Measuring Entanglement in Qubit System

Tabish Qureshi; Vignesh S

arxiv: 2606.05056 · v1 · pith:7J73NU6Wnew · submitted 2026-06-03 · 🪐 quant-ph

Measuring Entanglement in Qubit System

Vignesh S , Tabish Qureshi This is my paper

Pith reviewed 2026-06-28 05:36 UTC · model grok-4.3

classification 🪐 quant-ph

keywords entanglement measurementconcurrencequantum erasureinterferometerqubitancillaoutput asymmetrycoherence

0 comments

The pith

Concurrence of internal-ancilla entanglement is extracted directly from output channel asymmetry after quantum erasure in two-path interferometers.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops an operational method for measuring entanglement in qubit systems inside balanced two-path interferometers. Path information is encoded in an internal degree of freedom that becomes entangled with an ancilla; after tracing out the ancilla, a quantum-erasing step on the internal degree converts the resulting output asymmetry into a concurrence value that quantifies that entanglement. The same procedure applies to both a modified Stern-Gerlach setup with spin-1/2 particles and a Mach-Zehnder interferometer with polarized photons. The authors show that loss of coherence, quantum erasure, and entanglement estimation all arise from one underlying correlation structure, yielding a compact experimental protocol that does not require direct access to the ancilla.

Core claim

In the tripartite description of paths, internal qubit degree of freedom, and ancilla, tracing out the ancilla and applying a quantum-erasing procedure based on the internal degree allows the concurrence that measures entanglement between the internal degree and the ancilla to be read directly from the measurable intensity asymmetry between the two output channels.

What carries the argument

Quantum erasure performed on the internal qubit degree of freedom, which isolates the concurrence of internal-ancilla entanglement from the asymmetry of the two interferometer output channels.

If this is right

Loss of coherence, quantum erasure, and entanglement estimation all originate from the same correlation structure in the tripartite system.
Entanglement between the internal degree and ancilla can be quantified even when the ancilla itself is not experimentally accessible.
The method applies equally to matter-wave interferometers with spin-1/2 particles and optical interferometers with photon polarization.
Standard intensity measurements at the output ports suffice to obtain a concurrence-based entanglement measure.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The approach could be tested in other interferometric geometries where an environmental degree of freedom plays the role of the ancilla.
If the asymmetry-concurrence relation holds, it may simplify entanglement detection protocols that currently require full state tomography.
The shared correlation structure suggests that complementarity relations in interferometers can be re-expressed directly in terms of this measurable concurrence.

Load-bearing premise

The quantum-erasing procedure on the internal degree of freedom cleanly isolates the internal-ancilla concurrence from the output asymmetry without residual contributions from paths or other correlations.

What would settle it

An experiment in which the measured output asymmetry fails to match the concurrence calculated from the known internal-ancilla entanglement for the described Stern-Gerlach or Mach-Zehnder setups.

Figures

Figures reproduced from arXiv: 2606.05056 by Tabish Qureshi, Vignesh S.

**Figure 2.** Figure 2: FIG. 2. Mach–Zehnder interferometer geometry. PBS1 cre [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

read the original abstract

An operational way of measuring entanglement in a balanced two-path interferometers is presented, where path information is carried by some internal degree of freedom which, in turn, gets entangled with an ancilla system. The analysis is based on a tripartite description involving paths, an internal qubit degree of freedom, and some ancillary states entangled with the internal degree of freedom. It is then applied to two physically distinct experimental situations: a modified Stern-Gerlach interferometer with spin-1/2 particles and a Mach-Zehnder interferometer with photons carrying polarization. The ancilla degree of freedom may not be experimentally accessible. Tracing out the ancillary system, and employing a quantum erasing procedure based on the internal degree of freedom, it is demonstrated that a concurrence-based measure of the entanglement, between the internal degree of freedom and the ancilla, can be extracted directly from measurable asymmetry of the two output channels. These results show that loss of coherence, quantum erasure, and entanglement estimation in interferometric experiments arise from the same underlying correlation structure and provide a compact experimentally accessible framework for quantifying entanglement in qubit systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper shows how to extract a concurrence measure of entanglement from output asymmetry in two specific balanced interferometers after erasure, but the derivations are not visible here so novelty is unclear.

read the letter

The core claim is that in a balanced two-path interferometer where path info lives in an internal qubit degree of freedom entangled with an ancilla, you can trace out the ancilla, apply a quantum erase on the internal DOF, and read a concurrence-based entanglement measure straight off the measurable asymmetry between the two output channels.

It sets this up with a tripartite model (paths, internal qubit, ancilla) and works through two concrete cases: a modified Stern-Gerlach for spin-1/2 particles and a Mach-Zehnder for polarized photons. The paper ties loss of coherence, the erasure step, and the entanglement estimate to the same underlying correlations, which gives a compact operational picture that does not require direct access to the ancilla.

That link is the useful part for experiment design in these qubit systems. It keeps the method tied to standard interferometer outputs.

The main soft spot is scope. Everything is restricted to balanced two-path cases, so it does not speak to more general entanglement quantification. The abstract gives no equations or error analysis, which makes it impossible to check whether the extraction formula is new or reduces to earlier concurrence expressions already in the literature. The erasing procedure is presented as cleanly isolating the desired quantity, but that needs the full math to verify.

This is for people running interferometric experiments with qubits who want a direct readout of entanglement from asymmetry data. A reader focused on practical measurement techniques in quantum optics or information would get something concrete from it.

It is worth sending to peer review so the derivations and literature comparison can be checked properly.

Referee Report

2 major / 2 minor

Summary. The paper presents an operational procedure for extracting a concurrence-based measure of entanglement between an internal qubit degree of freedom and an ancilla in balanced two-path interferometers. Path information is encoded in the internal DOF, which is entangled with the ancilla; after tracing out the ancilla and applying a quantum-erasing procedure based on the internal DOF, the entanglement is claimed to be readable from the measurable asymmetry between the two output channels. The method is illustrated on a modified Stern-Gerlach interferometer with spin-1/2 particles and a Mach-Zehnder interferometer with polarized photons, with the tripartite (path-internal-ancilla) description used to link loss of coherence, quantum erasure, and entanglement quantification.

Significance. If the extraction procedure is rigorously derived, the work would supply a compact, experimentally accessible framework that unifies coherence loss, erasure, and entanglement estimation in qubit interferometry without requiring direct access to the ancilla. This could be useful for systems where the ancilla is inaccessible, provided the claimed mapping from output asymmetry to concurrence is shown to be parameter-free and independent of ancillary details.

major comments (2)

[Abstract / main text (no equations or sections numbered)] The manuscript states the central claim (concurrence extracted from post-erasure output asymmetry) only at the level of the abstract and high-level description; no explicit tripartite state, no derivation of the asymmetry-to-concurrence mapping, and no error analysis or numerical example are supplied. This absence prevents verification that the procedure is not circular or dependent on unstated assumptions about state preparation.
[Application sections (Stern-Gerlach and Mach-Zehnder)] The tripartite construction and quantum-erasing step are invoked to isolate the internal-ancilla concurrence, yet the manuscript provides neither the explicit form of the reduced density matrix after tracing the ancilla nor the expression relating channel asymmetry to concurrence. Without these, it is impossible to confirm that the extracted quantity is indeed the concurrence rather than a rescaled or fitted proxy.

minor comments (2)

Notation for the internal degree of freedom, ancilla states, and output channels should be defined consistently and introduced before use.
The two experimental examples would benefit from a side-by-side comparison table of the relevant parameters (e.g., which DOF plays the role of the ancilla) to clarify the claimed generality.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and for identifying the need for greater explicitness in the derivations. We agree that the original manuscript presented the central mapping at a descriptive level and will revise it to include the missing technical details. Below we respond to each major comment.

read point-by-point responses

Referee: [Abstract / main text (no equations or sections numbered)] The manuscript states the central claim (concurrence extracted from post-erasure output asymmetry) only at the level of the abstract and high-level description; no explicit tripartite state, no derivation of the asymmetry-to-concurrence mapping, and no error analysis or numerical example are supplied. This absence prevents verification that the procedure is not circular or dependent on unstated assumptions about state preparation.

Authors: We acknowledge that the current version relies on a high-level description without the explicit tripartite state or step-by-step derivation. In the revised manuscript we will introduce the full tripartite state (path-internal-ancilla), derive the reduced density matrix after tracing out the ancilla, obtain the post-erasure output probabilities, and show the direct algebraic mapping from the measured channel asymmetry to the concurrence. A numerical example with error propagation will also be added to illustrate independence from ancillary details and to rule out circularity. revision: yes
Referee: [Application sections (Stern-Gerlach and Mach-Zehnder)] The tripartite construction and quantum-erasing step are invoked to isolate the internal-ancilla concurrence, yet the manuscript provides neither the explicit form of the reduced density matrix after tracing the ancilla nor the expression relating channel asymmetry to concurrence. Without these, it is impossible to confirm that the extracted quantity is indeed the concurrence rather than a rescaled or fitted proxy.

Authors: We agree that the explicit reduced density matrix and the asymmetry-to-concurrence relation were not written out. The revision will contain the traced-out two-qubit state for both the Stern-Gerlach and Mach-Zehnder cases, followed by the quantum-erasure operation on the internal degree of freedom and the resulting expression that equates the observable output asymmetry directly to the concurrence (no fitting parameters). This will confirm that the extracted quantity is the standard concurrence of the internal-ancilla subsystem. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper presents an operational procedure to extract a concurrence-based entanglement measure from post-erasure output asymmetry in a tripartite interferometric setup. The abstract and description frame this as a derivation from the tripartite state construction and quantum erasure, without evidence that the extracted quantity is defined in terms of the asymmetry by construction or that any central step reduces to a fitted parameter or self-citation chain. No load-bearing self-citations, ansatz smuggling, or renaming of known results are indicated in the provided text. The derivation appears self-contained against the stated assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review limited to abstract; no free parameters, new entities, or ad-hoc axioms are visible in the provided text.

axioms (1)

standard math Standard quantum mechanics applies to the tripartite system of paths, internal qubit, and ancilla
The analysis is based on a tripartite description involving paths, an internal qubit degree of freedom, and some ancillary states entangled with the internal degree of freedom.

pith-pipeline@v0.9.1-grok · 5710 in / 1318 out tokens · 27983 ms · 2026-06-28T05:36:45.671242+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

10 extracted references · 1 linked inside Pith

[1]

D. S. Starke, J. Maziero, M. L. W. Basso, and T. Qureshi, ”Bohr’s complementarity,” arXiv:2605.26375 [quant-ph]

Pith/arXiv arXiv
[2]

Quantum Eraser: A Pro- posed Photon Correlation Experiment Concerning Ob- servation and ‘Delayed Choice’ in Quantum Mechanics,

M. O. Scully and K. Dr¨ uhl, “Quantum Eraser: A Pro- posed Photon Correlation Experiment Concerning Ob- servation and ‘Delayed Choice’ in Quantum Mechanics,” Phys. Rev. A 25, 2208 (1982)

1982
[3]

Delayed-choice gedanken experiments and their realizations

X. Ma, J. Kofler, and A. Zeilinger, “Delayed-choice gedanken experiments and their realizations”, Rev. Mod. Phys. 88, 015005 (2016)

2016
[4]

The Enigma of Delayed Choice Quantum Eraser,

T. Qureshi, “The Enigma of Delayed Choice Quantum Eraser,” Quanta 14, 66 (2025)

2025
[5]

Entanglement of a pair of quan- tum bits,

S. Hill, W.K. Wootters, “Entanglement of a pair of quan- tum bits,”Phys. Rev. Lett.78, 5022 (1997)

1997
[6]

Is spin coherence like Humpty-Dumpty? I. Simplified treat- ment,

B.-G. Englert, J. Schwinger, and M. O. Scully, “Is spin coherence like Humpty-Dumpty? I. Simplified treat- ment,” Found. Phys. 18, 1045 (1988)

1988
[7]

Qureshi and Z

T. Qureshi and Z. Rahman,Quantum eraser using a modified Stern-Gerlach setup, Prog. Theor. Phys. 127, 71 (2012)

2012
[8]

R. D. Barney and J.-F. S. Van Huele,Quantum coherence recovery through Stern-Gerlach erasure, Phys. Scr.94, 105105 (2019)

2019
[9]

Coherence, path predictability, and I-concurrence: A triality,

A. K. Roy, N. Pathania, N. K. Chandra, P. K. Pani- grahi, and T. Qureshi, “Coherence, path predictability, and I-concurrence: A triality,” Phys. Rev. A 105, 032209 (2022)

2022
[10]

Wave–particle duality and quantum erasure in polar- ized–neutron interferometry,

G. Badurek, R. J. Buchelt, B.-G. Englert, and H. Rauch, “Wave–particle duality and quantum erasure in polar- ized–neutron interferometry,” Nuclear Instruments and Methods in Physics Research Section A 440, 562 (2000)

2000

[1] [1]

D. S. Starke, J. Maziero, M. L. W. Basso, and T. Qureshi, ”Bohr’s complementarity,” arXiv:2605.26375 [quant-ph]

Pith/arXiv arXiv

[2] [2]

Quantum Eraser: A Pro- posed Photon Correlation Experiment Concerning Ob- servation and ‘Delayed Choice’ in Quantum Mechanics,

M. O. Scully and K. Dr¨ uhl, “Quantum Eraser: A Pro- posed Photon Correlation Experiment Concerning Ob- servation and ‘Delayed Choice’ in Quantum Mechanics,” Phys. Rev. A 25, 2208 (1982)

1982

[3] [3]

Delayed-choice gedanken experiments and their realizations

X. Ma, J. Kofler, and A. Zeilinger, “Delayed-choice gedanken experiments and their realizations”, Rev. Mod. Phys. 88, 015005 (2016)

2016

[4] [4]

The Enigma of Delayed Choice Quantum Eraser,

T. Qureshi, “The Enigma of Delayed Choice Quantum Eraser,” Quanta 14, 66 (2025)

2025

[5] [5]

Entanglement of a pair of quan- tum bits,

S. Hill, W.K. Wootters, “Entanglement of a pair of quan- tum bits,”Phys. Rev. Lett.78, 5022 (1997)

1997

[6] [6]

Is spin coherence like Humpty-Dumpty? I. Simplified treat- ment,

B.-G. Englert, J. Schwinger, and M. O. Scully, “Is spin coherence like Humpty-Dumpty? I. Simplified treat- ment,” Found. Phys. 18, 1045 (1988)

1988

[7] [7]

Qureshi and Z

T. Qureshi and Z. Rahman,Quantum eraser using a modified Stern-Gerlach setup, Prog. Theor. Phys. 127, 71 (2012)

2012

[8] [8]

R. D. Barney and J.-F. S. Van Huele,Quantum coherence recovery through Stern-Gerlach erasure, Phys. Scr.94, 105105 (2019)

2019

[9] [9]

Coherence, path predictability, and I-concurrence: A triality,

A. K. Roy, N. Pathania, N. K. Chandra, P. K. Pani- grahi, and T. Qureshi, “Coherence, path predictability, and I-concurrence: A triality,” Phys. Rev. A 105, 032209 (2022)

2022

[10] [10]

Wave–particle duality and quantum erasure in polar- ized–neutron interferometry,

G. Badurek, R. J. Buchelt, B.-G. Englert, and H. Rauch, “Wave–particle duality and quantum erasure in polar- ized–neutron interferometry,” Nuclear Instruments and Methods in Physics Research Section A 440, 562 (2000)

2000