Four Postulates of Quantum Mechanics Are Three.

  title={Four Postulates of Quantum Mechanics Are Three.},
  author={Gabriele Carcassi and Lorenzo Maccone and Christine A. Aidala},
  journal={Physical review letters},
  volume={126 11},
The tensor product postulate of quantum mechanics states that the Hilbert space of a composite system is the tensor product of the components' Hilbert spaces. All current formalizations of quantum mechanics that do not contain this postulate contain some equivalent postulate or assumption (sometimes hidden). Here we give a natural definition of a composite system as a set containing the component systems and show how one can logically derive the tensor product rule from the state postulate and… 

Figures from this paper

State space structure of tripartite quantum systems
State space structure of tripartite quantum systems is analyzed. In particular, it has been shown that the set of states separable across all the three bipartitions [say Bint(ABC)] is a strict subset
Analog Programmable-Photonic Computation
In this work, the foundations of a new computation theory are presented, explicitly designed to unleash the full potential of PIP, which enables overcoming some of the basic theoretical and technological limitations of existing computational models, can be implemented in other technologies and exhibits the potential to spark a ground-breaking impact on information society.
Towards Higher-Level Abstractions for Quantum Computing
It is argued that Software Engineering for QC needs to embark on a similar journey and create abstractions that shield developers from the basic QC building blocks as much as possible so that they can focus their attention on solving problems and less on how to manipulate quantum states using quantum circuits.
Reverse Physics: From Laws to Physical Assumptions
To answer foundational questions in physics, physicists turn more and more to abstract advanced mathematics, even though its physical significance may not be immediately clear. What if we started to
Local quantum state marking
Samrat Sen,1 Edwin Peter Lobo,1 Sahil Gopalkrishna Naik,1 Ram Krishna Patra,1 Tathagata Gupta,2 Subhendu B. Ghosh,2 Sutapa Saha,2 Mir Alimuddin,1 Tamal Guha,3 Some Sankar Bhattacharya,4 and Manik
ge nph ] 1 0 N ov 2 02 1 Reverse Physics
We introduce an approach to the foundations of physics that is more in line with the foundations of mathematics. The idea is to examine current theories and find a set of starting physical


The measurement postulates of quantum mechanics are operationally redundant
The mathematical structure of quantum measurements and the Born rule are usually imposed as axioms; the authors show instead that they are the only possible measurement postulates, if the authors require that arbitrary partitioning of systems does not change the theory’s predictions.
Quantum tensor product structures are observable induced.
A general algebraic framework aimed to formalize the partition of a quantum system into subsystems and the emergence of a multipartite tensor product structure of the state space and the associated notion of quantum entanglement are developed.
Probability theory in quantum mechanics
The abstract theory of probability and its interpretation are briefly reviewed, and it is explicitly demonstrated that the formalism of quantum mechanics satisfies the axioms of probability theory.
Hilbert space structure in quantum gravity: an algebraic perspective
A bstractIf quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum
Mathematical Foundations of Quantum Mechanics
Mathematical Foundations of Quantum Mechanics was a revolutionary book that caused a sea change in theoretical physics. Here, John von Neumann, one of the leading mathematicians of the twentieth
Virtual quantum subsystems.
The physical resources available to access and manipulate the degrees of freedom of a quantum system define the set A of operationally relevant observables, and the notion of compoundness for quantum systems is accordingly relativized.
Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that one is led to conclude that the description of reality as given by a wave function is not complete.
Quantum Darwinism
Quantum Darwinism describes the proliferation, in the environment, of multiple records of selected states of a quantum system. It explains how the fragility of a state of a single quantum system can
Classical interventions in quantum systems. II. Relativistic invariance
If several interventions performed on a quantum system are localized in mutually spacelike regions, they will be recorded as a sequence of ``quantum jumps'' in one Lorentz frame, and as a different
Particles, particle labels, and quanta: The toll of unacknowledged metaphysics
The practice of describing multiparticle quantum systems in terms of labeled particles indicates that we think of quantum entities as individuatable. The labels, together with particle