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Aalborg Universitet
Aalborg Universitet

... connected to ideal leads where the carriers are quasi free fermions, is completely characterized by a one particle scattering matrix. Many people have since contributed to the justification of this formalism, starting from the first principles of non-equilibrium quantum statistical mechanics. In thi ...
tions processing as well as in quantum information processing. In anal
tions processing as well as in quantum information processing. In anal

... Information is quantized in classical digital informations processing as well as in quantum information processing. In analogy to the classical bit, the elementary quantum of information in quantum information processing is called a qubit. In the first part of this chapter we will learn how qubits c ...
Time Evolution of States for Open Quantum
Time Evolution of States for Open Quantum

... and the state ρ̂S (0) of the system is pure i.e is an orthogonal projector on a unit vector ψ of HS . A non pure state will be called a mixed state. A density matrix ρ̂S is a mixed state if and only if ρ̂S has an eigenvalue λ, such that 0 < λ < 1. If ρ̂ is a pure state then ρ̂ = Πψ , ψ ∈ H, kψk = 1 ...
Properties of higher-order Trotter formulas
Properties of higher-order Trotter formulas

... Higher-order Trotter formulas provide a very general and systematic way to derive discrete approximations of path integrals for quantum mechanical or quantum statistical systems. These discretizations converge more rapidly while being only slightly more complicated than the usual low-order formulati ...
Entanglement measure for rank-2 mixed states
Entanglement measure for rank-2 mixed states

... to study the entanglement for a wide class of complex quantum systems. For example, consider a pure state 兩␺典 of an 共n + 1兲-partite quantum system AB1B2 ¯ Bn, where A is a qubit and B j are arbitrary quantum systems. Let ␳ be the state found by tracing out the qubit A. The I-tangle formula Eq. 共13兲 ...
Self-adjoint operators and solving the Schrödinger equation
Self-adjoint operators and solving the Schrödinger equation

Decoherence Versus Disentanglement For Two Qubits In A
Decoherence Versus Disentanglement For Two Qubits In A

... • Some Previous Concepts ...
Explicit solution of the continuous Baker-Campbell
Explicit solution of the continuous Baker-Campbell

... term in the expansion of Q. Lower order terms of this expansion have been calculated in the literature before by iterative methods. Recently, Wilcox (5) carried out this calculation up to n = 4. It can be generally proved, that in every order of perturbation theory D is a linear combination of integ ...
Aalborg Universitet The Landauer-Büttiker formula and resonant quantum transport
Aalborg Universitet The Landauer-Büttiker formula and resonant quantum transport

... dot levels across the fixed Fermi level of the system (recall that the latter is entirely controlled by the semi-infinite leads). Otherwise stated, the eigenvalues of H S (Vg ) equal the ones of H S (Vg = 0) (we denote them by {Ei }), up to a global shift Vg . Using the Landauer-Büttiker formula (8 ...
Problem set 7
Problem set 7

... Quantum Mechanics 3, Spring 2012 CMI Problem set 7 Due by beginning of class on Monday Mar 5, 2012 BCH formula for x and p , SHO 1. Consider the function f (t) = etA Be−tA where A, B are a pair of operators (e.g. position and momentum or creation and annihilation operators etc.). t is a parameter wh ...
< 1 2 3

Decoherence-free subspaces

A decoherence-free subspace (DFS) is a subspace of a system's Hilbert space that is invariant to non-unitary dynamics. Alternatively stated, they are a small section of the system Hilbert space where the system is decoupled from the environment and thus its evolution is completely unitary. DFSs can also be characterized as a special class of quantum error correcting codes. In this representation they are passive error-preventing codes since these subspaces are encoded with information that (possibly) won't require any active stabilization methods. These subspaces prevent destructive environmental interactions by isolating quantum information. As such, they are an important subject in quantum computing, where (coherent) control of quantum systems is the desired goal. Decoherence creates problems in this regard by causing loss of coherence between the quantum states of a system and therefore the decay of their interference terms, thus leading to loss of information from the (open) quantum system to the surrounding environment. Since quantum computers cannot be isolated from their environment (i.e. we cannot have a truly isolated quantum system in the real world) and information can be lost, the study of DFSs is important for the implementation of quantum computers into the real world.
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