Interaction without back-action in the context of quantum manipulation

Abstract

We address the interaction between two quantum systems (A and B) that is mediated by their common linear environment. If the environment is out of equilibrium the resulting interaction violates Onsager relations and cannot be described by a Hamiltonian. In simple terms the action of system A on system B does not necessarily produce a back-action. We derive general quantum equations describing the situation and analyze in details their classical correspondence. Changing the properties of the environment one can easily change and engineer the resulting interaction. It is tempting to use this for quantum manipulation of the systems. However the resulting quantum gate is not always unitary and may induce a loss of quantum coherence. For a relevant example we consider systems A and B to be spins of arbitrary values and arrange the interaction to realize an analogue of the two-qubit CNOT gate. The direction of spin A controls the rotation of spin B while spin A is not rotated experiencing no back-action from spin B. We solve the quantum dynamics equations and analyze the purity of the resulting density matrix. The resulting purity essentially depends on the initial states of the systems. We attempt to find a universal characteristics of the purity optimizing it for the worst choice of initial states. For both spins $s_A=s_B=1/2$, the optimized purity is bounded by 1/2 irrespective of the details of the gate. We also study in detail the semiclassical limit of large spins. In this case the optimized purity is bounded by $(1+\pi /2{)}^{-1}\approx 0.39$. This is much better than the typical purity of a large spin state $\sim s^{-1}$. We conclude that although the quantum manipulation without back-action inevitably causes decoherence of the quantum states the actual purity of the resulting state can be optimized and made relatively high.

References in corpus (16)

• Spintronics: Fundamentals and applications
• Quantum Computation with Quantum Dots
• Spins in few-electron quantum dots
• Introduction to Quantum Noise, Measurement and Amplification
• Silicon Quantum Electronics
• A Two Qubit Logic Gate in Silicon
• Quantum CNOT Gate for Spins in Silicon
• Environment Induced Entanglement in Markovian Dissipative Dynamics
• Long-range coherent coupling in a quantum dot array
• Single-Spin CCD
• Tunable Spin Qubit Coupling Mediated by a Multi-Electron Quantum Dot
• Induced decoherence and entanglement by interacting quantum spin baths
• PT-symmetric quantum state discrimination
• Decoherence and maximal violations of the Leggett-Garg inequality
• Resources needed for non-unitary quantum operations
• Nuclear spin pumping and electron spin susceptibilities