Related papers: Coexistence of qubit effects
Within ordinary ---unitary--- quantum mechanics there exist global protocols that allow to verify that no definite event ---an outcome to which a probability can be associated--- occurs. Instead, states that start in a coherent…
Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert…
Quantum coherence is a fundamental property of quantum systems, separating quantum from classical physics. Recently, there has been significant interest in the characterization of quantum coherence as a resource, investigating how coherence…
The landscape of causal relations that can hold among a set of systems in quantum theory is richer than in classical physics. In particular, a pair of time-ordered systems can be related as cause and effect or as the effects of a common…
A non-associative algebra of observables cannot be represented as operators on a Hilbert space, but it may appear in certain physical situations. This article employs algebraic methods in order to derive uncertainty relations and…
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…
The many-worlds interpretation (MWI) of quantum mechanics poses a simple question. What would reality look like if everything evolved in time according to the same quantum equations? There is an attractive consistency to treating…
The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutation relations. A method for constructing irreducible…
Recent arguments based on the quantum extremal surface formula or the gravitational path integral have given fairly compelling evidence that the Hilbert space of quantum gravity in a closed universe is one-dimensional and real. How can this…
Whereas complementarity manifests itself via two incompatible observables, quantum contextuality can only be revealed via the joint measurements among at least three observables. By incorporating unsharp measurements and joint measurements…
Quantum statistics is defined by Hilbert space products between the eigenstates associated with state preparation and measurement. The same Hilbert space products also describe the dynamics generated by a Hamiltonian when one of the states…
On finite dimensional spaces, it is apparent that an operator is the product of two positive operators if and only if it is similar to a positive operator. Here, the class ${\mathcal L}^{+2}$ of bounded operators on separable infinite…
We extend Pearl's definition of causal influence to the quantum domain, where two quantum systems $A$, $B$ with finite-dimensional Hilbert space are embedded in a common environment $C$ and propagated with a joint unitary $U$. For finite…
The quantum inequalities, and the closely related quantum interest conjecture, impose restrictions on the distribution of the energy density measured by any time-like observer, potentially preventing the existence of exotic phenomena such…
The effects of any quantum measurement can be described by a collection of measurement operators {M_m} acting on the quantum state of the measured system. However, the Hilbert space formalism tends to obscure the relationship between the…
Consider a proposed model of the universe with $\hbar$ much greater than its well-known value of $10^{-34} Js$. In this model universe, very large objects can show quantum behaviors. In a scenario with large extra dimensions, $\hbar$ can…
Given a preferred orthonormal basis $B$ in the Hilbert space of a quantum system we define a measure of the coherence generating power of a unitary operation with respect to $B$. This measure is the average coherence generated by the…
The limitation on the sharing of entanglement is a basic feature of quantum theory. For example, if two qubits are completely entangled with each other, neither of them can be at all entangled with any other object. In this paper we show,…
Simultaneous existence of correlation in complementary bases is a fundamental feature of quantum correlation, and we show that this characteristic is present in any non-product bipartite state. We propose a measure via mutually unbiased…
We show that a rank-1 quantum observable (POVM) M is jointly measurable with a quantum observable M' exactly when M' is a smearing of M. If M is extreme, rank-1 and discrete then M and M' are coexistent if and only if they are jointly…