin-chain Hamiltonian based on its identifiability, and provide the control protocols to engineer the nonidentifiable Hamiltonian to be an identifiable Hamiltonian.United States. Army Research Office (W911NF-11-1-0400)United States. Army Research Office (W911NF-15-1-0548)National Science Foundation (U.S.) (PHY0551153

Quantum and classical ergotropy from relative entropies

The quantum ergotropy quantifies the maximal amount of work that can be extracted from a quantum state without changing its entropy. We prove that the ergotropy can be expressed as the difference of quantum and classical relative entropies of the quantum state with respect to the thermal state. This insight is exploited to define the classical ergotropy, which quantifies how much work can be extracted from distributions that are inhomogeneous on the energy surfaces. A unified approach to treat both, quantum as well as classical scenarios, is provided by geometric quantum mechanics, for which we define the geometric relative entropy. The analysis is concluded with an application of the conceptual insight to conditional thermal states, and the correspondingly tightened maximum work theorem.Comment: 4.5 pages v3. fixed typo

Detailed Fluctuation Theorem from the One-Time Measurement Scheme

The quantum fluctuation theorem can be regarded as the first principle of quantum nonequilibrium thermodynamics. However, many different formulations have been proposed, which depend on how quantum work is defined. In this context, we have seen that for some situations the one-time measurement (OTM) scheme can be more informative than the two-time measurement (TTM) scheme. Yet, so far the focus of OTM has been on integral fluctuation theorems, since, the work distribution of the backward process has been lacking. To this end, we prove that the OTM scheme is the quantum nondemolition (QND) TTM scheme, in which the final state is a pointer state of the second measurement whose Hamiltonian is conditioned on the first measurement outcome. This insight leads to a derivation of the detailed fluctuation theorem for the characteristic functions of the forward and backward work distributions, which captures the detailed information about the irreversibility and can be applied to quantum thermometry. Finally, our conceptual findings are experimentally verified with the IBM quantum computerComment: v2: added new analyses on irreversibilit

Achieving quantum advantages for image filtering

Image processing is a fascinating field for exploring quantum algorithms. However, achieving quantum speedups turns out to be a significant challenge. In this work, we focus on image filtering to identify a class of images that can achieve a substantial speedup. We show that for images with efficient encoding and a lower bound on the signal-to-noise ratio, a quantum filtering algorithm can be constructed with a polynomial complexity in terms of the qubit number. Our algorithm combines the quantum Fourier transform with the amplitude amplification technique. To demonstrate the advantages of our approach, we apply it to three typical filtering problems. We highlight the importance of efficient encoding by illustrating that for images that cannot be efficiently encoded, the quantum advantage will diminish. Our work provides insights into the types of images that can achieve a substantial quantum speedup.Comment: 8 pages, 9 figure

Jarzynski-like Equality of Nonequilibrium Information Production Based on Quantum Cross Entropy

The two-time measurement scheme is well studied in the context of quantum fluctuation theorem. However, it becomes infeasible when the random variable determined by a single measurement trajectory is associated with the von-Neumann entropy of the quantum states. We employ the one-time measurement scheme to derive a Jarzynski-like equality of nonequilibrium information production by proposing an information production distribution based on the quantum cross entropy. The derived equality further enables one to explore the roles of the quantum cross entropy in quantum communications, quantum machine learning and quantum thermodynamics.Comment: v2: We removed the results of two-time measurement scheme, and added the relations of our main result of the one-time measurement scheme to the cost function of quantum autoencoder and maximum available work theore