相关论文: Bounds on $k$-Uniform Quantum States
R\"odl, Ruci\'nski, and Szemer\'edi determined the minimum $(k-1)$-degree threshold for the existence of fractional perfect matchings in $k$-uniform hypergrahs, and K\"uhn, Osthus, and Townsend extended this result by asymptotically…
The quantum central limit theorem for bosonic quantum systems states that the sequence of states $\rho^{\boxplus n}$ obtained from the $n$-fold convolution of a centered quantum state $\rho$ converges to a quantum Gaussian state $\rho_G$…
Concurrence, as one of entanglement measures, is a useful tool to characterize quantum entanglement in various quantum systems. However, the computation of the concurrence involves difficult optimizations and only for the case of two qubits…
We present the new exact upper bounds on the maximal Bell violation for the generalized N-qubit GHZ state, the N-qudit GHZ state and, in general, for an arbitrary N-partite quantum state, possibly infinite-dimensional. Our results indicate…
Quantum error correcting codes have a distance parameter, conveying the minimum number of single spin errors that could cause error correction to fail. However, the success thresholds of finite per-qubit error rate that have been proven for…
The Eastin-Knill theorem is a central result of quantum error correction theory and states that a quantum code cannot correct errors exactly, possess continuous symmetries, and implement a universal set of gates transversely. As a way to…
We prove a tight and close-to-optimal lower bound on the effectiveness of local quantum measurements (without classical communication) at discriminating any two bipartite quantum states. Our result implies, for example, that any two…
We study an optimum measurement for quantum state discrimination, which maximizes the probability of correct results when the probability of inconclusive results is fixed at a given value. The measurement describes minimum-error…
We show that a generic $N$-qudit pure quantum state is uniquely determined by only $2$ of its $\lceil\frac{N+1}{2}\rceil$-particle reduced density matrices. Therefore we give a method to uniquely determine a generic $N$-qudit pure state of…
We investigate various aspects of operator quantum error-correcting codes or, as we prefer to call them, subsystem codes. We give various methods to derive subsystem codes from classical codes. We give a proof for the existence of subsystem…
We consider the task of distinguishing whether a quantum system is prepared in a state from one of several sets of quantum states. Assuming their convexity and stability under tensor product, we prove that the optimal error exponent for…
In quantum purity amplification, one is given $n$ copies of a noisy quantum state $\rho \in \mathbb{C}^{d \times d}$ and asked to prepare $k$ copies of its principal eigenstate $|v_d\rangle$. Several prior works have derived…
We study quantum state testing where the goal is to test whether $\rho=\rho_0\in\mathbb{C}^{d\times d}$ or $\|\rho-\rho_0\|_1>\varepsilon$, given $n$ copies of $\rho$ and a known state description $\rho_0$. In practice, not all measurements…
Standard quantum error correction (QEC) models typically assume discrete, Markovian noise, obscuring the continuous quantum nature of physical environments. In this manuscript, we investigate the fundamental limits of an actively corrected…
Given a quantum channel and a state which satisfy a fixed point equation approximately (say, up to an error $\varepsilon$), can one find a new channel and a state, which are respectively close to the original ones, such that they satisfy an…
Quantum state discrimination enables the accurate identification of quantum states, which are generally nonorthogonal. Among various strategies, minimum-error discrimination and unambiguous state discrimination exhibit…
Most states in the Hilbert space are maximally entangled. This fact has proven useful to investigate - among other things - the foundations of statistical mechanics. Unfortunately, most states in the Hilbert space of a quantum many body…
The existence is proved of a class of open quantum systems that admits a linear subspace ${\cal C}$ of the space of states such that the restriction of the dynamical semigroup to the states built over $\cal C$ is unitary. Such subspace…
We investigate multipartite entanglement for composite quantum systems in a pure state. Using the generalized Bloch representation for n-qubit states, we express the condition that all k-qubit reductions of the whole system are maximally…
The quantum computing scheme described in Phys. Rev. Lett. 98, 190504 (2007), when viewed as a cluster state computation, features a 3-D cluster state, novel adjustable strength error correction capable of correcting general errors through…