Related papers: Mixed discrete variable Gaussian states
Continuous-variable bosonic systems stand as prominent candidates for implementing quantum computational tasks. While various necessary criteria have been established to assess their resourcefulness, sufficient conditions have remained…
The volume of the quantum mechanical state space over $n$-dimensional real, complex and quaternionic Hilbert-spaces with respect to the canonical Euclidean measure is computed, and explicit formulas are presented for the expected value of…
We argue that if de Sitter space is indeed represented by a finite dimensional quantum system, then semi-classical considerations, combined with the fundamental principles of quantum measurement theory, imply that any theoretical model of…
We investigate under which conditions a mixed state on a finite-dimensional multipartite quantum system may be the unique, globally stable fixed point of frustration-free semigroup dynamics subject to specified quasi-locality constraints.…
The Cahill-Glauber approach for quantum mechanics on phase-space is extended to the finite dimensional case through the use of discrete coherent states. All properties and features of the continuous formalism are appropriately generalized.…
Continuous-variable Gaussian cluster states are a potential resource for universal quantum computation. They can be efficiently and unconditionally built from sources of squeezed light using beam splitters. Here we report on the generation…
An algebraic analysis of Grover's quantum search algorithm is presented for the case in which the initial state is an arbitrary pure quantum state of n qubits. This approach reveals the geometrical structure of the quantum search process,…
Starting with a set of conditions for bipartite separability of arbitrary quantum states in any dimension and expressed in terms of arbitrary operators whose commutator is a $c$-number, we derive a hierarchy of conditions for tripartite…
We study the invariants of arbitrary dimensional multipartite quantum states under local unitary transformations. For multipartite pure states, we give a set of invariants in terms of singular values of coefficient matrices. For…
This article reports on a program to obtain and understand coherent states for general systems. Most recently this has included supersymmetric systems. A byproduct of this work has been studies of squeezed and supersqueezed states. To…
Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought…
Continuous limits of discrete systems with long-range interactions are considered. The map of discrete models into continuous medium models is defined. A wide class of long-range interactions that give the fractional equations in the…
Grid states form a discrete set of mixed quantum states that can be described by graphs. We characterize the entanglement properties of these states and provide methods to evaluate entanglement criteria for grid states in a graphical way.…
The Hilbert-Schmidt distance between a mixed three-qubit state and its closest state is used to quantify the amount of pairwise quantum correlations in a tripartite system. Analytical expressions of geometric quantum discord are derived. A…
We present a novel, non-parametric form for compactly representing entangled many-body quantum states, which we call a `Gaussian Process State'. In contrast to other approaches, we define this state explicitly in terms of a configurational…
In the quest of completely describing entanglement in the general case of a finite number of parties sharing a physical system of finite dimensional Hilbert space a new entanglement magnitude is introduced for its pure and mixed states:…
Most of the fundamental characteristics of quantum mechanics, such as non-locality and contextuality, are manifest in discrete, finite-dimensional systems. However, many quantum information tasks that exploit these properties cannot be…
Quantum theory is indeterministic, but not completely so. When a system is in a pure state there are properties it possesses with certainty, known as actual properties. The actual properties of a quantum system (in a pure state) fully…
We study the eigenstates of quantum systems with large Hilbert spaces, via their distribution of wavefunction amplitudes in a real-space basis. For single-particle 'quantum billiards', these real-space amplitudes are known to have Gaussian…
We construct a random unitary Gaussian circuit for continuous-variable (CV) systems subject to Gaussian measurements. We show that when the measurement rate is nonzero, the steady state entanglement entropy saturates to an area-law scaling.…