The minimal-coupling quantum heat engine is a thermal machine consisting of an explicit energy storage system, heat baths, and a working body, which alternatively couples to subsystems through discrete strokes --- energy-conserving two-body quantum operations. Within this paradigm, we present a general framework of quantum thermodynamics, where a work extraction process is fundamentally limited by a flow of non-passive energy (ergotropy), while energy dissipation is expressed through a flow of passive energy. It turns out that small dimensionality of the working body and a restriction only to two-body operations make the engine fundamentally irreversible. Our main result is finding the optimal efficiency and work production per cycle within the whole class of irreversible minimal-coupling engines composed of three strokes and with the two-level working body, where we take into account all possible quantum correlations between the working body and the battery. One of the key new tools is the introduced ``control-marginal state" --- one which acts only on a working body Hilbert space, but encapsulates all features regarding work extraction of the total working body-battery system. In addition, we propose a generalization of the many-stroke engine, and we analyze efficiency vs extracted work trade-offs, as well as work fluctuations after many cycles of the running of the engine.
The scenario of remote state preparation with shared correlated quantum state and one bit of forward communication [B. Dakić et al. Nature Physics 8, 666 (2012)] is considered. Optimisation of the transmission efficiency is extended to include general encoding and decoding strategies. The importance of use of linear fidelity is recognized. It is shown that separable states cannot exceed the efficiency of entangled states by means of "local operations plus classical communication" actions limited to 1 bit of forward communication. It is proven however that such a surprising phenomena may naturally occur when the decoding agent has limited resources in the sense that either (i) has to use decoding which is insensitive to change of coordinate system in the plane being in question (which is the natural choice if the receive does not know the latter) or (ii) is forced to use bistochastic operations which may be imposed by physically inconvenient local thermodynamical conditions. [3]. Originally the quantum advantage in realization of those task was due to quantum entanglement. However there is a more general phenomenon of quantum correlations involving the correlations beyond entanglement (see [4] and references therein). It turned out that efficiency of the protocols involving the latter may also exceed the efficiency of any classical solution of Deutsch-Jozsa problem [5], [6] or Knill-Laflamme scheme [7]. Quite recently two proposals of application of quantum correlations beyond entanglement (QCBE) have been provided. One of them have theoretically and experimentally supported the significance of their role in the analogue of quantum dense coding [8] on the level of continuous variables. The other [9] has addressed the issue of the importance of QCBE for the remote state preparation (RSP). Since RSP is one of the significant building blocks in quantum communication the question is very important. It has already been adapted to weak entanglement scenarios including bound entanglement [10] and preliminary results concerning advantage of QCBE in specific variant of RSP have been obtained [11]. The paper [9] announces the surprising possibility of the fact that in some cases the communication power of QCBE represented by separable states may exceed that of some entangled ones. The authors have also provided the direct connection of the transfer fidelity they have chosen to measure (called geometrical discord) of quantum correlations of the resource state. However this conclusion -unlike the experimental results of the paper fully transparent and impressive -seems to be not fully justified.
We study the decay of entanglement of quantum dot electron-spin qubits under hyperfine interaction mediated decoherence. We show that two qubit entanglement of a single entangled initial state may exhibit decay characteristic of the two disentanglement regimes in a single sample, when the external magnetic field is changed. The transition is manifested by the supression of time-dependent entanglement oscillations which are superimposed on the slowly varying entanglement decay related to phase decoherence (which result in oscillatory behaviour of entanglement sudden death time as a function of the magnetic field). This unique behaviour allows us to propose the double quantum dot two-electron spin Bell state as a promising candidate for precise measurements of the magnetic field.Systems of electron spins confined in quantum dots (QDs) have received much theoretical (see for review) and experimental (see for review) interest since the initial proposal for spin-based quantum computing [7]. This resulted in the development of a range of effective techniques for the initialization, manipulation, and readout of the spin state in two main trends. One, involving electrical (or magnetic) manipulation of lateral QDs [8][9][10], and the other, involving optical manipulation of self-assembled QDs [11][12][13]. Both prove sucessful in the generation of high fidelity initial states, also entangled, but the coherent evolution of spin states and manipulation thereof suffer from the destructive effects of the hyperfine interaction between the electron spin and the spins of the nuclei of the QD atoms. Hence, the current experiments focus mostly on few-spin qubits [14,15] which are more robust against decoherence, or on involved schemes for the minimization of decoherence effects [16][17][18]. The proficiency attained in the experiments has been very recently demonstrated in Ref. [19], where quantum state tomography of two initially entangled singlet-triplet qubits has been performed.The central idea of this paper is to propose, based on the high level of the experimental techniques used to study electron spin states in QDs, a scheme for sensing an external parameter (the magnetic field) by harnessing the entanglement present in a two-qubit system and the inbuilt decoherence processes. The idea is outside of traditional methods in quantum metrology, since it relies on decoherence, while metrology requires a high degree of quantum coherence. It is vital that the qubits be electron spins confined in QDs with a non-zero nuclear spin of the environment, because this leads to the specific system-environment interaction and results in a characteristic disentanglement process, which, as we have found, strongly and counter-intuitively depends on the magnetic field.The study of spin entanglement [20] decay in a twoelectron-two-QD system, has up-to-date been limited to a number of complex, yet solvable scenarios [21][22][23]. The complexity accounts for the nontrivial behavior of the reported evolution of entanglement. Hence, in Refs [21] ...
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