相关论文: Improved Lower Bounds for Learning Quantum Channel…

For a pair of quantum channels with the same input space, we show that the possibility of approximation of one channel by post-processings of the other channel can be characterized by comparing the success probabilities for the two…

Here, we study the problem of decoding information transmitted through unknown quantum states. We assume that Alice encodes an alphabet into a set of orthogonal quantum states, which are then transmitted to Bob. However, the quantum channel…

We consider the noise complexity of differentially private mechanisms in the setting where the user asks $d$ linear queries $f\colon\Rn\to\Re$ non-adaptively. Here, the database is represented by a vector in $\Rn$ and proximity between…

We show that $n = \Omega(rd/\varepsilon^2)$ copies are necessary to learn a rank $r$ mixed state $\rho \in \mathbb{C}^{d \times d}$ up to error $\varepsilon$ in trace distance. This matches the upper bound of $n = O(rd/\varepsilon^2)$ from…

We prove a near optimal round-communication tradeoff for the two-party quantum communication complexity of disjointness. For protocols with $r$ rounds, we prove a lower bound of $\tilde{\Omega}(n/r + r)$ on the communication required for…

A quantum analogue of the famous Blackwell Theorem in classical statistics has recently been proposed. Given two quantum channels A and B, a set of payoff functions have been proven to have values for B at least as high as they are for A if…

This paper provides novel insights into channel and subspace codes in nonadaptive channel sensing with a single RF chain. Observing that this problem naturally maps to a noncoherent decoding problem, we show that the sensing performance of…

The problem of identifying the channel with the highest capacity among several discrete memoryless channels (DMCs) is considered. The problem is cast as a pure-exploration multi-armed bandit problem, which follows the practical use of…

Uniform continuity bounds on entropies are generally expressed in terms of a single distance measure between a pair of probability distributions or quantum states, typically, the total variation distance or trace distance. However, if an…

We consider the problem of deterministic broadcasting in radio networks when the nodes have limited knowledge about the topology of the network. We show that for every deterministic broadcasting protocol there exists a network, of radius 2,…

Given a protocol ${\cal P}$ that implements multipartite quantum channel ${\cal E}$ by repeated rounds of local operations and classical communication (LOCC), we construct an alternate LOCC protocol for ${\cal E}$ in no more rounds than…

Decentralized bilevel optimization has received increasing attention recently due to its foundational role in many emerging multi-agent learning paradigms (e.g., multi-agent meta-learning and multi-agent reinforcement learning) over…

We show a new lower bound on the sample complexity of $(\varepsilon, \delta)$-differentially private algorithms that accurately answer statistical queries on high-dimensional databases. The novelty of our bound is that it depends optimally…

Random quantum circuits have played a central role in establishing the computational advantages of near-term quantum computers over their conventional counterparts. Here, we use ensembles of low-depth random circuits with local connectivity…

Quantum memories are a crucial precondition in many protocols for processing quantum information. A fundamental problem that illustrates this statement is given by the task of channel discrimination, in which an unknown channel drawn from a…

We show that $\Omega(rd/\epsilon)$ copies of an unknown rank-$r$, dimension-$d$ quantum mixed state are necessary in order to learn a classical description with $1 - \epsilon$ fidelity. This improves upon the tomography lower bounds…

Quantum state and process tomography are typically analyzed under the assumption that devices emit independent and identically distributed (i.i.d.) states or channels. In realistic experiments, however, noise, drift, feedback, or…

This thesis includes a survey of the results known for private and approximate private quantum channels. We develop the best known upper bound for $\epsilon$-randomizing maps, $n+2\log(1/\epsilon)+c$ bits required to $\epsilon$-randomize an…

We establish optimal Statistical Query (SQ) lower bounds for robustly learning certain families of discrete high-dimensional distributions. In particular, we show that no efficient SQ algorithm with access to an $\epsilon$-corrupted binary…

We give tight statistical query (SQ) lower bounds for learnining halfspaces in the presence of Massart noise. In particular, suppose that all labels are corrupted with probability at most $\eta$. We show that for arbitrary $\eta \in…