Related papers: Compatibility of representations of quantum system…
We experimentally demonstrate the migration of coherence between composite quantum systems and their subsystems. The quantum systems are implemented using polarization states of photons in two experimental setups. The first setup is based…
We consider two systems of harmonically trapped particles in a typical pure state of the Hilbert space defined by given values of the particle numbers and energies of the two gases. Such a state is entangled but we show that, for large…
In quantum logic, i.e., within the structure of the Hilbert lattice imposed on all closed linear subspaces of a Hilbert space, the assignment of truth values to quantum propositions (i.e., experimentally verifiable propositions relating to…
We prove that the vast majority of symmetric states of qubits can be decomposed in a unique way into a superposition of spin 1/2 coherent states. For the case of two qubits, the proposed decomposition reproduces the Schmidt decomposition…
We present an equivalence theorem to unify the two classes of uncertainty relations, i.e., the variance-based ones and the entropic forms, which shows that the entropy of an operator in a quantum system can be built from the variances of a…
I propose a new class of interpretations, {\it real world interpretations}, of the quantum theory of closed systems. These interpretations postulate a preferred factorization of Hilbert space and preferred projective measurements on one…
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…
Starting from any proper action of any locally compact quantum group on any discrete quantum space, we show that its equivariant representation theory yields a concrete unitary 2-category of finite type Hilbert bimodules over the discrete…
There is an extensive philosophical literature on the interrelated issues of identity, individuality, and distinguishability in quantum systems. A key consideration is whether quantum systems are subject to a strong form of individuality…
Given a unitary representation of a finite group on a finite-dimensional Hilbert space, we show how to find a state whose translates under the group are distinguishable with the highest probability. We apply this to several quantum oracle…
The sets of contexts and properties of a concept are embedded in the complex Hilbert space of quantum mechanics. States are unit vectors or density operators, and contexts and properties are orthogonal projections. The way calculations are…
We extend the classical construction of operator colligations and characteristic functions. Consider the group $G$ of finite block unitary matrices of size $\alpha+\infty+...+\infty$ ($k$ times). Consider the subgroup $K=U(\infty)$, which…
The standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system: a classical particle running along a circle. Duality here means that there is a one-to-one relation between all…
Quantum mechanics allows coherent superposition between different states of matter. This quality is responsible for major non-classical phenomena that occur in quantum systems. Beyond states, coherent superpositions are also possible…
In consistent history quantum theory, a description of the time development of a quantum system requires choosing a framework or consistent family, and then calculating probabilities for the different histories which it contains. It is…
Any unitary transformation of quantum computational networks is explicitly decomposed, in an exact and unified form, into a sequence of a limited number of one-qubit quantum gates and the two-qubit diagonal gates that have diagonal unitary…
Matchgates are an especially multiflorous class of two-qubit nearest neighbour quantum gates, defined by a set of algebraic constraints. They occur for example in the theory of perfect matchings of graphs, non-interacting fermions, and…
The quantum equivalence principle says that, for any given point, it is possible to find a quantum coordinate system with respect to which we have definite causal structure in the vicinity of that point. It is conjectured that this…
This thesis is concerned with the representation theory of the Heisenberg group and its applications to both classical and quantum mechanics. We continue the development of $p$-mechanics which is a consistent physical theory capable of…
We investigate bicomplex Hamiltonian systems in the framework of an analogous version of the Schrodinger equation. Since in such a setting three different types of conjugates of bicomplex numbers appear, each is found to define in a natural…