arXiv subjects

Francesco Buscemi

Publications and source records attributed to Francesco Buscemi.

At least 73 records · Page 4Linked to original sources

arXiv2016

Degradable channels, less noisy channels, and quantum statistical morphisms: an equivalence relation

Two partial orderings among communication channels, namely, `being degradable into' and `being less noisy than,' are reconsidered in the light of recent results about statistical comparisons of quantum channels. Though our analysis covers at once both classical and quantum channels, we also provide a separate treatment of classical noisy channels, and show how, in this case, an alternative self-contained proof can be constructed, with its own particular merits with respect to the general result.

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arXiv2016

Device independent witnessing of unknown quantum channels

Quantum process tomography, the standard procedure to characterize any quantum channel in nature, is affected by a circular argument: in order to characterize the channel, the tomographic preparation and measurement need in turn to be already characterized. We break this loop by designing an operational framework able to optimally characterize any given unknown quantum channel in a device-independent fashion, namely, by only looking at its input-output statistics, under the sole assumption that quantum theory is valid. We provide explicit solutions, in closed form, for practically relevant cases such as the erasure, depolarizing, and amplitude-damping channels.

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arXiv2016

Approximate reversibility in the context of entropy gain, information gain, and complete positivity

There are several inequalities in physics which limit how well we can process physical systems to achieve some intended goal, including the second law of thermodynamics, entropy bounds in quantum information theory, and the uncertainty principle of quantum mechanics. Recent results provide physically meaningful enhancements of these limiting statements, determining how well one can attempt to reverse an irreversible process. In this paper, we apply and extend these results to give strong enhancements to several entropy inequalities, having to do with entropy gain, information gain, entropic disturbance, and complete positivity of open quantum systems dynamics. Our first result is a remainder term for the entropy gain of a quantum channel. This result implies that a small increase in entropy under the action of a subunital channel is a witness to the fact that the channel's adjoint can be used as a recovery map to undo the action of the original channel. Our second result regards the information gain of a quantum measurement, both without and with quantum side information. We find here that a small information gain implies that it is possible to undo the action of the original measurement if it is efficient. The result also has operational ramifications for the information-theoretic tasks known as measurement compression without and with quantum side information. Our third result shows that the loss of Holevo information caused by the action of a noisy channel on an input ensemble of quantum states is small if and only if the noise can be approximately corrected on average. We finally establish that the reduced dynamics of a system-environment interaction are approximately completely positive and trace-preserving if and only if the data processing inequality holds approximately.

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arXiv2016

Equivalence between divisibility and monotonic decrease of information in classical and quantum stochastic processes

The crucial feature of a memoryless stochastic process is that any information about its state can only decrease as the system evolves. Here we show that such a decrease of information is equivalent to the underlying stochastic evolution being divisible. The main result, which holds for both classical and quantum stochastic processes, rely on a quantum version of the so-called Blackwell-Sherman-Stein theorem in classical statistics.

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arXiv2015

Experimental test of entropic noise-disturbance uncertainty relations for spin-1/2 measurements

Information-theoretic definitions for noise and disturbance in quantum measurements were given in Phys. Rev. Lett. 112, 050401 (2014) and a state-independent noise-disturbance uncertainty relation was obtained. Here, we derive a tight noise-disturbance uncertainty relation for complementary qubit observables and carry out an experimental test. Successive projective measurements on the neutron's spin-1/2system, together with a correction procedure which reduces the disturbance, are performed. Our experimental results saturate the tight noise-disturbance uncertainty relation for qubits when an optimal correction procedure is applied.

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arXiv2015

Fully quantum second-law--like statements from the theory of statistical comparisons

In generalized resource theories, one aims to reformulate the problem of deciding whether a suitable transition (typically a transition that preserves the Gibbs state of the theory) between two given states $ρ$ and $σ$ exists or not, into the problem of checking whether a set of second-law--like inequalities hold or not. The aim of these preliminary notes is to show how the theory of statistical comparisons (in the sense of Blackwell, LeCam, and Torgersen) can be useful in such scenarios. In particular, we propose one construction, in which the second laws are formulated in terms of a suitable conditional min-entropy. Though a general, fully quantum result is also presented, stronger results are obtained for the case of qubits, and the case of $σ$ commuting with the Gibbs state.

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arXiv2014

Game-theoretic characterization of antidegradable channels

We introduce a guessing game involving a quantum channel, three parties - the sender, the receiver and an eavesdropper, Eve - and a quantum public side channel. We prove that a necessary and sufficient condition for the quantum channel to be antidegradable, is that Eve wins the game. We thus obtain a complete operational characterization of antidegradable channels in a game-theoretic framework.

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arXiv2014

On complete positivity, Markovianity, and the quantum data-processing inequality, in the presence of initial system-environment correlations

We show that complete positivity is not only sufficient but also necessary for the validity of the quantum data-processing inequality. As a consequence, the reduced dynamics of a quantum system are completely positive, even in the presence of initial correlations with its surrounding environment, if and only if such correlations do not allow any anomalous backward flow of information from the environment to the system. Our approach provides an intuitive information-theoretic framework to unify and extend a number of previous results.

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arXiv2014

Universal Optimal Quantum Correlator

Recently, a novel operational strategy to access quantum correlation functions of the form Tr[A rho B] was provided in [F. Buscemi, M. Dall'Arno, M. Ozawa, and V. Vedral, arXiv:1312.4240]. Here we propose a realization scheme, that we call partial expectation values, implementing such strategy in terms of a unitary interaction with an ancillary system followed by the measurement of an observable on the ancilla. Our scheme is universal, being independent of rho, A, and B, and it is optimal in a statistical sense. Our scheme is suitable for implementation with present quantum optical technology, and provides a new way to test uncertainty relations.

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arXiv2014

Tight Bounds on the Accessible Information and the Informational Power

The accessible information quantifies the amount of classical information that can be extracted from an ensemble of quantum states. Analogously, the informational power quantifies the amount of classical information that can be extracted by a quantum measurement. For both quantities, we provide upper and lower bounds that depend only on the dimension of the system, and we prove their tightness. In the case of symmetric informationally complete (SIC) ensembles and measurements, stronger bounds are provided and their tightness proved for qubits and qutrits. From our upper bounds, we notice, perhaps surprisingly, that the statistics generated by SIC ensembles or measurements in arbitrary dimension, though optimal for tomographic purposes, in fact never contains more than just one bit of information, the rest being constituted by completely random bits. On the other hand, from our lower bounds, we obtain an explicit strategy beating the so-called "pretty-good" one for the extraction of mutual information in the case of SIC ensembles and measurements.

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arXiv2014

Noise and disturbance in quantum measurements: an information-theoretic approach

We introduce information-theoretic definitions for noise and disturbance in quantum measurements and prove a state-independent noise-disturbance tradeoff relation that these quantities have to satisfy in any conceivable setup. Contrary to previous approaches, the information-theoretic quantities we define are invariant under relabelling of outcomes, and allow for the possibility of using quantum or classical operations to `correct' for the disturbance. We also show how our bound implies strong tradeoff relations for mean square deviations.

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arXiv2013

Direct observation of any two-point quantum correlation function

The existence of noncompatible observables in quantum theory makes a direct operational interpretation of two-point correlation functions problematic. Here we challenge such a view by explicitly constructing a measuring scheme that, independently of the input state $ρ$ and observables $A$ and $B$, performs an unbiased optimal estimation of the two-point correlation function $\operatorname{Tr}[A \ ρ\ B]$. This shows that, also in quantum theory, two-point correlation functions are as operational as any other expectation value. A very simple probabilistic implementation of our proposal is presented.

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arXiv2013

General theory of environment-assisted entanglement distillation

We evaluate the one-shot entanglement of assistance for an arbitrary bipartite state. This yields another interesting result, namely a characterization of the one-shot distillable entanglement of a bipartite pure state. This result is shown to be stronger than that obtained by specializing the one-shot hashing bound to pure states. Finally, we show how the one-shot result yields the operational interpretation of the asymptotic entanglement of assistance proved in [Smolin et al., Phys. Rev. A 72, 052317 (2005)].

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arXiv2012

The information-theoretic costs of simulating quantum measurements

Winter's measurement compression theorem stands as one of the most penetrating insights of quantum information theory (QIT). In addition to making an original and profound statement about measurement in quantum theory, it also underlies several other general protocols in QIT. In this paper, we provide a full review of Winter's measurement compression theorem, detailing the information processing task, giving examples for understanding it, reviewing Winter's achievability proof, and detailing a new approach to its single-letter converse theorem. We prove an extension of the theorem to the case in which the sender is not required to receive the outcomes of the simulated measurement. The total cost of common randomness and classical communication can be lower for such a "non-feedback" simulation, and we prove a single-letter converse theorem demonstrating optimality. We then review the Devetak-Winter theorem on classical data compression with quantum side information, providing new proofs of its achievability and converse parts. From there, we outline a new protocol that we call "measurement compression with quantum side information," announced previously by two of us in our work on triple trade-offs in quantum Shannon theory. This protocol has several applications, including its part in the "classically-assisted state redistribution" protocol, which is the most general protocol on the static side of the quantum information theory tree, and its role in reducing the classical communication cost in a task known as local purity distillation. We also outline a connection between measurement compression with quantum side information and recent work on entropic uncertainty relations in the presence of quantum memory. Finally, we prove a single-letter theorem characterizing measurement compression with quantum side information when the sender is not required to obtain the measurement outcome.

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arXiv2012

All Entangled Quantum States Are Nonlocal

Departing from the usual paradigm of local operations and classical communication adopted in entanglement theory, here we study the interconversion of quantum states by means of local operations and shared randomness. A set of necessary and sufficient conditions for the existence of such a transformation between two given quantum states is given in terms of the payoff they yield in a suitable class of nonlocal games. It is shown that, as a consequence of our result, such a class of nonlocal games is able to witness quantum entanglement, however weak, and reveal nonlocality in any entangled quantum state. An example illustrating this fact is provided.

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arXiv2011

Comparison of quantum statistical models: equivalent conditions for sufficiency

A family of probability distributions (i.e. a statistical model) is said to be sufficient for another, if there exists a transition matrix transforming the probability distributions in the former to the probability distributions in the latter. The Blackwell-Sherman-Stein (BSS) theorem provides necessary and sufficient conditions for one statistical model to be sufficient for another, by comparing their information values in statistical decision problems. In this paper we extend the BSS theorem to quantum statistical decision theory, where statistical models are replaced by families of density matrices defined on finite-dimensional Hilbert spaces, and transition matrices are replaced by completely positive, trace-preserving maps (i.e. coarse-grainings). The framework we propose is suitable for unifying results that previously were independent, like the BSS theorem for classical statistical models and its analogue for pairs of bipartite quantum states, recently proved by Shmaya. An important role in this paper is played by statistical morphisms, namely, affine maps whose definition generalizes that of coarse-grainings given by Petz and induces a corresponding criterion for statistical sufficiency that is weaker, and hence easier to be characterized, than Petz's.

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arXiv2011

Entanglement cost in practical scenarios

We quantify the one-shot entanglement cost of an arbitrary bipartite state, that is the minimum number of singlets needed by two distant parties to create a single copy of the state up to a finite accuracy, using local operations and classical communication only. This analysis, in contrast to the traditional one, pertains to scenarios of practical relevance, in which resources are finite and transformations can only be achieved approximately. Moreover, it unveils a fundamental relation between two well-known entanglement measures, namely, the Schmidt number and the entanglement of formation. Using this relation, we are able to recover the usual expression of the entanglement cost as a special case.

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arXiv2010

Distilling entanglement from arbitrary resources

We obtain the general formula for the optimal rate at which singlets can be distilled from any given noisy and arbitrarily correlated entanglement resource, by means of local operations and classical communication (LOCC). Our formula, obtained by employing the quantum information spectrum method, reduces to that derived by Devetak and Winter, in the special case of an i.i.d. resource. The proofs rely on a one-shot version of the so-called "hashing bound," which in turn provides bounds on the one-shot distillable entanglement under general LOCC.

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