A recoverable qubit at maximal nonclassical discrimination

We study discrimination of $m$ quantum measurements in the scenario when the unknown measurement with $n$ outcomes can be used only once. We show that ancilla-assisted discrimination procedures provide a nontrivial advantage over simple (ancilla-free) schemes for perfect distinguishability and we prove that inevitably $m\ensuremath{\le}n$. We derive necessary and sufficient conditions of perfect distinguishability of general binary measurements. We show that the optimization of the discrimination of projective qubit measurements and their mixtures with white noise is equivalent to the discrimination of specific quantum states. In particular, the optimal protocol for discrimination of projective qubit measurements with fixed failure rate (exploiting maximally entangled test state) is described. While minimum-error discrimination of two projective qubit measurements can be realized without any need of entanglement, we show that discrimination of three projective qubit measurements requires a bipartite probe state. Moreover, when the measurements are not projective, the non-maximally entangled test states can outperform the maximally entangled ones. Finally, we rephrase the unambiguous discrimination of measurements as quantum key distribution protocol.We study discrimination of $m$ quantum measurements in the scenario when the unknown measurement with $n$ outcomes can be used only once. We show that ancilla-assisted discrimination procedures provide a nontrivial advantage over simple (ancilla-free) schemes for perfect distinguishability and we prove that inevitably $m\ensuremath{\le}n$. We derive necessary and sufficient conditions of perfect distinguishability of general binary measurements. We show that the optimization of the discrimination of projective qubit measurements and their mixtures with white noise is equivalent to the discrimination of specific quantum states. In particular, the optimal protocol for discrimination of projective qubit measurements with fixed failure rate (exploiting maximally entangled test state) is described. While minimum-error discrimination of two projective qubit measurements can be realized without any need of entanglement, we show that discrimination of three projective qubit measurements requires a bipartite probe state. Moreover, when the measurements are not projective, the non-maximally entangled test states can outperform the maximally entangled ones. Finally, we rephrase the unambiguous discrimination of measurements as quantum key distribution protocol.

arXiv:1408.0934Physical Review ANov 10, 201425 citations

Classical, quantum, and general probabilistic state-discrimination profiles

Mihály Weiner

For a collection of states indexed by $[n]={1,\ldots,n}$ , let $F(H)$ denote the optimal unnormalized minimum discrimination error for each nonempty subfamily $H\subseteq[n]$ . We call $F$ the discrimination profile and characterize exactly which profiles can arise in a general probabilistic theory (GPT). For fixed $n$ , the GPT region $\mathfrak{G}_n$ is a bounded rational polytope, giving a hierarchy $\mathfrak{C}_n\subseteq\mathfrak{Q}_n\subseteq\mathfrak{G}_n$ of classical, quantum, and GPT profiles, analogous to the local--quantum--no-signalling hierarchy in Bell theory. For $n=3$ we determine the classical and GPT polytopes explicitly. Within $\mathfrak{G}_3$ , the classical region is characterized by $β:=F(123)-F(12)-F(13)-F(23)\le0$ , while the GPT maximum is $1$ . For qubit triples, the maximal value is attained by the trine, $β_{\mathrm{tr}}=3\sqrt3/2-2$ , and we prove the dimension-independent quantum bound $β_{\mathrm Q}\le2/3$ , with a slight further improvement. Hence $0=β_{\mathrm C}<3\sqrt3/2-2\leβ_{\mathrm Q}\le2/3<1=β_{\mathrm{GPT}}$ . We conjecture $β_{\mathrm Q}=β_{\mathrm{tr}}$ and prove this for arbitrary pure-state triples, together with further supporting evidence. For arbitrary $n$ , every classical facet admitting a GPT violation already admits a quantum violation in dimension at most $3$ . A four-state qubit example shows that quantum success profiles need not be submodular, unlike for $n=3$ . Finally, we exhibit a four-dimensional quantum triple whose discrete profile is classical for all subfamilies but becomes nonclassical when unequal priors are allowed.For a collection of states indexed by $[n]={1,\ldots,n}$, let $F(H)$ denote the optimal unnormalized minimum discrimination error for each nonempty subfamily $H\subseteq[n]$. We call $F$ the discrimination profile and characterize exactly which profiles can arise in a general probabilistic theory (GPT). For fixed $n$, the GPT region $\mathfrak{G}_n$ is a bounded rational polytope, giving a hierarchy $\mathfrak{C}_n\subseteq\mathfrak{Q}_n\subseteq\mathfrak{G}_n$ of classical, quantum, and GPT profiles, analogous to the local--quantum--no-signalling hierarchy in Bell theory. For $n=3$ we determine the classical and GPT polytopes explicitly. Within $\mathfrak{G}_3$, the classical region is characterized by $β:=F(123)-F(12)-F(13)-F(23)\le0$, while the GPT maximum is $1$. For qubit triples, the maximal value is attained by the trine, $β_{\mathrm{tr}}=3\sqrt3/2-2$, and we prove the dimension-independent quantum bound $β_{\mathrm Q}\le2/3$, with a slight further improvement. Hence $0=β_{\mathrm C}<3\sqrt3/2-2\leβ_{\mathrm Q}\le2/3<1=β_{\mathrm{GPT}}$. We conjecture $β_{\mathrm Q}=β_{\mathrm{tr}}$ and prove this for arbitrary pure-state triples, together with further supporting evidence. For arbitrary $n$, every classical facet admitting a GPT violation already admits a quantum violation in dimension at most $3$. A four-state qubit example shows that quantum success profiles need not be submodular, unlike for $n=3$. Finally, we exhibit a four-dimensional quantum triple whose discrete profile is classical for all subfamilies but becomes nonclassical when unequal priors are allowed.

quant-pharXiv:2609.17920Sep 17, 20260 citations

A Unique Qubit at an Extremal Discrimination Boundary

Xinjun Wang

Oct 24, 20260 citations

On the discrimination of qubit channels

Meisheng Zhao, Tao Qin, Yongde Zhang

Physics Letters AOct 26, 20071 citation

A Capacity-Calibrated Protocol for Testing Penrose Objective Reduction

Aernoud Dekker

This document specifies a single prospective experiment: a mesoscopic visibility-loss test that discriminates Penrose objective reduction (OR) from standard physics, in the regime where OR's mass-geometry timescale and the framework's finite-rate basis-tracking timescale fall in the same window. Penrose OR assigns an unrecoverable, mass-geometry-dependent loss; the basis-reference channel of Bandwidth-Limited Quantum Control (BLQC) produces a capacity-dependent but recoverable loss, κ = h_KS − C_eff ln 2 — reference-frame physics within standard quantum mechanics, not a rival prediction. The design's distinctive feature is that the reference channel is calibrated and frozen in advance, and that recoverability (from a passive shadow log) classifies each contrast loss as observer-relative reference bookkeeping (recoverable, R_rec ≈ 1) or collapse-type (unrecoverable, R_rec ≈ 0, mass-geometry-tracking, persistent at maximal tracking capacity). Because the reference physics is measured rather than estimated, it becomes the experiment's calibration arm — the subtrahend — rather than a nuisance background. The core question is then sharp: at fixed thermal, readout, pulse, latency, and plant conditions, is there a κ-independent, unrecoverable visibility floor that follows mass geometry? A positive result is evidence for Penrose OR; a null becomes a quantitative bound on OR rather than an inconclusive absence. The discrimination is of OR against standard physics, not of the framework against quantum mechanics — the framework predicts no floor of its own and cannot win the test, only make it decidable. The protocol defines the platform, control variables, confound controls, statistical tests, and decision rules. Companion documents: IOF framework parent at osf.io/fcdsn, BLQC technical core at osf.io/g5wrh, retrospective forensic data at osf.io/m5tb9.This document specifies a single prospective experiment: a mesoscopic visibility-loss test that discriminates Penrose objective reduction (OR) from standard physics, in the regime where OR's mass-geometry timescale and the framework's finite-rate basis-tracking timescale fall in the same window. Penrose OR assigns an unrecoverable, mass-geometry-dependent loss; the basis-reference channel of Bandwidth-Limited Quantum Control (BLQC) produces a capacity-dependent but recoverable loss, κ = h_KS − C_eff ln 2 — reference-frame physics within standard quantum mechanics, not a rival prediction. The design's distinctive feature is that the reference channel is calibrated and frozen in advance, and that recoverability (from a passive shadow log) classifies each contrast loss as observer-relative reference bookkeeping (recoverable, R_rec ≈ 1) or collapse-type (unrecoverable, R_rec ≈ 0, mass-geometry-tracking, persistent at maximal tracking capacity). Because the reference physics is measured rather than estimated, it becomes the experiment's calibration arm — the subtrahend — rather than a nuisance background. The core question is then sharp: at fixed thermal, readout, pulse, latency, and plant conditions, is there a κ-independent, unrecoverable visibility floor that follows mass geometry? A positive result is evidence for Penrose OR; a null becomes a quantitative bound on OR rather than an inconclusive absence. The discrimination is of OR against standard physics, not of the framework against quantum mechanics — the framework predicts no floor of its own and cannot win the test, only make it decidable. The protocol defines the platform, control variables, confound controls, statistical tests, and decision rules. Companion documents: IOF framework parent at osf.io/fcdsn, BLQC technical core at osf.io/g5wrh, retrospective forensic data at osf.io/m5tb9.

Jan 1, 20250 citations

We study discrimination of

m

quantum measurements in the scenario when the unknown measurement with

n

outcomes can be used only once. We show that ancilla-assisted discrimination procedures provide a nontrivial advantage over simple (ancilla-free) schemes for perfect distinguishability and we prove that inevitably $m\ensuremath{\le}n$. We derive necessary and sufficient conditions of perfect distinguishability of general binary measurements. We show that the optimization of the discrimination of projective qubit measurements and their mixtures with white noise is equivalent to the discrimination of specific quantum states. In particular, the optimal protocol for discrimination of projective qubit measurements with fixed failure rate (exploiting maximally entangled test state) is described. While minimum-error discrimination of two projective qubit measurements can be realized without any need of entanglement, we show that discrimination of three projective qubit measurements requires a bipartite probe state. Moreover, when the measurements are not projective, the non-maximally entangled test states can outperform the maximally entangled ones. Finally, we rephrase the unambiguous discrimination of measurements as quantum key distribution protocol.

For a collection of states indexed by

[n]={1,\ldots,n}

, let

F(H)

denote the optimal unnormalized minimum discrimination error for each nonempty subfamily

H\subseteq[n]

. We call

F

the discrimination profile and characterize exactly which profiles can arise in a general probabilistic theory (GPT). For fixed

n

, the GPT region

\mathfrak{G}_n

is a bounded rational polytope, giving a hierarchy

\mathfrak{C}_n\subseteq\mathfrak{Q}_n\subseteq\mathfrak{G}_n

of classical, quantum, and GPT profiles, analogous to the local--quantum--no-signalling hierarchy in Bell theory. For

n=3

we determine the classical and GPT polytopes explicitly. Within

\mathfrak{G}_3

, the classical region is characterized by

β:=F(123)-F(12)-F(13)-F(23)\le0

, while the GPT maximum is

1

. For qubit triples, the maximal value is attained by the trine,

β_{\mathrm{tr}}=3\sqrt3/2-2

, and we prove the dimension-independent quantum bound

β_{\mathrm Q}\le2/3

, with a slight further improvement. Hence

0=β_{\mathrm C}<3\sqrt3/2-2\leβ_{\mathrm Q}\le2/3<1=β_{\mathrm{GPT}}

. We conjecture

β_{\mathrm Q}=β_{\mathrm{tr}}

and prove this for arbitrary pure-state triples, together with further supporting evidence. For arbitrary

n

, every classical facet admitting a GPT violation already admits a quantum violation in dimension at most

3

. A four-state qubit example shows that quantum success profiles need not be submodular, unlike for

n=3

. Finally, we exhibit a four-dimensional quantum triple whose discrete profile is classical for all subfamilies but becomes nonclassical when unequal priors are allowed.