Related papers: A universal property for sequential measurement
In this paper, we study the tensor product of two unitary irreducible representations, as well as the tensor product of a unitary irreducible representation with a finite-dimensional one, and determine the corresponding Clebsch-Gordan…
A sequence $A$ of positive integers having the property that no element $a_i \in A$ divides the sum $a_j+a_k$ of two larger elements is said to have `Property P'. We construct an infinite set $S\subset \mathbb{N}$ having Property P with…
We consider a large family of product operations of formal power series in noncommuting indeterminates, the classes of automata they define, and the respective equivalence problems. A $P$-product of series is defined coinductively by a…
The coexistence relation of quantum effects is a fundamental structure, describing those pairs of experimental events that can be implemented in a single setup. Only in the simplest case of qubit effects an analytic characterization of…
A sequential effect algebra (SEA) is an effect algebra equipped with a sequential product operation modeled after the L\"uders product $(a,b)\mapsto \sqrt{a}b\sqrt{a}$ on C*-algebras. A SEA is called normal when it has all suprema of…
We present two new quantum union bounds for sequential projective measurements. These bounds estimate the disturbance accumulation and probability of outcomes when the measurements are performed sequentially. These results are based on a…
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…
The canonical commutation relation, $[Q,P] = i\hbar$, stands at the foundation of quantum theory and the original Hilbert space. The interpretation of $P$ & $Q$ as observables has always relied on the analogies that exist between the…
We consider the product of infinitely many copies of a spin-$1\over 2$ system. We construct projection operators on the corresponding nonseparable Hilbert space which measure whether the outcome of an infinite sequence of $\sigma^x$…
This is an expository paper on tensor products where the standard approaches for constructing concrete instances of algebraic tensor products of linear spaces, via quotient spaces or via linear maps of bilinear maps, are reviewed by…
We sketch applications of the so-called J-equation to quantum information theory concerning fundamental properties of the von Neumann entropy. The J-equation has recently be proposed as a sort of progenitor of the various versions of the…
Quantum coherence characterizes the non-classical feature of a single party system with respect to a local basis. Based on a recently introduced resource framework, coherence can be regarded as a resource and be systematically manipulated…
Consecutive quantum measurements performed on the same system can reveal fundamental insights into quantum theory's causal structure, and probe different aspects of the quantum measurement problem. According to the Copenhagen…
The mathematical formulation of Quantum Mechanics in terms of complex Hilbert space is derived for finite dimensions, starting from a general definition of "physical experiment" and from five simple Postulates concerning "experimental…
The topical quantum computation paradigm is a transposition of the Turing machine into the quantum framework. Implementations based on this paradigm have limitations as to the number of: qubits, computation steps, efficient quantum…
We introduce a general scheme for sequential one-way quantum computation where static systems with long-living quantum coherence (memories) interact with moving systems that may possess very short coherence times. Both the generation of the…
Studying sequential measurements is of the utmost importance to both the foundational aspects of quantum theory and the practical implementations of quantum technologies, with both of these applications being abstractly described by the…
We define the graph product of unital completely positive maps on a universal graph product of unital C*-algebras and show that it is unital completely positive itself. To accomplish this, we introduce the notion of the non-commutative…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…
Any observable with finite eigenvalue spectrum can be measured using a multiport apparatus realizing an appropriate unitary transformation and an array of detector instruments, where each detector operates as an indicator of one possible…