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[en] Given an unknown state of a qudit that has already been measured optimally, can one still extract any information about the original unknown state? Clearly, after a maximally informative measurement, the state of the system collapses into a postmeasurement state from which the same observer cannot obtain further information about the original state of the system. However, the system still encodes a significant amount of information about the original preparation for a second observer who is unaware of the actions of the first one. We study how a series of independent observers can obtain, or can scavenge, information about the unknown state of a system (quantified by the fidelity) when they sequentially measure it. We give closed-form expressions for the estimation fidelity when one or several qudits are available to carry information about the single-qudit state, and we study the classical limit when an arbitrarily large number of observers can obtain (nearly) complete information on the system. In addition to the case where all observers perform most informative measurements, we study the scenario where a finite number of observers estimates the state with equal fidelity, regardless of their position in the measurement sequence and the scenario where all observers use identical measurement apparatuses (up to a mutually unknown orientation) chosen so that a particular observer's estimation fidelity is maximized.
[en] In the context of a physical theory, two devices, A and B, described by the theory are called incompatible if the theory does not allow the existence of a third device C that would have both A and B as its components. Incompatibility is a fascinating aspect of physical theories, especially in the case of quantum theory. The concept of incompatibility gives a common ground for several famous impossibility statements within quantum theory, such as ‘no-cloning’ and ‘no information without disturbance’; these can be all seen as statements about incompatibility of certain devices. The purpose of this paper is to give a concise overview of some of the central aspects of incompatibility. (topical review)
[en] Complete sets of mutually unbiased bases (MUBs) offer interesting applications in quantum information processing ranging from quantum cryptography to quantum state tomography. Different construction schemes provide different perspectives on these bases which are typically also deeply connected to various mathematical research areas. In this talk we discuss characteristic properties resulting from a recently established connection between construction methods for cyclic MUBs and Fibonacci polynomials. As a remarkable fact this connection leads to construction methods which do not involve any relations to mathematical properties of finite fields.
[en] Recently, an interesting quantity called the quantum Rényi divergence (or ‘sandwiched’ Rényi relative entropy) was defined for pairs of positive semi-definite operators ρ and σ. It depends on a parameter α and acts as a parent quantity for other relative entropies which have important operational significance in quantum information theory: the quantum relative entropy and the min- and max-relative entropies. There is, however, another relative entropy, called the 0-relative Rényi entropy, which plays a key role in the analysis of various quantum information-processing tasks in the one-shot setting. We prove that the 0-relative Rényi entropy is obtainable from the quantum Rényi divergence only if ρ and σ have equal supports. This, along with existing results in the literature, suggests that it suffices to consider two essential parent quantities from which operationally relevant entropic quantities can be derived—the quantum Rényi divergence with parameter α ⩾ 1/2, and the α-relative Rényi entropy with α ∈ [0, 1). (paper)
[en] We study quantum Darwinism, the redundant recording of information about the preferred states of a decohering system by its environment, for an object illuminated by a blackbody. We calculate the quantum mutual information between the object and its photon environment for blackbodies that cover an arbitrary section of the sky. In particular, we demonstrate that more extended sources have a reduced ability to create redundant information about the system, in agreement with previous evidence that initial mixedness of an environment slows-but does not stop-the production of records. We also show that the qualitative results are robust for more general initial states of the system.
[en] We present a new decoding protocol to realize transmission of classical information through a quantum channel at asymptotically maximum capacity, achieving the Holevo bound and thus the optimal communication rate. At variance with previous proposals, our scheme recovers the message bit by bit, making use of a series of “yes-no” measurements, organized in bisection fashion, thus determining which codeword was sent in log_2 N steps, N being the number of codewords.
[en] We study the local distinguishability of general multiqubit states and show that local projective measurements and classical communication are as powerful as the most general local measurements and classical communication. Remarkably, this indicates that the local distinguishability of multiqubit states can be decided efficiently. Another useful consequence is that a set of orthogonal n-qubit states is locally distinguishable only if the summation of their orthogonal Schmidt numbers is less than the total dimension 2n. Employing these results, we show that any orthonormal basis of a subspace spanned by arbitrary three-qubit orthogonal unextendible product bases (UPB) cannot be exactly distinguishable by local operations and classical communication. This not only reveals another intrinsic property of three-qubit orthogonal UPB but also provides a class of locally indistinguishable subspaces with dimension 4. We also explicitly construct locally indistinguishable subspaces with dimensions 3 and 5, respectively. Similar to the bipartite case, these results on multipartite locally indistinguishable subspaces can be used to estimate the one-shot environment-assisted classical capacity of a class of quantum broadcast channels.
[en] Topological features have become an intensively studied subject in many fields of physics. As a witness of topological phase, the edge states are topologically protected and may be helpful in quantum information processing. In this paper, we define a measure to quantify the dynamical localization of the system and simulate the localization in the one-dimensional Aubry–André model. We find an interesting connection between the edge states and the dynamical localization of the system, this connection may be used as a signature of the edge state and topological phase. (paper)
[en] We formulate and prove a quantum Shannon-McMillan theorem. The theorem demonstrates the significance of the von Neumann entropy for translation invariant ergodic quantum spin systems on ℤν-lattices: the entropy gives the logarithm of the essential number of eigenvectors of the system on large boxes. The one-dimensional case covers quantum information sources and is basic for coding theorems.
[en] Reverse coherent information, as a symmetric counterpart of the coherent information, has been firstly defined by R. Garcia-Patron et al. This quantity allows to define reverse coherent information capacity which is additive. In this Letter, we prove the convexity of such capacity for a general quantum channel, and investigate the effect of convex decomposition of quantum channel on its (reverse) coherent information. Finally, we apply the convexity property to provide an upper bound on the reverse coherent information capacity for some important channels. -- Highlights: → It is proved that reverse coherent information capacity is convex. → Reverse coherent information is more sensitive to convex decomposition than counterpart. → Upper bounds on reverse coherent information capacity for some channels are provided.