Related papers: Hidden tensor structures
We discuss the dynamical quantum systems which turn out to be bi-unitary with respect to the same alternative Hermitian structures in a infinite-dimensional complex Hilbert space. We give a necessary and sufficient condition so that the…
Empirical evidence has confirmed that quantum effects occur frequently also outside the microscopic domain, while quantum structures satisfactorily model various situations in several areas of science, including biological, cognitive and…
Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of…
We develop a means of simulating the evolution and measurement of a multipartite quantum state under discrete or continuous evolution using another quantum system with states and operators lying in a real Hilbert space. This extends…
Bosonic quantum systems operate in an infinite-dimensional Hilbert space, unlike discrete-variable quantum systems. This distinct mathematical structure leads to fundamental differences in quantum information processing, such as an…
Just as a coherent state may be considered as a quantum point, its restriction to a factor space of the full Hilbert space can be interpreted as a quantum plane. The overlap of such a factor coherent state with a full pure state is akin to…
A subspace of a multipartite Hilbert space is completely entangled if it contains no product states. Such subspaces can be large with a known maximum size, S, approaching the full dimension of the system, D. We show that almost all…
Nonequilibrium dynamics of quantum many-body systems is challenging for classical computing, providing opportunities for demonstrating practical quantum computational advantage with analogue quantum simulators. Owing to the intimate…
Generic low-dimensional Hamiltonian systems feature a structured, mixed classical phase-space. The traditional Percival classification of quantum spectra into regular states supported by quasi-integrable regions and irregular states…
The Schmidt decomposition is the go-to tool for measuring bipartite entanglement of pure quantum states. Similarly, it is possible to study the entangling features of a quantum operation using its operator-Schmidt, or tensor product…
Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It…
The hidden-variable question is whether or not various properties --- randomness or correlation, for example --- that are observed in the outcomes of an experiment can be explained via introduction of extra (hidden) variables which are…
Vibrational degrees of freedom in trapped-ion systems have recently been gaining attention as a quantum resource, beyond the role as a mediator for entangling quantum operations on internal degrees of freedom, because of the large available…
A quantum set is defined to be simply a set of nonzero finite-dimensional Hilbert spaces. Together with binary relations, essentially the quantum relations of Weaver, quantum sets form a dagger compact category. Functions between quantum…
We provide a simple construction of bipartite entangled states that are positive under partial transposition, and hence undistillable. The construction makes use of the properties of the projectors onto the symmetric and antisymmetric…
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…
We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert…
A `whole-part' theory is developed for a set of finite quantum systems $\Sigma (n)$ with variables in ${\mathbb Z}(n)$. The partial order `subsystem' is defined, by embedding various attributes of the system $\Sigma (m)$ (quantum states,…
Assuming that quantum mechanics is obeyed exactly after averaging over hidden variables, and considering models that obey both the hypotheses of free will and locality, we establish the form of all possible hidden-variable models that…
In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by…