Multi-Party Pseudo-Telepathy

Quantum entanglement, perhaps the most non-classical manifestation of quantum information theory, cannot be used to transmit information between remote parties. Yet, it can be used to reduce the amount of communication required to process a variety of distributed computational tasks. We speak of pseudo-telepathy when quantum entanglement serves to eliminate the classical need to communicate. In earlier examples of pseudo-telepathy, classical protocols could succeed with high probability unless the inputs were very large. Here we present a simple multi-party distributed problem for which the inputs and outputs consist of a single bit per player, and we present a perfect quantum protocol for it. We prove that no classical protocol can succeed with a probability that differs from 1/2 by more than a fraction that is exponentially small in the number of players. This could be used to circumvent the detection loophole in experimental tests of nonlocality.Comment: 11 pages. To be appear in WADS 2003 proceeding

Supercatalysis

We show that entanglement-assisted transformations of bipartite entangled states can be more efficient than catalysis [D. Jonathan and M. B. Plenio, Phys. Rev. Lett. 83, 3566 (1999)}, i.e., given two incomparable bipartite states not only can the transformation be enabled by performing collective operations with an auxiliary entangled state, but the entanglement of the auxiliary state itself can be enhanced. We refer to this phenomenon as supercatalysis. We provide results on the properties of supercatalysis and its relationship with catalysis. In particular, we obtain a useful necessary and sufficient condition for catalysis, provide several sufficient conditions for supercatalysis and study the extent to which entanglement of the auxiliary state can be enhanced via supercatalysis.Comment: Latex, 5 page

New classes of n-copy undistillable quantum states with negative partial transposition

The discovery of entangled quantum states from which one cannot distill pure entanglement constitutes a fundamental recent advance in the field of quantum information. Such bipartite bound-entangled (BE) quantum states \emph{could} fall into two distinct categories: (1) Inseparable states with positive partial transposition (PPT), and (2) States with negative partial transposition (NPT). While the existence of PPT BE states has been confirmed, \emph{only one} class of \emph{conjectured} NPT BE states has been discovered so far. We provide explicit constructions of a variety of multi-copy undistillable NPT states, and conjecture that they constitute families of NPT BE states. For example, we show that for every pure state of Schmidt rank greater than or equal to three, one can construct n-copy undistillable NPT states, for any $n\geq1$. The abundance of such conjectured NPT BE states, we believe, considerably strengthens the notion that being NPT is only a necessary condition for a state to be distillable.Comment: Latex, 10 page

An entanglement monotone derived from Grover's algorithm

This paper demonstrates that how well a state performs as an input to Grover's search algorithm depends critically upon the entanglement present in that state; the more entanglement, the less well the algorithm performs. More precisely, suppose we take a pure state input, and prior to running the algorithm apply local unitary operations to each qubit in order to maximize the probability P_max that the search algorithm succeeds. We prove that, for pure states, P_max is an entanglement monotone, in the sense that P_max can never be decreased by local operations and classical communication.Comment: 7 page

Local transformation of mixed states of two qubits to Bell diagonal states

The optimal entanglement manipulation for a single copy of mixed states of two qubits is to transform it to a Bell diagonal state. In this paper we derive an explicit form of the local operation that can realize such a transformation. The result obtained is universal for arbitrary entangled two-qubit states and it discloses that the corresponding local filter is not unique for density matrices with rank $n=2$ and can be exclusively determined for that with $n=3$ and 4. As illustrations, a four-parameters family of mixed states are explored, the local filter as well as the transformation probability are given explicitly, which verify the validity of the general result.Comment: 5 pages, to be published in Phys. Rev.

Hyperpigmentation of hard palate induced by chloroquine therapy

The antimalarials are one of the most commonly prescribed drugs for conditions such as lupus erythematosus and rheumatoid arthritis, and the side effects, though infrequent, are well known. The antimalarial agent chloroquine diphosphate usually causes pigmentary changes in the oral mucosa characterized by a bluish-grey to black discolorations mainly in the hard palate. Considering only the hard palate hyperpigmentation caused by chloroquine, to the best of our knowledge, only 13 cases have been reported in the English language literature. We described an additional case of palate hyperpigmentation related to the chronic use of chloroquine diphosphate in a 60-year-old Mexican woman. Although the diagnosis is usually made based on medication history and clinical presentation, a biopsy specimen may be helpful to confirm the diagnosis. Clinicians must be aware of these drugs and their adverse effects in order to make the correct diagnosis and decide on the optimal treatment for the condition

Reversible transformations from pure to mixed states, and the unique measure of information

Transformations from pure to mixed states are usually associated with information loss and irreversibility. Here, a protocol is demonstrated allowing one to make these transformations reversible. The pure states are diluted with a random noise source. Using this protocol one can study optimal transformations between states, and from this derive the unique measure of information. This is compared to irreversible transformations where one does not have access to noise. The ideas presented here shed some light on attempts to understand entanglement manipulations and the inevitable irreversibility encountered there where one finds that mixed states can contain "bound entanglement".Comment: 10 pages, no figures, revtex4, table added, to appear in Phys. Rev.

Stabilizer notation for Spekkens' toy theory

Spekkens has introduced a toy theory [Phys. Rev. A, 75, 032110 (2007)] in order to argue for an epistemic view of quantum states. I describe a notation for the theory (excluding certain joint measurements) which makes its similarities and differences with the quantum mechanics of stabilizer states clear. Given an application of the qubit stabilizer formalism, it is often entirely straightforward to construct an analogous application of the notation to the toy theory. This assists calculations within the toy theory, for example of the number of possible states and transformations, and enables superpositions to be defined for composite systems.Comment: 7+4 pages, 5 tables. v2: Clarifications added and typos fixed in response to referee comment

Faithful remote state preparation using finite classical bits and a non-maximally entangled state

We present many ensembles of states that can be remotely prepared by using minimum classical bits from Alice to Bob and their previously shared entangled state and prove that we have found all the ensembles in two-dimensional case. Furthermore we show that any pure quantum state can be remotely and faithfully prepared by using finite classical bits from Alice to Bob and their previously shared nonmaximally entangled state though no faithful quantum teleportation protocols can be achieved by using a nonmaximally entangled state.Comment: 6 page

The quantum dynamic capacity formula of a quantum channel

The dynamic capacity theorem characterizes the reliable communication rates of a quantum channel when combined with the noiseless resources of classical communication, quantum communication, and entanglement. In prior work, we proved the converse part of this theorem by making contact with many previous results in the quantum Shannon theory literature. In this work, we prove the theorem with an "ab initio" approach, using only the most basic tools in the quantum information theorist's toolkit: the Alicki-Fannes' inequality, the chain rule for quantum mutual information, elementary properties of quantum entropy, and the quantum data processing inequality. The result is a simplified proof of the theorem that should be more accessible to those unfamiliar with the quantum Shannon theory literature. We also demonstrate that the "quantum dynamic capacity formula" characterizes the Pareto optimal trade-off surface for the full dynamic capacity region. Additivity of this formula simplifies the computation of the trade-off surface, and we prove that its additivity holds for the quantum Hadamard channels and the quantum erasure channel. We then determine exact expressions for and plot the dynamic capacity region of the quantum dephasing channel, an example from the Hadamard class, and the quantum erasure channel.Comment: 24 pages, 3 figures; v2 has improved structure and minor corrections; v3 has correction regarding the optimizatio