相关论文: Bounds for Approximation in Total Variation Distan…
This work identifies a necessary condition for any variational quantum approach to reach the exact ground state. Briefly, the norms of the projections of the input and the ground state onto each group module must match, implying that module…
We give bounds on the average fidelity achievable by any quantum state estimator, which is arguably the most prominently used figure of merit in quantum state tomography. Moreover, these bounds can be computed online---that is, while the…
We consider the problem of discriminating two different quantum states in the setting of asymptotically many copies, and determine the optimal strategy that minimizes the total probability of error. This leads to the identification of the…
Large-scale quantum computation will only be achieved if experimentally implementable quantum error correction procedures are devised that can tolerate experimentally achievable error rates. We describe a quantum error correction procedure…
We consider energy-constrained infinite-dimensional quantum channels from a given system (satisfying a certain condition) to any other systems. We show that dealing with basic capacities of these channels we may assume (accepting…
The communication complexity of a quantum channel is the minimal amount of classical communication required for classically simulating a process of state preparation, transmission through the channel and subsequent measurement. It…
The problem of computing distances of error-correcting codes is fundamental in both the classical and quantum settings. While hardness for the classical version of these problems has been known for some time (in both the exact and…
The classical information metric provides a unique notion of distance on the space of probability distributions with a well-defined operational interpretation: two distributions are far apart if they are readily distinguishable from one…
Characterizing entanglement in all but the simplest case of a two qubit pure state is a hard problem, even understanding the relevant experimental quantities that are related to entanglement is difficult. It may not be necessary, however,…
Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought…
Incorporating sample efficiency, by requiring the number of states consumed by broadcasting does not exceed that of a naive prepare-and-distribute strategy, gives rise to the no practical quantum broadcasting theorem. To navigate this…
One of the most exciting quantum emulation [1] breakthroughs was the first analog signal-based emulation of a universal quantum computer [2]. This yielded a very interesting paper, but no practical use - even for theorists. The reason for…
2D Total Variation Denoising (TVD) is a widely used technique for image denoising. It is also an important nonparametric regression method for estimating functions with heterogenous smoothness. Recent results have shown the TVD estimator to…
Metric data plays an important role in various settings such as metric-based indexing, clustering, classification, and approximation algorithms in general. Due to measurement error, noise, or an inability to completely gather all the data,…
Unextendibility of quantum states and channels is inextricably linked to the no-cloning theorem of quantum mechanics, it has played an important role in understanding and quantifying entanglement, and more recently it has found applications…
The quantum relative entropy is a fundamental quantity in quantum information science, characterizing the distinguishability between two quantum states. However, this quantity is not additive in general for correlated quantum states,…
We establish rigorous connections between quantum circuit complexity and approximate quantum error correction (AQEC) capability, two properties of fundamental importance to the physics and practical use of quantum many-body systems,…
The Earth Mover Distance (EMD) between two sets of points $A, B \subseteq \mathbb{R}^d$ with $|A| = |B|$ is the minimum total Euclidean distance of any perfect matching between $A$ and $B$. One of its generalizations is asymmetric EMD,…
The intuition that the precision of observables is constrained by thermodynamic costs has recently been formalized through thermodynamic and kinetic uncertainty relations. While such trade-offs have been extensively studied in Markovian…
It is imperative that useful quantum computers be very difficult to simulate classically; otherwise classical computers could be used for the applications envisioned for the quantum ones. Perfect quantum computers are unarguably…