Related papers: Random Real Valued and Complex Valued States Canno…
We study the classic Text-to-Pattern Hamming Distances problem: given a pattern $P$ of length $m$ and a text $T$ of length $n$, both over a polynomial-size alphabet, compute the Hamming distance between $P$ and $T[i\, .\, . \, i+m-1]$ for…
A coarse description of a subset A of omega is a subset D of omega such that the symmetric difference of A and D has asymptotic density 0. We study the extent to which noncomputable information can be effectively recovered from all coarse…
Recently, Halder \emph{et al.} [S. Halder \emph{et al.}, Phys. Rev. Lett. \textbf{122}, 040403 (2019)] present two sets of strong nonlocality of orthogonal product states based on the local irreducibility. However, for a set of locally…
A nice and interesting property of any pure tensor-product state is that each such state has distillable entangled states at an arbitrarily small distance $\epsilon$ in its neighborhood. We say that such nearby states are…
Entanglement is a cornerstone in quantum information science, yet detecting it efficiently remains a challenging task. Focusing on non-positive partially transposed (NPT) states, we establish a hierarchy among entropy-based, majorization,…
We analyze the properties of entangled random pure states of a quantum system partitioned into two smaller subsystems of dimensions $N$ and $M$. Framing the problem in terms of random matrices with a fixed-trace constraint, we establish,…
Randomization of quantum states is the quantum analogue of the classical one-time pad. We present an improved, efficient construction of an approximately randomizing map that uses O(d/epsilon^2) Pauli operators to map any d-dimensional…
Random number has many applications, it plays an important role in quantum information processing. It's not difficult to generate true random numbers, the main difficulty is how to certify the random numbers generated by untrusted devices.…
We show that entanglement guarantees difficulty in the discrimination of orthogonal multipartite states locally. The number of pure states that can be discriminated by local operations and classical communication is bounded by the total…
In this paper we find an integer $h=h(n)$ such that the minimum number of variables of a first order sentence that distinguishes between two independent uniformly distributed random graphs of size $n$ with the asymptotically largest…
The state overlap, quantified via $\tr[\rho \sigma]$, is a metric widely used to assess the closeness between two quantum states $\rho$ and $\sigma$. Although global state overlap alone does not directly capture entanglement properties, we…
Statistical properties of non--symmetric real random matrices of size $M$, obtained as truncations of random orthogonal $N\times N$ matrices are investigated. We derive an exact formula for the density of eigenvalues which consists of two…
An ensemble of random unistochastic (orthostochastic) matrices is defined by taking squared moduli of elements of random unitary (orthogonal) matrices distributed according to the Haar measure on U(N) (or O(N), respectively). An ensemble of…
The question of how quantities, like entanglement and coherence, depend on the number of copies of a given state $\rho$ is addressed. This is a hard problem, often involving optimizations over Hilbert spaces of large dimensions. Here, we…
In [Science 340, 1205, 7 June (2013)], via polytopes Michael Walter et al. proposed a sufficient condition detecting the genuinely entangled pure states. In this paper, assume that a state with six non-zero coefficients is not a trivially…
The imaginary unit $i$ has recently been experimentally proven to be indispensable for quantum mechanics. We study the differences in detection power between real and complex entanglement witnesses (EWs) distinguished by whether their…
We prove a lower bound on the number of copies needed to test the property of a multipartite quantum state being product across some bipartition (i.e. not genuinely multipartite entangled), given the promise that the input state either has…
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…
Quantum resources like entanglement and magic are essential for characterizing the complexity of quantum states. However, when the number of copies of quantum states and the computational time are limited by numbers polynomial in the system…
Invariant tensors are states in the (local) SU(2) tensor product representation but invariant under global SU(2) action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An…