Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1204.1030

Contradiction of the DENSITY MATRIX notion in quantum mechanics

V. K. Ignatovich

Published Apr 4, 2012• 0 citations
arXivHTMLPDF

Abstract

It is shown that description of a nonpolarized neutron beam by density matrix is contradictory. Density matrix is invariant with respect to choice of quantization axis, while experimental devices can discriminate between different quantization axes.
DOI
10.48550/arxiv.1204.1030

Related papers

CONDITIONAL DENSITY MATRIX in the CONTEXT of NONCONTEXTUALITY

Vladimir Viktorovich Belokurov, Oleg Antonovich Khrustalev, Victor Antonovich Sadovnichy +1 more

Conditional density matrix represents a quantum state of subsystem in different schemes of quantum communication. Here we discuss some properties of conditional density matrix and its place in general scheme of quantum mechanics.

arXiv:quant-ph/0406187•Lomonosov Conference on Elementary Particle Physics•Apr 1, 2005•0 citations

QUANTUM DENSITY MATRIX AND ENTROPIC UNCERTAINTY

R. Blankenblecler

A discussion of the determination of the quantum density matrix from realistic measurements using the maximum entropy principle is presented.

•Feb 3, 2022•0 citations

Underlining some limitations of the statistical formalism in quantum mechanics

F. Fratini, A G Hayrapetyan

We show that two chosen ensembles of spin states, which are differently prepared but are described by the same density matrix in quantum mechanics, do not fully share the same measurable characteristics. One characteristic in which they differ is shown to be the variance of the spin along a given direction. We conclude that the statistical description of an ensemble of states as given by its density matrix, although sufficient in many cases, should be considered incomplete, as it does not fully describe the measurable characteristics of the ensemble. A discussion a posteriori on the problem is provided.

arXiv:1108.6249•Physica Scripta•Aug 31, 2011•8 citations

Contradiction of the DENSITY MATRIX Notion in Quantum Mechanics

V. K. Ignatovich

It is shown for the first time that description of an unpolarized neutron beam by density matrix can be contradictory. Density matrix is invariant with respect to choice of a quantization axis, while experimental devices can discriminate between different quantization axes. An experiment is proposed to discriminate a direction of a quantization axis of a specially prepared nonpolarized beam. The discrimination can be seen by observation of oscillations in statistical uncertainties. The success of the experiment will mean that an entanglement, following from the EPR paradox permits communication with a superluminal speed. A criticism of the EPR paradox and of some experiments on proof of Bell’s inequalities violation is presented.

Universal Journal of Physics and Application•Sep 1, 2013•2 citations

A Note Concerning Propositions in Quantum Mechanics

Joachim Schröter

Abstract It is shown that the interpretation of quantum mechanics as a theory describing systems for which their propositions are always valid or not leads to a contradiction within the theory. The proof does not depend on any specific property of measurements, but only the usual description of ensembles of quantum objects by statistical operators is used.

Annalen der Physik•Jan 1, 1970•1 citation

Experimental quantum state learning with pairs of photons

C. Pria Dobney, Johan Henaff, Allen Kasum +5 more

Tomography allows one to estimate the density matrix describing the state an ensemble of quantum systems are prepared in (for example, polarization tomography determines the polarization state of a beam of identically prepared photons). In general, it is not possible to uniquely decompose the density matrix into its pure state components. Agarwal et al. proposed a protocol which, for a mixture composed of any two pure states of a qubit (with arbitrary probabilities), allows an observer to infer not only the density matrix but the identity of those specific pure states and their weights - the additional requirement being that the qubits arrive in pairs, where both qubits in each pair are in the same state. We experimentally demonstrate this learning-from-pairs concept using photons in the polarization degree of freedom. We use tomography to measure a sequence of single photons and make use of their time-of-arrival information to 'pair up' the photons after the measurement. From here we are able to infer the photons' polarization states and their respective probabilities, and we demonstrate this for various different choices of polarization states and ratios. Finally, we investigate our ability to discriminate between two equal mixtures of distinct pairs of orthogonal polarization states. We find that on the order of approx. 10e4 photons is typically enough to achieve tomography fidelities of approximately 0.9999. This is sufficient to discriminate between two different preparations of the same mixed state, differing by angles of less than 5 degrees between the pure states used in the two preparations.

quant-pharXiv:2606.16932•Jun 16, 2026•0 citations
We show that two chosen ensembles of spin states, which are differently prepared but are described by the same density matrix in quantum mechanics, do not fully share the same measurable characteristics. One characteristic in which they differ is shown to be the variance of the spin along a given direction. We conclude that the statistical description of an ensemble of states as given by its density matrix, although sufficient in many cases, should be considered incomplete, as it does not fully describe the measurable characteristics of the ensemble. A discussion a posteriori on the problem is provided.
It is shown for the first time that description of an unpolarized neutron beam by density matrix can be contradictory. Density matrix is invariant with respect to choice of a quantization axis, while experimental devices can discriminate between different quantization axes. An experiment is proposed to discriminate a direction of a quantization axis of a specially prepared nonpolarized beam. The discrimination can be seen by observation of oscillations in statistical uncertainties. The success of the experiment will mean that an entanglement, following from the EPR paradox permits communication with a superluminal speed. A criticism of the EPR paradox and of some experiments on proof of Bell’s inequalities violation is presented.
Tomography allows one to estimate the density matrix describing the state an ensemble of quantum systems are prepared in (for example, polarization tomography determines the polarization state of a beam of identically prepared photons). In general, it is not possible to uniquely decompose the density matrix into its pure state components. Agarwal et al. proposed a protocol which, for a mixture composed of any two pure states of a qubit (with arbitrary probabilities), allows an observer to infer not only the density matrix but the identity of those specific pure states and their weights - the additional requirement being that the qubits arrive in pairs, where both qubits in each pair are in the same state. We experimentally demonstrate this learning-from-pairs concept using photons in the polarization degree of freedom. We use tomography to measure a sequence of single photons and make use of their time-of-arrival information to 'pair up' the photons after the measurement. From here we are able to infer the photons' polarization states and their respective probabilities, and we demonstrate this for various different choices of polarization states and ratios. Finally, we investigate our ability to discriminate between two equal mixtures of distinct pairs of orthogonal polarization states. We find that on the order of approx. 10e4 photons is typically enough to achieve tomography fidelities of approximately 0.9999. This is sufficient to discriminate between two different preparations of the same mixed state, differing by angles of less than 5 degrees between the pure states used in the two preparations.