Assessments of macroscopicity for quantum optical states

Laghaout, Amine; Neergaard-Nielsen, Jonas S.; Andersen, Ulrik L.

doi:10.1016/j.optcom.2014.07.046

Cited by 14 publications

(14 citation statements)

References 27 publications

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“…Let us adapt some of them to our purposes. The first, which we shall generically refer to as "distinguishability" and denote by D, is based on the Bhattacharyya coefficient [35][36][37],…”

Section: Distinguishabilitymentioning

confidence: 99%

Algebraic and algorithmic frameworks for optimized quantum measurements

Laghaout

Andersen

2015

Phys. Rev. A

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Von Neumann projections are the main operations by which information can be extracted from the quantum to the classical realm. They are however static processes that do not adapt to the states they measure. Advances in the field of adaptive measurement have shown that this limitation can be overcome by "wrapping" the von Neumann projectors in a higher-dimensional circuit which exploits the interplay between measurement outcomes and measurement settings. Unfortunately, the design of adaptive measurement has often been ad hoc and setup-specific. We shall here develop a unified framework for designing optimized measurements. Our approach is two-fold: The first is algebraic and formulates the problem of measurement as a simple matrix diagonalization problem. The second is algorithmic and models the optimal interaction between measurement outcomes and measurement settings as a cascaded network of conditional probabilities. Finally, we demonstrate that several figures of merit, such as Bell factors, can be improved by optimized measurements. This leads us to the promising observation that measurement detectors which-taken individually-have a low quantum efficiency can be be arranged into circuits where, collectively, the limitations of inefficiency are compensated for.

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“…Let us adapt some of them to our purposes. The first, which we shall generically refer to as "distinguishability" and denote by D, is based on the Bhattacharyya coefficient [35][36][37],…”

Section: Distinguishabilitymentioning

confidence: 99%

Algebraic and algorithmic frameworks for optimized quantum measurements

Laghaout

Andersen

2015

Phys. Rev. A

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“…For a counterexample, Leggett mentions superconductivity on visible scales. In order to further elaborate on this difference, several proposals to formalize the concept of macroscopic distinctness based on the 'dead and alive' structure of a quantum state have been put forward [3][4][5][6][7][8]. For instance, the redundancy of information encoding in subparts of the system (like in the cells of the biological cat) [5], or the distance measured in units of 'microscopic steps' [6] have been suggested.…”

Section: Introductionmentioning

confidence: 99%

General measure for macroscopic quantum states beyond ‘dead and alive’

et al. 2018

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We consider the characterization of quantum superposition states beyond the pattern 'dead and alive'. We propose a measure that is applicable to superpositions of multiple macroscopically distinct states, superpositions with different weights as well as mixed states. The measure is based on the mutual information to characterize the distinguishability between the multiple branches of the superposition. This allows us to overcome limitations of previous proposals, and to bridge the gap between general measures for macroscopic quantumness and measures for Schrödinger-cat type superpositions. We discuss a number of relevant examples, provide an alternative definition using basis-dependent quantum discord and reveal connections to other proposals in the literature. Finally, we also show the connection between the size of quantum states as quantified by our measure and their vulnerability to noise.

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“…In the literature, there exist different criteria for quantifying the macroscopic quantumness [1,[22][23][24][25][26][27][28][29][30][31][32]. Typically, this includes a definition that assigns to a quantum state a number, which is here called effective size (or simply size).…”

Section: Introduction -mentioning

confidence: 99%

“…When the χ 2 -nonlinearity is seeded by coherent states and/or embedded in a high finesse cavity, entanglement in squeezed states can be demonstrated with a huge number of photons -so huge that they can be detected with classical power-meters [8][9][10][11][12][13][14]. This naturally raises the question of whether squeezed states have macroscopic quantum features -a question of deep relevance because so far squeezed states have been combined with conditional detections [15][16][17][18][19][20][21] for exploring quantum effects in many photon states.In the literature, there exist different criteria for quantifying the macroscopic quantumness [1,[22][23][24][25][26][27][28][29][30][31][32]. Typically, this includes a definition that assigns to a quantum state a number, which is here called effective size (or simply size).…”

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confidence: 99%

Two-mode squeezed states as Schrödinger cat-like states

et al. 2015

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In recent years, there has been an increased interest in the generation of superposition of coherent states with opposite phases, the so-called photonic Schrödinger-cat states. These experiments are very challenging and so far, cats involving small photon numbers only have been implemented. Here, we propose to consider two-mode squeezed states as examples of a Schrödinger-cat-like state. In particular, we are interested in several criteria aiming to identify quantum states that are macroscopic superpositions in a more general sense. We show how these criteria can be extended to continuous variable entangled states. We apply them to various squeezed states, argue that two-mode squeezed vacuum states belong to a class of general Schrödinger-cat states and compare the size of states obtained in several experiments. Our results not only promote two-mode squeezed states for exploring quantum effects at the macroscopic level but also provide direct measures to evaluate their usefulness for quantum metrology. Introduction -The question of what is a macroscopic quantum state has received quite a lot of attention over the last decade [1][2][3][4]. The motivation is not to address a new question -not at all, as it dates back from the early days of quantum theory [5] -but rather comes from the experimental progress, now allowing one to harness large systems while highlighting their quantum nature. Quantum optics experiments reporting on squeezing operations provide a nice example. They are obtained from a χ 2 -nonlinearity and can result in largely entangled states. The entanglement can further be detected with homodyne detections, by means of the Duan -Simon criterion [6,7]. When the χ 2 -nonlinearity is seeded by coherent states and/or embedded in a high finesse cavity, entanglement in squeezed states can be demonstrated with a huge number of photons -so huge that they can be detected with classical power-meters [8][9][10][11][12][13][14]. This naturally raises the question of whether squeezed states have macroscopic quantum features -a question of deep relevance because so far squeezed states have been combined with conditional detections [15][16][17][18][19][20][21] for exploring quantum effects in many photon states.In the literature, there exist different criteria for quantifying the macroscopic quantumness [1,[22][23][24][25][26][27][28][29][30][31][32]. Typically, this includes a definition that assigns to a quantum state a number, which is here called effective size (or simply size). Surprisingly, none of them unambiguously applies to two-mode squeezed states and, at the same time, is able to compare their size to those of other states. These criteria can be grouped into two categories. The first one addresses the question of whether a two component superposition |φ 0 + |φ 1 is macroscopic, i.e., whether |φ 0 and |φ 1 are macroscopically distinct. For example, the proposal of Ref. [27] states that two spin states are macroscopically distinct if they can be distinguished from a small number of their spins -as a dea...

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Assessments of macroscopicity for quantum optical states

Cited by 14 publications

References 27 publications

Algebraic and algorithmic frameworks for optimized quantum measurements

Algebraic and algorithmic frameworks for optimized quantum measurements

General measure for macroscopic quantum states beyond ‘dead and alive’

Two-mode squeezed states as Schrödinger cat-like states

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