Information capacity enhancement through the coherent control of channels has attracted much attention of late, with work exploring the effect of coherent control of channel causal orders, channel ...superpositions, and information encoding. Coherently controlling channels necessitates a non-trivial expansion of the channel description, which for superposing qubit channels, is equivalent to expanding the channel to act on qutrits. Here we explore the nature of this capacity enhancement for the superposition of channels by comparing the maximum coherent information through depolarizing qubit channels and relevant superposed and qutrit channels. We show that the expanded qutrit channel description in itself is sufficient to explain the capacity enhancement without any use of superposition.
Information capacity enhancement through the coherent control of channels has attracted much attention of late, with work exploring the effect of coherent control of channel causal orders, channel ...superpositions, and information encoding. Coherently controlling channels necessitates a non-trivial expansion of the channel description, which for superposing qubit channels, is equivalent to expanding the channel to act on qutrits. Here we explore the nature of this capacity enhancement for the superposition of channels by comparing the maximum coherent information through depolarizing qubit channels and relevant superposed and qutrit channels. We show that the expanded qutrit channel description in itself is sufficient to explain the capacity enhancement without any use of superposition.
The de Broglie-Bohm theory is a hidden-variable interpretation of quantum mechanics which involves particles moving through space along deterministic trajectories. This theory singles out position as ...the primary ontological variable. Mathematically, it is possible to construct a similar theory where particles are moving through momentum-space, and momentum is singled out as the primary ontological variable. In this paper, we construct the putative particle trajectories for a two-slit experiment in both the position and momentum-space theories by simulating particle dynamics with coherent light. Using a method for constructing trajectories in the primary and non-primary spaces, we compare the phase-space dynamics offered by the two theories and show that they do not agree. This contradictory behaviour underscores the difficulty of selecting one picture of reality from the infinite number of possibilities offered by Bohm-like theories.
It is often thought that the super-sensitivity of a quantum state to an observable comes at the cost of a decreased sensitivity to other non-commuting observables. For example, a squeezed state ...squeezed in position quadrature is super-sensitive to position displacements, but very insensitive to momentum displacements. This misconception was cleared with the introduction of the compass state Nature 412 , 712 ( 2001 ) 10.1038/35089017 , a quantum state equally super-sensitive to displacements in position and momentum. When looking at quantum states used to measure spin rotations, N 00 N states are known to be more advantageous than classical methods as long as they are aligned to the rotation axis. When considering the estimation of a rotation with unknown direction and amplitude, a certain class of states stands out with interesting properties. These states are equally sensitive to rotations around any axis, are second-order unpolarized, and can possess the rotational properties of Platonic solids in particular dimensions. Importantly, these states are optimal for simultaneously estimating the three parameters describing a rotation. In the asymptotic limit, estimating all d parameters describing a transformation simultaneously rather than sequentially can lead to a reduction of the appropriately weighted sum of the measured parameters’ variances by a factor of d . We report the experimental creation and characterization of the lowest-dimensional such state, which we call the “tetrahedron state” due to its tetrahedral symmetry. This tetrahedron state is created in the symmetric subspace of four optical photons’ polarization in a single spatial and temporal mode, which behaves as a spin-2 particle. While imperfections due to the hardware limited the performance of our method, ongoing technological advances will enable this method to generate states which out-perform any other existing strategy in per-photon comparisons.
The traditional formalism of quantum measurement (hereafter ``TQM'') describes processes where some properties of quantum states are extracted and stored as classical information. While TQM is a ...natural and appropriate description of how humans interact with quantum systems, it is silent on the question of how a more general, quantum, agent would do so. How do we describe the observation of a system by an observer with the ability to store not only classical information but quantum states in its memory? In this paper, we extend the idea of measurement to a more general class of sensors for quantum agents which interact with a system in such a way that the agent's memory stores information (classical or quantum) about the system under study. For appropriate sensory interactions, the quantum agent may ``learn'' more about the system than would be possible under any set of classical measurements -- but as we show, this comes at the cost of additional measurement disturbance. We experimentally demonstrate such a system and characterize the tradeoffs, which can be done by considering the information required to erase the effects of a measurement.
It is often thought that the super-sensitivity of a quantum state to an observable comes at the cost of a decreased sensitivity to other non-commuting observables. For example, a squeezed state ...squeezed in position quadrature is super-sensitive to position displacements, but very insensitive to momentum displacements. This misconception was cleared with the introduction of the compass state, a quantum state equally super-sensitive to displacements in position and momentum. When looking at quantum states used to measure spin rotations, N00N states are known to be more advantageous than classical methods as long as they are aligned to the rotation axis. When considering the estimation of a rotation with unknown direction and amplitude, a certain class of states stands out with interesting properties. These states are equally sensitive to rotations around any axis, are second-order unpolarized, and can possess the rotational properties of platonic solids in particular dimensions. Importantly, these states are optimal for simultaneously estimating the three parameters describing a rotation. In the asymptotic limit, estimating all d parameters describing a transformation simultaneously rather than sequentially can lead to a reduction of the appropriately-weighted sum of the measured parameters' variances by a factor of d. We report the experimental creation and characterization of the lowest-dimensional such state, which we call the "tetrahedron state" due to its tetrahedral symmetry. This tetrahedron state is created in the symmetric subspace of four optical photons' polarization in a single spatial and temporal mode, which behaves as a spin-2 particle. While imperfections due to the hardware limit the performance of our method, we argue that better technology can improve our method to the point of outperforming any other existing strategy in per-photon comparisons.
Operator noncommutation, a hallmark of quantum theory, limits measurement precision, according to uncertainty principles. Wielded correctly, though, noncommutation can boost precision. A recent ...foundational result relates a metrological advantage with negative quasiprobabilities -- quantum extensions of probabilities -- engendered by noncommuting operators. We crystallize the relationship in an equation that we prove theoretically and observe experimentally. Our proof-of-principle optical experiment features a filtering technique that we term partially postselected amplification (PPA). Using PPA, we measure a waveplate's birefringent phase. PPA amplifies, by over two orders of magnitude, the information obtained about the phase per detected photon. In principle, PPA can boost the information obtained from the average filtered photon by an arbitrarily large factor. The filter's amplification of systematic errors, we find, bounds the theoretically unlimited advantage in practice. PPA can facilitate any phase measurement and mitigates challenges that scale with trial number, such as proportional noise and detector saturation. By quantifying PPA's metrological advantage with quasiprobabilities, we reveal deep connections between quantum foundations and precision measurement.
The de Broglie-Bohm theory is a hidden variable interpretation of quantum mechanics which involves particles moving through space with definite trajectories. This theory singles out position as the ...primary ontological variable. Mathematically, it is possible to construct a similar theory where particles are moving through momentum space, and momentum is singled out as the primary ontological variable. In this paper we experimentally show how the two theories lead to different ontological descriptions. We construct the putative particle trajectories for a two-slit experiment in both the position and momentum space theories by simulating particle dynamics with coherent light. Using a method for constructing trajectories through the primary and derived (i.e. non-primary) spaces, we compare the ontological pictures offered by the two theories and show that they do not agree. This contradictory behaviour brings into question which ontology for Bohmian mechanics is to be preferred.
Uncertainty principles limit measurement precision, via operator noncommutation. Wielded correctly, noncommutation can boost precision. We relate metrological enhancement with negative ...quasiprobabilities, quantum extensions of probabilities. In a phase measurement, we amplify the precision per detected photon by two orders of magnitude.
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