相关论文: Approximate Private Quantum Channels

This paper shows that the logarithm of the epsilon-error capacity (average error probability) for n uses of a discrete memoryless channel is upper bounded by the normal approximation plus a third-order term that does not exceed 1/2 log n +…

Preparing the ground state of a local Hamiltonian is a crucial problem in understanding quantum many-body systems, with applications in a variety of physics fields and connections to combinatorial optimization. While various quantum…

We prove tight lower bounds for the following variant of the counting problem considered by Aaronson, Kothari, Kretschmer, and Thaler (2020). The task is to distinguish whether an input set $x\subseteq [n]$ has size either $k$ or…

This paper establishes several converse bounds on the private transmission capabilities of a quantum channel. The main conceptual development builds firmly on the notion of a private state, which is a powerful, uniquely quantum method for…

We establish connections between state tomography, pseudorandomness, quantum state synthesis, and circuit lower bounds. In particular, let $\mathfrak{C}$ be a family of non-uniform quantum circuits of polynomial size and suppose that there…

While the channel capacity reflects a theoretical upper bound on the achievable information transmission rate in the limit of infinitely many bits, it does not characterise the information transfer of a given encoding routine with finitely…

Random quantum states have various applications in quantum information science. We discover a new ensemble of quantum states that serve as an $\epsilon$-approximate state $t$-design while possessing extremely low entanglement, magic, and…

We study the average case approximation of the Boolean mean by quantum algorithms. We prove general query lower bounds for classes of probability measures on the set of inputs. We pay special attention to two probabilities, where we show…

In the approximate quantiles problem, the goal is to output $m$ quantile estimates, the ranks of which are as close as possible to $m$ given quantiles $0 \leq q_1 \leq\dots \leq q_m \leq 1$. We present a mechanism for approximate quantiles…

This paper is the first of a series where we study quantum channels from the random matrix point of view. We develop a graphical tool that allows us to compute the expected moments of the output of a random quantum channel. As an…

In this paper we obtain new bounds for the minimum output entropies of random quantum channels. These bounds rely on random matrix techniques arising from free probability theory. We then revisit the counterexamples developed by Hayden and…

We extend the framework of quantum pushforward designs to the approximate setting, where averaging is achieved only up to finite precision. Using Schatten $p$-norms and Lipschitz continuity arguments, we derive bounds on the approximation…

One of the fundamental tasks in quantum information processing is to measure the quantum channels. Similar to measurements of quantum states, measurements of quantum channels are inherently stochastic, that is, quantum theory provides a…

The study of properties of randomly chosen quantum states has in recent years led to many insights into quantum entanglement. In this work, we study private quantum states from this point of view. Private quantum states are bipartite…

Quantum hypothesis testing is a central task in the entire field of quantum information theory. Understanding its ultimate limits will give insight into a wide range of quantum protocols and applications, from sensing to communication.…

Estimating the second frequency moment of a stream up to $(1\pm\varepsilon)$ multiplicative error requires at most $O(\log n / \varepsilon^2)$ bits of space, due to a seminal result of Alon, Matias, and Szegedy. It is also known that at…

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…

Channel simulation algorithms can efficiently encode random samples from a prescribed target distribution $Q$ and find applications in machine learning-based lossy data compression. However, algorithms that encode exact samples usually have…

The random purification channel maps n copies of any mixed quantum state to n copies of a random purification of the state. We generalize this construction to arbitrary symmetries: for any group G of unitaries, we construct a quantum…

We present a quantum algorithm for approximating maximum independent sets of a graph based on quantum non-Abelian adiabatic mixing in the sub-Hilbert space of degenerate ground states, which generates quantum annealing in a secondary…