Related papers: Cycle Index Polynomials and Generalized Quantum Se…
This thesis aims to establish notions of symmetry for quantum states and channels as well as describe algorithms to test for these properties on quantum computers. Ideally, the work will serve as a self-contained overview of the subject. We…
We study the quantum separability problem by using general symmetric informationally complete measurements and present separability criteria for both $d$-dimensional bipartite and multipartite systems. The criterion for bipartite quantum…
We investigate classification and detection of entanglement of multipartite quantum states in a very general setting, and obtain efficient $k$-separability criteria for mixed multipartite states in arbitrary dimensional quantum systems.…
The state of a quantum system, consisting of two distinct subsystems, is called separable if it can be prepared by two distant experimenters who receive instructions from a common source, via classical communication channels. A necessary…
Bounds analogous to entropic uncertainty relations allow one to design practical tests to detect quantum entanglement by a collective measurement performed on several copies of the state analyzed. This approach, initially worked out for…
We identify a formal connection between physical problems related to the detection of separable (unentangled) quantum states and complexity classes in theoretical computer science. In particular, we show that to nearly every quantum…
For distinguishing quantum states sampled from a fixed ensemble, the gap in bipartite and single-party distinguishability can be interpreted as a nonlocality of the ensemble. In this paper, we consider bipartite state discrimination in a…
We introduce a new family of separability criteria that are based on the existence of extensions of a bipartite quantum state $\rho$ to a larger number of parties satisfying certain symmetry properties. It can be easily shown that all…
Testing the symmetries of quantum states and channels provides a way to assess their usefulness for different physical, computational, and communication tasks. Here, we establish several complexity-theoretic results that classify the…
Using a recently introduced framework, we derive criteria for quantum k-separability, which are very easily computed. In the case k = 2, our criteria are equally strong to the best methods known so far, while in all other cases there are…
Recently, a technique known as quantum symmetry test has gained increasing attention for detecting bipartite entanglement in pure quantum states. In this work we show that, beyond qualitative detection, a family of well-defined measures of…
For a given pure state of a composite quantum system we analyze the product of its projections onto a set of locally orthogonal separable pure states. We derive a bound for this product analogous to the entropic uncertainty relations. For…
Quantum entanglement is essential to the development of quantum computation, communications, and technology. The controlled SWAP test, widely used for state comparison, can be adapted to an efficient and useful test for entanglement of a…
We compute the probability that a bipartite quantum state is separable by Monte Carlo sampling. This is carried out for rebits, qubits and quaterbits. We sampled $5\times 10^{11}$ points for each of these three cases. The results strongly…
We show that the bipartite separability of a pure qubit state hinges critically on the combinatorial structure of its computational-basis support. Using Boolean cube geometry, we introduce a taxonomy that distinguishes support-guaranteed…
The concept of entanglement and separability of quantum states is relevant for several fields in physics. Still, there is a lack of effective operational methods to characterise these features. We propose a method to certify quantum…
Characterizing large quantum systems with minimal assumptions is a central challenge in quantum information science. Self-testing provides the strongest form of certification by identifying the underlying quantum state solely from observed…
In this work we are interested the problem of testing quantum entanglement. More specifically, we study the separability problem in quantum property testing, where one is given $n$ copies of an unknown mixed quantum state $\varrho$ on…
Suppose that a polynomial-time mixed-state quantum circuit, described as a sequence of local unitary interactions followed by a partial trace, generates a quantum state shared between two parties. One might then wonder, does this quantum…
We propose experimentally feasible separability criteria for bipartite systems based on local symmetric measurements. Through detailed examples, we demonstrate that our criteria can detect entanglement more effectively compared to existing…