Extendibility of Bosonic Gaussian States

Lami, Ludovico; Khatri, Sumeet; Adesso, Gerardo; Wilde, Mark M.

doi:10.1103/physrevlett.123.050501

Cited by 21 publications

(15 citation statements)

References 89 publications

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“…A calculation of the quantity φ s | id ⊗Λ j [ψ r ]|φ s can be found in [55]. By exploiting that result we find…”

Section: Discussionmentioning

confidence: 89%

“…N in order to have Ē ≤ E satisfied for all possible values of N. This is equivalent to evaluate an unconstrained supremum, for which we can use the calculation performed in [55] to obtain µ(Λ) ≥ 2 sup Our analysis therefore led to the following result: when the dynamics from A to B 1 , ..., B N is given by Eq. (B.1) and the maximum energy of system A satisfies E ≥ 2 N , for all j and for all POVM {M l } l and sets {τ j,l } entering the definition of E j it holds that…”

Section: Discussionmentioning

confidence: 94%

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Refined diamond norm bounds on the emergence of objectivity of observables

Colafranceschi,

Lami,

Adesso

et al. 2020

Preprint

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The theory of Quantum Darwinism aims to explain how our objective classical reality arises from the quantum world, by analysing the distribution of information about a quantum system that is accessible to multiple observers, who probe the system by intercepting fragments of its environment. Previous work showed that, when the number of environmental fragments grows, the quantum channels modelling the information flow from system to observers become arbitrarily close -in terms of diamond norm distance -to "measure-andprepare" channels, ensuring objectivity of observables; the convergence is formalised by an upper bound on the diamond norm distance, which decreases with increasing number of fragments. Here, we derive tighter diamond norm bounds on the emergence of objectivity of observables for quantum systems of arbitrary (finite or infinite) dimension. Furthermore, we probe the tightness of our bounds by considering a specific model of a system-environment dynamics given by a pure loss channel. Finally, we generalise to infinite dimensions a result obtained by Brandão et al. [Nat. Commun. 6, 7908 (2015)], which provides an operational characterisation of quantum discord in terms of one-sided redistribution of correlations to many parties. Our results provide an improved and unified framework to benchmark quantitatively the rise of objectivity in the quantum-to-classical transition.

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“…A calculation of the quantity φ s | id ⊗Λ j [ψ r ]|φ s can be found in [55]. By exploiting that result we find…”

Section: Discussionmentioning

confidence: 89%

Section: Discussionmentioning

confidence: 94%

Refined diamond norm bounds on the emergence of objectivity of observables

Colafranceschi,

Lami,

Adesso

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…A description in terms of positive semi-definite constraints, instead, can be formulated not only for quantum theory itself (Example 4), but also for several GPTs that are of great interest in entanglement theory [41]. Notable examples in this context include the theory of NPT entanglement [42,43,44,45,46] and that of extendibility [47,48,49,50,51]. Lemma 17.…”

Section: Perfect Distinguishability As a Convex Programmentioning

confidence: 99%

A Post-Quantum Associative Memory

Lami¹,

Goldwater²,

Adesso³

2022

Preprint

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Associative memories are devices storing information that can be fully retrieved given partial disclosure of it. We examine a toy model of associative memory and the ultimate limitations it is subjected to within the framework of general probabilistic theories (GPTs), which represent the most general class of physical theories satisfying some basic operational axioms. We ask ourselves how large the dimension of a GPT should be so that it can accommodate 2 m states with the property that any N of them are perfectly distinguishable. Invoking an old result by Danzer and Grünbaum, we prove that when N = 2 the optimal answer to this question is m + 1, to be compared with O(2 m ) when the theory is required to be either classical or quantum. This yields an example of a task where GPTs outperform both classical and quantum theory exponentially. The same problem for N ≥ 3 is left open.

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“…Here, anti-degradable channels are precisely those that are 2-extendible. The complete characterisation of the k-extendibility regions of all thermal attenuators has been put forward recently [57].…”

Section: B Beam Splittersmentioning

confidence: 99%

“…It is known that E λ,ν is anti-degradable -and hence its quantum capacity vanishes -when λ ≤ 1/2 [11, p. 3]. In fact, all k-extendibility regions have been precisely described [57]. On a different note, we can also consider a generalised depolarising channel in finite dimension d, acting as ρ → ∆ λ,σ (ρ) .…”

mentioning

confidence: 99%

Bosonic quantum communication across arbitrarily high loss channels

Lami,

Plenio,

Giovannetti

et al. 2020

Preprint

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A general attenuator Φ λ,σ is a bosonic quantum channel that acts by combining the input with a fixed environment state σ in a beam splitter of transmissivity λ. If σ is a thermal state the resulting channel is a thermal attenuator, whose quantum capacity vanishes for λ ≤ 1/2. We study the quantum capacity of these objects for generic σ, proving a number of unexpected results. Most notably, we show that for any arbitrary value of λ > 0 there exists a suitable single-mode state σ(λ) such that the quantum capacity of Φ λ,σ(λ) is larger than a universal constant c > 0. Our result holds even when we fix an energy constraint at the input of the channel, and implies that quantum communication at a constant rate is possible even in the limit of arbitrarily low transmissivity, provided that the environment state is appropriately controlled. We also find examples of states σ such that the quantum capacity of Φ λ,σ is not monotonic in λ. These findings may have implications for the study of communication lines running across integrated optical circuits, of which general attenuators provide natural models.

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Extendibility of Bosonic Gaussian States

Cited by 21 publications

References 89 publications

Refined diamond norm bounds on the emergence of objectivity of observables

Refined diamond norm bounds on the emergence of objectivity of observables

A Post-Quantum Associative Memory

Bosonic quantum communication across arbitrarily high loss channels

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