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Francesco Buscemi

Publications and source records attributed to Francesco Buscemi.

At least 91 records · Page 5Linked to original sources
arXiv2009

Private quantum decoupling and secure disposal of information

Given a bipartite system, correlations between its subsystems can be understood as information that each one carries about the other. In order to give a model-independent description of secure information disposal, we propose the paradigm of private quantum decoupling, corresponding to locally reducing correlations in a given bipartite quantum state without transferring them to the environment. In this framework, the concept of private local randomness naturally arises as a resource, and total correlations get divided into eliminable and ineliminable ones. We prove upper and lower bounds on the amount of ineliminable correlations present in an arbitrary bipartite state, and show that, in tripartite pure states, ineliminable correlations satisfy a monogamy constraint, making apparent their quantum nature. A relation with entanglement theory is provided by showing that ineliminable correlations constitute an entanglement parameter. In the limit of infinitely many copies of the initial state provided, we compute the regularized ineliminable correlations to be measured by the coherent information, which is thus equipped with a new operational interpretation. In particular, our results imply that two subsystems can be privately decoupled if their joint state is separable.

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arXiv2009

The quantum capacity of channels with arbitrarily correlated noise

We study optimal rates for quantum communication over a single use of a channel, which itself can correspond to a finite number of uses of a channel with arbitrarily correlated noise. The corresponding capacity is often referred to as the one-shot quantum capacity. In this paper, we prove bounds on the one-shot quantum capacity of an arbitrary channel. This allows us to compute the quantum capacity of a channel with arbitrarily correlated noise, in the limit of asymptotically many uses of the channel. In the memoryless case, we explicitly show that our results reduce to known expressions for the quantum capacity.

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arXiv2009

Polygamy of Distributed Entanglement

While quantum entanglement is known to be monogamous (i.e. shared entanglement is restricted in multi-partite settings), here we show that distributed entanglement (or the potential for entanglement) is by nature polygamous. By establishing the concept of one-way unlocalizable entanglement (UE) and investigating its properties, we provide a polygamy inequality of distributed entanglement in tripartite quantum systems of arbitrary dimension. We also provide a polygamy inequality in multi-qubit systems, and several trade offs between UE and other correlation measures.

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arXiv2008

Towards a unified approach to information-disturbance tradeoffs in quantum measurements

We show that the global balance of information dynamics for general quantum measurements given in [F. Buscemi, M. Hayashi, and M. Horodecki, Phys.Rev.Lett. 100, 210504 (2008)] makes it possible to unify various and generally inequivalent approaches adopted in order to derive information-disturbance tradeoffs in quantum theory. We focus in particular on those tradeoffs, constituting the vast majority of the literature on the subject, where disturbance is defined either in terms of average output fidelity or of entanglement fidelity.

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arXiv2008

Irreversibility of entanglement loss

The action of a channel on a quantum system, when non trivial, always causes deterioration of initial quantum resources, understood as the entanglement initially shared by the input system with some reference purifying it. One effective way to measure such a deterioration is by measuring the loss of coherent information, namely the difference between the initial coherent information and the final one: such a difference is ``small'', if and only if the action of the channel can be ``almost perfectly'' corrected with probability one. In this work, we generalise this result to different entanglement loss functions, notably including the entanglement of formation loss, and prove that many inequivalent entanglement measures lead to equivalent conditions for approximate quantum error correction. In doing this, we show how different measures of bipartite entanglement give rise to corresponding distance-like functions between quantum channels, and we investigate how these induced distances are related to the cb-norm.

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arXiv2008

Global information balance in quantum measurements

We perform an information-theoretical analysis of quantum measurement processes and obtain the global information balance in quantum measurements, in the form of a closed chain equation for quantum mutual entropies. Our balance provides a tight and general entropic information-disturbance trade-off, and explains the physical mechanism underlying it. Finally, the single-outcome case, that is, the case of measurements with post-selection, is briefly discussed.

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arXiv2008

Entanglement measures and approximate quantum error correction

It is shown that, if the loss of entanglement along a quantum channel is sufficiently small, then approximate quantum error correction is possible, thereby generalizing what happens for coherent information. Explicit bounds are obtained for the entanglement of formation and the distillable entanglement, and their validity naturally extends to other bipartite entanglement measures in between. Robustness of derived criteria is analyzed and their tightness compared. Finally, as a byproduct, we prove a bound quantifying how large the gap between entanglement of formation and distillable entanglement can be for any given finite dimensional bipartite system, thus providing a sufficient condition for distillability in terms of entanglement of formation.

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arXiv2007

Channel correction via quantum erasure

By exploiting a generalization of recent results on environment-assisted channel correction, we show that, whenever a quantum system undergoes a channel realized as an interaction with a probe, the more efficiently the information about the input state can be erased from the probe, the higher is the corresponding entanglement fidelity of the corrected channel, and vice-versa. The present analysis applies also to channels for which perfect quantum erasure is impossible, thus extending the original quantum eraser arrangement, and naturally embodies a general information-disturbance tradeoff.

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arXiv2006

Information-Disturbance Tradeoff in Quantum State Discrimination

When discriminating between two pure quantum states, there exists a quantitative tradeoff between the information retrieved by the measurement and the disturbance caused on the unknown state. We derive the optimal tradeoff and provide the corresponding quantum measurement. Such an optimal measurement smoothly interpolates between the two limiting cases of maximal information extraction and no measurement at all.

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arXiv2006

A minimum-disturbing quantum state discriminator

We propose two experimental schemes for quantum state discrimination that achieve the optimal tradeoff between the probability of correct identification and the disturbance on the quantum state.

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arXiv2006

Economical realization of phase covariant devices in arbitrary dimensions

We describe a unified framework of phase covariant multi user quantum transformations for d-dimensional quantum systems. We derive the optimal phase covariant cloning and transposition tranformations for multi phase states. We show that for some particular relations between the input and output number of copies they correspond to economical tranformations, which can be achieved without the need of auxiliary systems. We prove a relation between the optimal phase covariant cloning and transposition maps, and optimal estimation of multiple phases for equatorial states.

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arXiv2006

Optimization and Realization of Quantum Devices

This manuscript must be intended as an informal review of the research works carried out during three years of PhD. "Informal" in the sense that technical proofs are often omitted (they can be found in the papers) as one could do for a presentation in a public talk. Clearly, some background of Quantum Mechanics is needed, even if I tried to minimize the prerequisites.

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arXiv2006

Universal and phase covariant superbroadcasting for mixed qubit states

We describe a general framework to study covariant symmetric broadcasting maps for mixed qubit states. We explicitly derive the optimal N to M superbroadcasting maps, achieving optimal purification of the single-site output copy, in both the universal and the phase covariant cases. We also study the bipartite entanglement properties of the superbroadcast states.

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arXiv2005

Optimal superbroadcasting of mixed qubit states

"Broadcasting", namely distributing information over many users, suffers in-principle limitations when the information is quantum. This poses a critical issue in quantum information theory, for distributed processing and networked communications. For pure states ideal broadcasting coincides with the so-called "quantum cloning", describing an hypothetical ideal device capable of producing from a finite number N of copies of a state (drawn from a set) a larger number M>N of output copies of the same state. Since such a transformation is not isometric, it cannot be achieved by any physical machine for a quantum state drawn from a non orthogonal set: this is essentially the content of the "no-cloning" theorem. For mixed states the situation is quite different, since from the point of view of each single user a local marginal mixed state is indistinguishable from the partial trace of an entangled state, and there are infinitely many joint output states that correspond to ideal broadcasting. Indeed, for sufficiently large number $N$ of input copies, not only ideal broadcasting of noncommuting mixed states is possible, but one can even purify the state in the process. Such state purification with an increasing number of copies has been named "superbroadcasting". In this paper we will review some recent results on superbroadcasting of qubits, for two different sets of input states, corresponding to universally covariant broadcasting and to phase-covariant broadcasting of equatorial states.

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arXiv2005

Optimal Time-Reversal of Multi-phase Equatorial States

Even though the time-reversal is unphysical (it corresponds to the complex conjugation of the density matrix), for some restricted set of states it can be achieved unitarily, typically when there is a common de-phasing in a n-level system. However, in the presence of multiple phases (i. e. a different de-phasing for each element of an orthogonal basis occurs) the time reversal is no longer physically possible. In this paper we derive the channel which optimally approaches in fidelity the time-reversal of multi-phase equatorial states in arbitrary (finite) dimension. We show that, in contrast to the customary case of the Universal-NOT on qubits (or the universal conjugation in arbitrary dimension), the optimal phase covariant time-reversal for equatorial states is a nonclassical channel, which cannot be achieved via a measurement/preparation procedure. Unitary realizations of the optimal time-reversal channel are given with minimal ancillary dimension, exploiting the simplex structure of the optimal maps.

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