arXiv subjects

Lucien Hardy

Publications and source records attributed to Lucien Hardy.

50 records · Page 3Linked to original sources

arXiv2001

Nonlinear Qubit Transformations

We generalise our previous results of universal linear manipulations [Phys. Rev. A63, 032304 (2001)] to investigate three types of nonlinear qubit transformations using measurement and quantum based schemes. Firstly, nonlinear rotations are studied. We rotate different parts of a Bloch sphere in opposite directions about the z-axis. The second transformation is a map which sends a qubit to its orthogonal state (which we define as ORTHOG). We consider the case when the ORTHOG is applied to only a partial area of a Bloch sphere. We also study nonlinear general transformation, i.e. (theta,phi)->(theta-alpha,phi), again, applied only to part of the Bloch sphere. In order to achieve these three operations, we consider different measurement preparations and derive the optimal average (instead of universal) quantum unitary transformations. We also introduce a simple method for a qubit measurement and its application to other cases.

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arXiv2000

Universal Manipulation of a Single Qubit

We find the optimal universal way of manipulating a single qubit, |psi(theta,phi)>, such that (theta,phi)->(theta-k,phi-l). Such optimal transformations fall into two classes. For 0 =< k =< pi/2 the optimal map is the identity and the fidelity varies monotonically from 1 (for k=0) to 1/2 (for k=pi/2). For pi/2 =< k =< pi the optimal map is the universal-NOT gate and the fidelity varies monotonically from 1/2 (for k=pi/2) to 2/3 (for k=pi). The fidelity 2/3 is equal to the fidelity of measurement. It is therefore rather surprising that for some values of k the fidelity is lower than 2/3.

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arXiv2000

Local Distinguishability of Multipartite Orthogonal Quantum States

We consider one copy of a quantum system prepared in one of two orthogonal pure states, entangled or otherwise, and distributed between any number of parties. We demonstrate that it is possible to identify which of these two states the system is in by means of local operations and classical communication alone. The protocol we outline is both completely reliable and completely general - it will correctly distinguish any two orthogonal states 100% of the time.

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arXiv2000

Entanglement Swapping Chains for General Pure States

We consider entanglement swapping schemes with general (rather than maximally) entangled bipartite states of arbitary dimension shared pairwise between three or more parties in a chain. The intermediate parties perform generalised Bell measurements with the result that the two end parties end up sharing a entangled state which can be converted into maximally entangled states. We obtain an expression for the average amount of maximal entanglement concentrated in such a scheme and show that in a certain reasonably broad class of cases this scheme is provably optimal and that, in these cases, the amount of entanglement concentrated between the two ends is equal to that which could be concentrated from the weakest link in the chain.

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arXiv2000

Quantum Anti-Cloning

We derive the transformation for the optimal universal quantum anti-cloner which produces two anti-parallel outputs for a single input state. The fidelity is shown to be 2/3 which is same as the measurement fidelity. We consider a probabilistic quantum anti-cloner and show quantum states can be anti-cloned exactly with non-zero probability and its efficiency is higher than the efficiency of distinguishing between the two states.

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arXiv2000

Cloning and quantum computation

We discuss how quantum information distribution can improve the performance of some quantum computation tasks. This distribution can be naturally implemented with different types of quantum cloning procedures. We give two examples of tasks for which cloning provides some enhancement in performance, and briefly discuss possible extensions of the idea.

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arXiv1999

Building multiparticle states with teleportation

We describe a protocol which can be used to generate any N-partite pure quantum state using Einstein-Podolsky-Rosen (EPR) pairs. This protocol employs only local operations and classical communication between the N parties (N-LOCC). In particular, we rely on quantum data compression and teleportation to create the desired state. This protocol can be used to obtain upper bounds for the bipartite entanglement of formation of an arbitrary N-partite pure state, in the asymptotic limit of many copies. We apply it to a few multipartite states of interest, showing that in some cases it is not optimal. Generalizations of the protocol are developed which are optimal for some of the examples we consider, but which may still be inefficient for arbitrary states.

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arXiv1999

Disentangling Nonlocality and Teleportation

Quantum entanglement can be used to demonstrate nonlocality and to teleport a quantum state from one place to another. The fact that entanglement can be used to do both these things has led people to believe that teleportation is a nonlocal effect. In this paper it is shown that teleportation is conceptually independent of nonlocality. This is done by constructing a toy local theory in which cloning is not possible (without a no-cloning theory teleportation makes limited sense) but teleportation is. Teleportation in this local theory is achieved in an analogous way to the way it is done with quantum theory. This work provides some insight into what type of process teleportation is.

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arXiv1999

No Signalling and Probabilistic Quantum Cloning

We show that the condition of no faster-than-light signalling restricts the number of quantum states that can be cloned in a given Hilbert space. This condition leads to the constraints on a probabilistic quantum cloning machine (PQCM) recently found by Duan and Guo.

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arXiv1999

A Method of Areas for Manipulating the Entanglement Properties of One Copy of a Two-Particle Pure State

We consider the problem of how to manipulate the entanglement properties of a general two-particle pure state, shared between Alice and Bob, by using only local operations at each end and classical communication between Alice and Bob. A method is developed in which this type of problem is found to be equivalent to a problem involving the cutting and pasting of certain shapes along with a certain colouring problem. We consider two problems. Firstly we find the most general way of manipulating the state to obtain maximally entangled states. After such a manipulation the entangled state |11>+|22>+....|mm> is obtained with probability p_m. We obtain an expression for the optimal average entanglement. Also, some results of Lo and Popescu pertaining to this problem are given simple geometric proofs. Secondly, we consider how to manipulate one two particle entangled pure state to another with certainty. We derive Nielsen's theorem (which states the necessary and sufficient condition for this to be possible) using the method of areas.

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arXiv1998

Entanglement of projection and a new class of quantum erasers

We define a new measurement of entanglement, the entanglement of projection, and find that it is natural to write the entanglements of formation and assistance in terms of it. Our measure allows us to describe a new class of quantum erasers which restore entanglement rather than just interference. Such erasers can be implemented with simple quantum computer components. We propose realistic optical versions of these erasers.

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arXiv1998

Quantum Whispers

It is shown that with the use of entanglement a specific two party communication task can be done with a systematically smaller expected error than any possible classical protocol could do. The example utilises the very tight correlation between separate spin measurements on a singlet state for small differences in the angles of these two measurements. An extension of this example to many parties arranged in a row with only local, one-to-one communication (whispering) is then considered. It is argued that in this scenario there exists no reliable classical protocol, whereas in the quantum case there does.

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arXiv1997

Revisiting Bell's theorem for a class of down-conversion experiments

A certain class of parametric down-conversion Bell type experiments has the following features. In the idealized perfect situation it is in only 50% of cases that each observer receives a photon; in the other 50% of cases one observer receives both photons of a pair while the other observer receives none. The standard approach is to discard the events of the second type. Only the remaining ones are used as the data input to some Bell inequalities. This raises justified doubts whether such experiments could be ever genuine tests of local realism. We propose to take into account these "unfavorable" cases and to analyze the entire pattern of polarization and localization correlations. This departure from the standard reasoning enables one to show that indeed the experiments are true test of local realism.

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arXiv1995

Realism and Time Symmetry in Quantum Mechanics

We describe a gedanken experiment with an interferometer in the case of pre- and postselection in two different time symmetric ways: We apply the ABL formalism and the de Broglie--Bohm model. Interpreting these descriptions ontologically, we get two very different concepts of reality. Finally, we discuss some problems implied by these concepts.

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