Milestone Gallery
Milestone Overview
Ph.D. Defense in Theoretical Physics: Tomographic Methods in Quantum Mechanics & Optics
Successfully Defended at Moscow Institute of Physics and Technology (MIPT) — December 17, 2010
This research milestone marks the formal presentation and defense of the doctoral thesis introducing a probabilistic approach to quantum mechanics. By mapping non-classical quantum states onto non-negative probability distributions (quantum tomograms) via Radon transforms, the work bridges classical statistical mechanics and quantum information theory.
Degree Awarded | Ph.D. in Theoretical Physics (Specialty 01.04.02) |
Institution | Moscow Institute of Physics and Technology (MIPT) |
Scientific Advisor | Prof. Vladimir I. Manko, Dr.Sc. (Lebedev Physical Institute) |
Leading Organization | Skobeltsyn Institute of Nuclear Physics, MSU (SINP MSU) |
Official Opponents | Prof. G.G. Amosov (D.Sc., Steklov Mathematical Institute, RAS), Dr. V.A. Andreev (Ph.D., P.N. Lebedev Physical Institute - FIAN) |
Defense Verdict | Unanimously Approved (13–0 Vote) |
Key Scientific Breakthroughs
Probabilistic Representation of Quantum States Developed a complete mathematical framework representing quantum states via non-negative, normalized probability distributions (tomograms). Demonstrated how quantum tomograms directly replace abstract wavefunctions and density matrices with measurable probability functions.
Generalized CHSH Inequalities & Upper Bounds Established generalized Clauser-Horne-Shimony-Holt (CHSH) inequalities for multi-qubit and multi-qutrit quantum systems using stochastic matrices. Derived precise classical and quantum upper limits, including a novel upper bound for qubit-qutrit systems (B = 4.0612).
Tomographic Entropies & Correlation Independence Introduced joint and relative tomographic entropies extending Shannon and von Neumann entropy concepts. Proved that violations of CHSH inequalities and entropic Shannon inequalities in quantum domains represent mathematically independent aspects of non-locality.
Quantum Optics & Squeezed Light Tomography Calculated symplectic, center-of-mass, and photon-counting tomograms for single-mode and two-mode squeezed vacuum states. Uncovered new integral relations connecting multidimensional Hermite and Laguerre polynomials.
Defense Highlights & Oral Examination
In response to board inquiries regarding the term "tomogram", Loran Jacobs explains that while classical tomography measures density slices of a physical object, in quantum state tomography the state itself is the object. The tomogram represents a positive-definite probability distribution function from which any quantum state can be fully reconstructed without relying on complex wavefunctions.
Explanation of spatial non-locality in quantum correlations between distant, non-interacting particles. Loran Jacobs details how tomographic CHSH inequalities test the fundamental boundaries of local realism in the context of the Einstein-Podolsky-Rosen (EPR) paradox.
Official address by thesis advisor Prof. V.I. Manko evaluating the candidate's research independence and highlighting the fundamental importance of replacing density matrices with true probability distribution functions in quantum mechanics.
The official announcement of the secret ballot results by the Tally Commission (13 votes "In Favor", 0 "Against", 0 "Invalid"), unanimously awarding the Ph.D. degree in Theoretical Physics.
Defense Q&A & Transcript Excerpts
Physical Meaning of "Quantum Tomogram"
Board Question (Prof. A.V. Masalov): "When you use the term 'tomogram', what physical object or slice do you imply behind it?"
Candidate Answer (Loran Jacobs): "In classical statistical mechanics, a tomogram measures density distributions of an object via Radon transformation. In our framework, the state itself is the object. The tomogram is a positive-definite probability distribution function from which any quantum state — observable or non-observable — can be fully reconstructed without relying on complex wavefunctions."
Quantum Non-Locality & the EPR Paradox
Board Question (Prof. A.V. Masalov):
"In what sense do you understand 'non-locality', and why is it important for your work?"
Candidate Answer (Loran Jacobs):
"Non-locality refers to spatial correlations between distant, non-interacting particles that cannot be explained within classical mechanics. It is rooted in the Einstein-Podolsky-Rosen (EPR) paradox and is formally tested via violations of CHSH-type inequalities."
Endorsement by Scientific Advisor Prof. V.I. Manko
Scientific Advisor Statement (Prof. Vladimir I. Manko):
"The essential physical meaning of this dissertation — and of the entire tomographic approach — is that quantum mechanics can be completely reformulated using true probability distribution functions instead of density matrices. This provides a unified probabilistic language for classical and quantum physics."
Experimental Implementation & Squeezed States
Board Question (Prof. Yu.M. Belousov):
"How do your theoretical results regarding squeezed state tomograms correspond to experimental setups?"
Candidate Answer (Loran Jacobs):
"The derived tomographic distribution functions represent direct physical observables. They can be experimentally measured using optical homodyne detection and photon-counting detectors to directly verify non-classical field correlations and CHSH violations in squeezed vacuum states."
Digital Archive & Primary Sources
Key Peer-Reviewed Journal Publications (2009–2011)
L.V. Akopyan, V.I. Man'ko, General Bell-CHSH type and entropic inequalities based on quantum tomograms. Optics and Spectroscopy, 111(4), 690–699 (2011).
L.V. Jacobs, V.I. Man'ko, Two-mode squeezed vacuum states in tomographic-probability representation. Journal of Russian Laser Research, 31(6), 520–532 (2010).
L.V. Jacobs, V.I. Man'ko, Bell-type inequalities and upper bounds for multiqudit states. Journal of Russian Laser Research, 30(4), 338–358 (2009).
L.V. Jacobs, V.I. Man'ko, Bell-type Inequalities in Classical Probability Theory. Journal of Russian Laser Research, 30(1), 82–100 (2009).
Note: Academic records, VAK registry certificates, and original publications for this defense are registered under the historical name Loran V. Akopyan (Акопян Л. В.).