We demonstrate in straightforward calculations that even under ideally weak noise the relaxation of bipartite open quantum systems contains elements not previously encountered in quantum noise physics. While additivity of decay rates is known to be generic for decoherence of a single system, we demonstrate that it breaks down for bipartite coherence of even the simplest composite systems.
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YU, T. and EBERLY, J. H., 2006. Quantum Open System Theory: Bipartite Aspects. Physical Review Letters. 3 October 2006. Vol. 97, no. 14, p. 140403. DOI 10.1103/PhysRevLett.97.140403.
To the present time, treatments of open quantum system theory [3–5] are based on this scenario in which a ‘‘small’’ system has a weak interaction with one or more reservoirs, and this is the cause of its relaxation (its loss of selfcoherence). Now we extend the discussion very slightly and consider in detail the simplest quantum system made of two parts, a pair of qubits. Remarkably, this simple step takes us onto new ground within the theory of quantum open systems. We will show that the internal coherence of the two-qubit system exhibits a nonadditive response. We believe that this is the first demonstration of the effect.
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[…] information about an open bipartite quantum system will become degraded with time as an indivisible quantum unit, no matter how its parts are engaged by weak noises, and the degradation is not predicted by the familiar smoothly decaying behavior familiar from the quantum theory of single open systems.
To summarize, in this Letter we introduced a commonly occurring category of two-system mixed states, shown in (6). By following their time-dependent behavior under the influence of ideally weak noises, we demonstrated the presence of elements of open quantum system theory not previously encountered. These become interesting whenever a small system has different quantum parts that can be entangled. Exactly this situation will arise, for example, in a quantum computer, where it is most desirable that two qubits retain a nonzero degree of mutual cross entanglement. It must be emphasized that none of our key AB results come from interaction or communication between the A and B parts of the two-party system or between their separate reservoirs.
This is perhaps the most striking aspect of the properties described: They are properties of joint-system information rather than joint-system interaction. To the extent that joint-system information is a resource of substantial value in one or another practical application of qubit networks, this aspect of time-dependent entanglement will be important. At the same time, it illuminates further the difficult fundamental challenge to understand the nature of coherence in multipartite mixed states, particularly in its timedependent behavior, which has recently come under examination in both continuous spaces [13–15] and discrete spaces (qubit pairs [16 –20], finite spin chains, and elementary lattices [21–24]) and decoherence dynamics in adiabatic entanglement [25], as well as in situations without relaxation [26] and in connection with direct entanglement observation [27]. These have all contributed to increased awareness of this domain.
Finally, it should be emphasized that, although entanglement measured by concurrence is not an observable represented by an Hermitian operator, nevertheless it is still possible to express the concurrence (7) in terms of the expectation values of certain ordinary physical observables [28]. Moreover, the recent proposals to directly measure the dissipative entanglement evolution have opened up a possibility of experimentally demonstrating the onset of the nonadditivity when nonlocal coherence decay is concerned [27,29].