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arXiv:1304.1435 · Physical Review Letters

Duality in Entanglement Enabling a Test of Quantum Indistinguishability Unaffected by Interactions

Sougato Bose, Dipankar Home

Published Apr 3, 2013• 34 citations
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Abstract

We point out an earlier unnoticed implication of quantum indistinguishability, namely, a property which we call "dualism" that characterizes the entanglement of two identical particles (say, two ions of the same species)--a feature which is absent in the entanglement of two nonidentical particles (say, two ions of different species). A crucial application of this property is that it can be used to test quantum indistinguishability without bringing the relevant particles together, thereby avoiding the effects of mutual interaction. This is in contrast to the existing tests of quantum indistinguishability. Such a scheme, being independent of the nature and strength of mutual interactions of the identical particles involved, has potential applications, including the probing of the transition from quantum indistinguishability to classical distinguishability.

DOI
10.1103/physrevlett.110.140404

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We point out an earlier unnoticed implication of quantum indistinguishability, namely, a property which we call "dualism" that characterizes the entanglement of two identical particles (say, two ions of the same species)--a feature which is absent in the entanglement of two nonidentical particles (say, two ions of different species). A crucial application of this property is that it can be used to test quantum indistinguishability without bringing the relevant particles together, thereby avoiding the effects of mutual interaction. This is in contrast to the existing tests of quantum indistinguishability. Such a scheme, being independent of the nature and strength of mutual interactions of the identical particles involved, has potential applications, including the probing of the transition from quantum indistinguishability to classical distinguishability.
It was shown recently that entanglement of identical particles has a feature called dualism (Bose and Home 2013 Phys. Rev. Lett. 110 140404 ), which is fundamentally connected with quantum indistinguishability. Here we report an experiment that observes the entanglement duality for the first time with two identical photons, which manifest polarization entanglement when labeled by different paths or path entanglement when labeled by polarization states. By adjusting the mismatch in frequency or arrival time of the entangled photons, we tune the photon indistinguishability from the quantum to the classical limit and observe that the entanglement duality disappears under the emergence of classical distinguishability, confirming it as a characteristic feature of quantum indistinguishable particles.
We show a hitherto unexplored consequence of the property of identicity in quantum mechanics. If two identical objects, distinguished by a dynamical variable A, are in certain entangled states of another dynamical variable B, then, for such states, they are also entangled in variable A when distinguished from each other by variable B. This dualism is independent of quantum statistics. Departures from identicity of the objects due to arbitrarily small differences in their innate attributes destroy this dualism. A system independent scheme to test the dualism is formulated which is readily realizable with photons. This scheme can be performed without requiring the entangled objects to be brought together. Thus whether two macro-systems behave as quantum identical objects can be probed without the complications of scattering. Such a study would complement the program of testing the validity of quantum superposition principle in the macro-domain which has stimulated considerable experimentation.
Particles in classical physics are distinguishable objects, which can be picked out individually on the basis of their unique physical properties. By contrast, in the philosophy of physics, the standard view is that particles of the same kind ("identical particles") are completely indistinguishable from each other and lack identity. This standard view is problematic: Particle indistinguishability is irreconcilable not only with the very meaning of "particle" in ordinary language and in classical physical theory, but also with how this term is actually used in the practice of present-day physics. Moreover, the indistinguishability doctrine prevents a smooth transition from quantum particles to what we normally understand by "particles" in the classical limit of quantum mechanics. Elaborating on earlier work, we here analyze the premises of the standard view and discuss an alternative that avoids these and similar problems. As it turns out, this alternative approach connects to recent discussions in quantum information theory.
We show how the property of dualism, which can exist in the entanglement of identical particles, can be tested in the usual photonic Bell measurement apparatus with minor modifications. Two different sets of coincidence measurements on the same experimental setup consisting of a Hong-Ou-Mandel interferometer demonstrate how the same two-photon state can emerge entangled in the polarization or the momentum degree of freedom depending on the dynamical variables used for labeling the particles. Our experiment demonstrates how the same source can be used as both a polarization entangled state as well as a dichotomic momentum entangled state shared between distant users Alice and Bob in accordance with which sets of detectors they access. When the particles become distinguishable by letting the information about one of the variables be imprinted in yet another (possibly inaccessible) system or degree of freedom, the feature of dualism is expected to vanish. We verify this feature by polarization decoherence (polarization information in the environment) or arrival time difference, which both respectively destroy one of the dual forms of entanglement.
The entanglement between two bosons or fermions can be accessed if there exists an auxiliary degree of freedom which can be used to label and effectively distinguish the two particles. For some types of entanglement between two indistinguishable particles one can observe a duality, i.e., if the entanglement is present in a Hilbert space H\mathcal{H}H and an auxiliary Hilbert space ${\mathcal{H}}^{\ensuremath{'}}$ is used to label the particles, then if we use H\mathcal{H}H as a label, entanglement will be present in ${\mathcal{H}}^{\ensuremath{'}}$. For distinguishable particles this effect does not occur because of superselection rules which prevent superpositions of different types of particles. However, it is known that superselection rules can be bypassed if one uses special auxiliary states that are known as reference frames. Here we study properties of reference frames which allow for the observation of a duality in entanglement between two distinguishable particles. Finally, we discuss the consequences of this result from a resource-theoretic point of view.
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.