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arXiv:quant-ph/0606242 · Open Systems & Information Dynamics

False Qubits?: Polarization of Light and Josephson Junction

Robert Alicki

Published May 30, 2007• 3 citations
arXivHTMLPDF

Abstract

We compare two physical systems: polarization degrees of freedom of a macroscopic light beam and the Josephson junction (JJ) in the “charge qubit regime”. The first system obviously cannot carry genuine quantum information and we show that the maximal entanglement which could be encoded into polarization of two light beams scales like 1/(photon number). Two theories of JJ, one leading to the picture of “JJ-qubit” and the other based on the mean-field approach are discussed. The later, which seems to be more appropriate, implies that the JJ system is, essentially, mathematically equivalent to the polarization of a light beam with the number of photons replaced by the number of Cooper pairs. The existing experiments consistent with the “JJ-qubit” picture and the theoretical arguments supporting, on the contrary, the classical model are briefly discussed. The Franck-Hertz-type experiment is suggested as an ultimate test of the JJ nature.

DOI
10.1007/s11080-007-9039-1

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We compare two physical systems: polarization degrees of freedom of a macroscopic light beam and the Josephson junction (JJ) in the “charge qubit regime”. The first system obviously cannot carry genuine quantum information and we show that the maximal entanglement which could be encoded into polarization of two light beams scales like 1/(photon number). Two theories of JJ, one leading to the picture of “JJ-qubit” and the other based on the mean-field approach are discussed. The later, which seems to be more appropriate, implies that the JJ system is, essentially, mathematically equivalent to the polarization of a light beam with the number of photons replaced by the number of Cooper pairs. The existing experiments consistent with the “JJ-qubit” picture and the theoretical arguments supporting, on the contrary, the classical model are briefly discussed. The Franck-Hertz-type experiment is suggested as an ultimate test of the JJ nature.
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There exists a large number of experimental and theoretical results supporting the picture of "macroscopic qubits" implemented, for instance, by Rydberg atoms, Josephson junctions or Bose-Einstein condensates - the systems which should rather emerge in localized semiclassical states. In this note it is shown how, under realistic conditions, the false qubit interpretation can be consistent with the restricted set of experimental data collected for semiclassical systems. The recent experiments displaying semiclassical character of Bose-Einstein condensates and possible quantumness tests for a single system are briefly invoked also.
The recent experimental evidence for entangled states of two Josephson junction qubits is briefly discussed. It is argued that the interpretation of the experimental data strongly depends on the assumed theoretical model. Namely, the qubit states are supposed to be the lowest lying eigenstates of a certain effective Hamiltonian and hence automatically orthogonal, while the simple analysis within a more fundamental many-particle model shows that those states should strongly overlap. This makes the standard interpretation of the measurement procedure questionable.
We investigate duality in entanglement of a bipartite multiphoton system generated from a coherent state of light. The system can exhibit polarization entanglement if the two parts are distinguished by their parity, or parity entanglement if the parts are distinguished by polarization. It was shown in Phys. Rev. Lett. 110, 140404 (2013) that this phenomenon can be exploited as a method to test indistinguishability of two particles and it was conjectured that one can also test indistinguishability of macroscopic systems. We propose a setup to test this conjecture. Contrary to the previous studies using two-particle interference effect as in the Hong-Ou- Mandel setup, our setup neither assumes that the tested state is composed of single particles nor requires that the total number of particles be fixed. Consequently, the notion of entanglement duality is shown to be compatible with a broader class of physical systems. Moreover, by observing duality in entanglement in the above system one can confirm that macroscopic systems exhibit quantum behavior. As a practical side, entanglement duality is a useful concept that enables adaptive conversion of entanglement of one degree of freedom (DOF) to that of another DOF according to varying quantum protocols.
According to quantum theory, two ensembles of quantum systems that are described by the same density operator are indistinguishable. For example, unpolarized light can be obtained either by an incoherent mixture of two orthogonal pure states or by tracing out a photon from a maximally polarization-entangled photon pair. In both cases, one is unable to guess with probability greater than 50% the outcome of any polarization measurement, but the reasons are conceptually different: whereas the first case is a matter of classical ignorance (the photons were prepared in a definite but unknown way), the second one is of the quantum ignorance kind - if one cannot access the other degrees of freedom of the quantum state, there is no information that could be used to predict a measurement result. We use these concepts to discuss the quantum-physical interpretation of partially polarized light from the point of view of quantum communication and whether a polarization scrambler can really depolarize light. A novel definition of the degree of polarization of a single photon which does not depend on classical ignorance is also provided.
In quantum information processing, one of the most common methods to represent a qubit is by means of the polarization degree of freedom of a photon. Efficient methods to determine the photon polarization state are hence the fundamental tools in the studies of qubit systems. In fact, both theoretically optimal and practical polarization measurement schemes have been investigated extensively in the past two decades. These studies nevertheless focus on the situation when a definite number of photons are given and the results demonstrate the polarization estimation performance in terms of the mean fidelity [1, 2].