We consider the problem of discriminating two different quantum states in the setting of asymptotically many copies, and determine the minimal probability of error. This leads to the identification of the quantum Chernoff bound, thereby solving a long-standing open problem. The bound reduces to the classical Chernoff bound when the quantum states under consideration commute. The quantum Chernoff bound is the natural symmetric distance measure between quantum states because of its clear operational meaning and because it does not seem to share some of the undesirable features of other distance measures.
In this paper we investigate the possibility to make complete Bell measurements on a product Hilbert space of two two-level bosonic systems. We restrict our tools to linear elements, like beam splitters and phase shifters, delay lines and electronically switched linear elements, photo-detectors, and auxiliary bosons. As a result we show that with these tools a never failing Bell measurement is impossible.
We devise a protocol in which general nonclassical multipartite correlations produce a physically relevant effect, leading to the creation of bipartite entanglement. In particular, we show that the relative entropy of quantumness, which measures all nonclassical correlations among subsystems of a quantum system, is equivalent to and can be operationally interpreted as the minimum distillable entanglement generated between the system and local ancillae in our protocol. We emphasize the key role of state mixedness in maximizing nonclassicality: Mixed entangled states can be arbitrarily more nonclassical than separable and pure entangled states.PACS numbers: 03.65. Ud, 03.67.Ac, 03.67.Mn, 03.65.Ta The study of quantum correlations has traditionally focused on entanglement [1]. It is generally believed that entanglement is a necessary resource for quantum computers to outperform their classical counterparts. Indeed, it has been shown that for the setting of pure-state computation, the amount of entanglement present must grow with the system size for an exponential speed-up to occur [2]. In the context of mixedstate quantum information processing, however, there are computational and communication feats which are seemingly impossible to achieve with a classical computer, and yet can be attained with a quantum computer using little or no entanglement (e.g. [3,4]). For example, the Deterministic Quantum Computation with one Qubit (DQC1) model is believed to estimate the trace of a unitary matrix exponentially faster than any classical algorithm, yet with vanishing entanglement during the computation [5]. A second example is the ability for certain bipartite quantum systems to contain a large amount of "locked" classical correlations, which can then be "unlocked" with a disproportionately small amount of classical communication [4]. This task is impossible classically, yet the quantum states involved are separable, that is, unentangled. This raises the crucial question about which, if not entanglement, is the fundamental resource enabling such feats.One plausible explanation is associated with the presence in (generic [6]) quantum states of correlations which have nonclassical signatures that go beyond entanglement. Indeed, much attention has recently been devoted to understanding and quantifying such correlations for this very reason [6][7][8][9][10][11][12][13][14][15][16]. In particular, the separable quantum states of the systems involved in DQC1 and the locking protocol have been shown to possess non-zero amounts of such correlations [5,17], as measured by the quantum discord [7]. The latter strives to capture nonclassical correlations beyond entanglement and has recently received operational interpretations in terms of the quantum state merging protocol [18], but is unfortunately not a faithful measure [19]. A more accurate quantification of nonclassical correlations is provided by the so-called relative entropy of quantumness (REQ) [8,[10][11][12][13], defined as the minimum distance, in terms of relative entr...
We propose the entanglement potential (EP) as a measure of nonclassicality for quantum states of a single-mode electromagnetic field. It is the amount of two-mode entanglement that can be generated from the field using linear optics, auxiliary classical states, and ideal photodetectors. The EP detects nonclassicality, has a direct physical interpretation, and can be computed efficiently. These three properties together make it stand out from previously proposed nonclassicality measures. We derive closed expressions for the EP of important classes of states and analyze as an example of the degradation of nonclassicality in lossy channels.
In a photonic realization of qubits the implementation of quantum logic is rather difficult due the extremely weak interaction on the few photon level. On the other hand, in these systems interference is available to process the quantum states. We formalize the use of interference by the definition of a simple class of operations which include linear optical elements, auxiliary states and conditional operations. We investigate an important subclass of these tools, namely linear optical elements and auxiliary modes in the vacuum state. For this tools, we are able to extend a previous quantitative result, a no-go theorem for perfect Bell state analyzer on two qubits in polarization entanglement, by a quantitative statement. We show, that within this subclass it is not possible to discriminate unambiguously four equiprobable Bell states with a probability higher than 50 %.Comment: 6 pages, 2 fig
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