Related papers: Limitations on quantum dimensionality reduction
We generalize the notion of joint measurability to continuous variable systems by extending a recently introduced compression algorithm of quantum measurements to this realm. The extension results in a property that asks for the minimal…
Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of…
Let $\mathsf{S}_1$ (the Schatten--von Neumann trace class) denote the Banach space of all compact linear operators $T:\ell_2\to \ell_2$ whose nuclear norm $\|T\|_{\mathsf{S}_1}=\sum_{j=1}^\infty\sigma_j(T)$ is finite, where…
By carrying out appropriate continuous quantum measurements with a family of projection operators, a unitary channel can be approximated in an arbitrary precision in the trace norm sense. In particular, the quantum Zeno effect is described…
Quantum theory is known to be nonlocal in the sense that separated parties can perform measurements on a shared quantum state to obtain correlated probability distributions, which cannot be achieved if the parties share only classical…
A single-mode squeezed vacuum is a foundational quantum state that, despite its nonclassical nature, exhibits classical-like, super-Poissonian photon statistics. This feature motivates a ``quantum-of-quantum'' inquiry: can the superposition…
Optimal transport theory has recently been extended to quantum settings, where the density matrices generalize the probability measures. In this paper, we study the computational aspects of the order 2 quantum Wasserstein distance,…
A major open problem in the field of metric embedding is the existence of dimension reduction for $n$-point subsets of Euclidean space, such that both distortion and dimension depend only on the {\em doubling constant} of the pointset, and…
A more conventional realization of a symmetry which had been proposed towards the solution of cosmological constant problem is considered. In this study the multiplication of the coordinates by the imaginary number $i$ in the literature is…
Under which conditions and with which distortions can we preserve the pairwise-distances of low-complexity vectors, e.g., for structured sets such as the set of sparse vectors or the one of low-rank matrices, when these are mapped in a…
The variational two-electron reduced density matrix (v2RDM) method is generalized for the description of total angular momentum ($J$) and projection of total angular momentum ($M_{J}$) states in atomic systems described by non-relativistic…
Reduced density matrices are a powerful tool in the analysis of entanglement structure, approximate or coarse-grained dynamics, decoherence, and the emergence of classicality. It is straightforward to produce a reduced density matrix with…
We discuss an alternative to relative entropy as a measure of distance between mixed quantum states. The proposed quantity is an extension to the realm of quantum theory of the Jensen-Shannon divergence (JSD) between probability…
New quantum distance is introduced as a half-sum of several singular values of difference between two density operators. This is, up to factor, the metric induced by so-called Ky Fan norm. The partitioned trace distances enjoy similar…
A viable quantum theory of gravity is one of the biggest challenges facing physicists. We discuss the confluence of two highly expected features which might be instrumental in the quest of a finite and renormalizable quantum gravity --…
Several lines of evidence suggest that quantum gravity at very short distances may behave effectively as a two-dimensional theory. I summarize these hints, and offer an additional argument based on the strong-coupling limit of the…
Jain's iterative rounding theorem is a well-known result in the area of approximation algorithms and, more broadly, in combinatorial optimization. The theorem asserts that LP relaxations of several problems in network design and…
We consider the sensor network localization problem, which is closely related to multidimensional scaling and Euclidean distance matrix completion. Given a ground truth configuration of $n$ points in $\mathbb{R}^\ell$, we observe a subset…
In this work, we explore modewise Johnson-Lindenstrauss embeddings (JLEs) as a tool to reduce the computational cost and memory requirements of nuclear many-body methods. JLEs are randomized projections of high-dimensional data tensors onto…
Let $S \subset {\mathbb R}^d$ be contained in the unit ball. Let $\Delta(S)=\{||a-b||:a,b \in S\}$, the Euclidean distance set of $S$. Falconer conjectured that the $\Delta(S)$ has positive Lebesque measure if the Hausdorff dimension of $S$…