Related papers: Volume of Separable States for Arbitrary $N$-dimen…
It is proven that recently introduced states with perfectly secure bits of cryptographic key (private states representing secure bit) [K. Horodecki et al., Phys. Rev. Lett. 94, 160502 (2005)] as well as its multipartite and higher dimension…
The class of quantum operations known as Local Operations and Classical Communication (LOCC) induces a partial ordering on quantum states. We present the results of systematic numerical computations related to the volume (with respect to…
Working in relativistic quantum field theory, we derive the quantization condition satisfied by coupled two- and three-particle systems of identical scalar particles confined to a cubic spatial volume with periodicity $L$. This gives the…
The distillable randomness of a bipartite quantum state is an information-theoretic quantity equal to the largest net rate at which shared randomness can be distilled from the state by means of local operations and classical communication.…
The description of the complex separability structure of quantum states in terms of partially ordered sets has been recently put forward. In this work, we address the question of how to efficiently determine these structures for unknown…
We determine the minimal volume of arithmetic hyperbolic orientable n-dimensional orbifolds (compact and non-compact) for every odd dimension n>3. Combined with the previously known results it solves the minimal volume problem for…
We discuss the notion of bound entanglement (BE) for continuous variables (CV). We show that the set of non--distillable states (NDS) for CV is nowhere dense in the set of all states, i.e., the states of infinite--dimensional bipartite…
One of the most central and controversial element of quantum mechanics is the use of non zero vectors of a Hilbert space (or, more generally, of one dimension subspaces) for representing the state of a quantum system. In particular, the…
We investigate local distinguishability of quantum states by use of the convex analysis about joint numerical range of operators on a Hilbert space. We show that any two orthogonal pure states are distinguishable by local operations and…
We initiate an investigation into separable, but physically reasonable, states in relativistic quantum field theory. In particular we will consider the minimum amount of energy density needed to ensure the existence of separable states…
In this paper we present the necessary and sufficient conditions of separability for multipartite pure states. These conditions are very simple, and they don't require Schmidt decomposition or tracing out operations. We also give a…
We develop the first steps towards an analysis of geometry on the quantum spacetime proposed in [1]. The homogeneous elements of the universal differential algebra are naturally identified with operators living in tensor powers of Quantum…
The volume of a Cartier divisor on a projective variety is a nonnegative real number that measures the asymptotic growth of sections of multiples of the divisor. It is known that the set of these numbers is countable and has the structure…
Recently, it has been argued that quantum mechanics is complete, and that quantum states vectors are necessarily in one-to-one correspondence with the elements of reality, under the assumptions that quantum theory is correct and that…
We prove an optimal one-volume Wegner estimate for interacting systems of $N$ quantum particles moving in the presence of random potentials. The proof is based on the scale-free unique continuation principle recently developed for the…
Pushdown Vector Addition Systems with States (PVASS) consist of finitely many control states, a pushdown stack, and a set of counters that can be incremented and decremented, but not tested for zero. Whether the reachability problem is…
We investigate the joint (separable) numerical range of multiple measurements, i.e., the regions of expectation values accessible with (separable) quantum states for given observables. This not only enables efficient entanglement detection,…
We elaborate on the intimate connection between the largest volume of an empty axis-parallel box in a set of $n$ points from $[0,1]^d$ and cover-free families from the extremal set theory. This connection was discovered in a recent paper of…
We study the reachability problem of a quantum system modelled by a quantum automaton. The reachable sets are chosen to be boolean combinations of (closed) subspaces of the state space of the quantum system. Four different reachability…
Absolute separable (AS) quantum states are those states from which it is impossible to create entanglement, even under global unitary operations. It is known from the resource theory of non-absolute separability that the set of absolute…