By Ivan B. Djordjevic

This e-book is a self-contained, tutorial-based advent to quantum info thought and quantum biology. It serves as a single-source connection with the subject for researchers in bioengineering, communications engineering, electric engineering, utilized arithmetic, biology, machine technological know-how, and physics. The booklet presents the entire crucial ideas of the quantum organic info concept required to explain the quantum info move from DNA to proteins, the resources of genetic noise and genetic error in addition to their effects.

  • Integrates quantum info and quantum biology concepts;
  • Assumes in simple terms wisdom of easy ideas of vector algebra at undergraduate level;
  • Provides a radical creation to easy techniques of quantum details processing, quantum details conception, and quantum biology;
  • Includes in-depth dialogue of the quantum organic channel modelling, quantum organic channel capability calculation, quantum versions of getting older, quantum types of evolution, quantum versions on tumor and melanoma improvement, quantum modeling of chicken navigation compass, quantum features of photosynthesis, quantum organic errors correction.

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We therefore, formulate the no-cloning theorem as follows. No-cloning Theorem. No quantum copier exists that can clone an arbitrary quantum state. This result raises a related question: do there exist some specific states for which cloning is possible? The answer to this question is (surprisingly) yes. Remember, a key result of quantum mechanics is that unitary operators preserve probabilities. This implies that inner (dot) products hφjφi and hφ0 jφ0 i should be identical. The inner products hφjφi and hφ0 jφ0 i are, respectively, given by    À Á φφ ¼ hψ jα* þ hχ jβ* ðαjψ i þ βjχ iÞ             ¼ jαj2 ψ ψ þ jβj2 χ χ þ α* β ψ χ þ αβ* χ ψ  0 0 À Á φ φ ¼ hψ jhψ jα* þ hχ jhχ jβ* ðαjψ ijψ i þ βjχ ijχ iÞ    2   2   2   2 ¼ jαj2  ψ ψ  þ jβj2  χ χ  þ α* β ψ χ  þ αβ*  χ ψ  : ð2:80Þ       We know that ψ ψ ¼ χ χ ¼ 1.

Because the composite system is closed, its dynamic is unitary, and final state is specified by a unitary operator U as follows: U ðρ  ε0 ÞU { , where ρ is a density operator of initial state of quantum register Q and ε0 is the initial density operator of the environment E. The reduced density operator of Q upon interaction ρf can be obtained by tracing out the environment: Â Ã ρ f ¼ TrE U ðρ  ε0 ÞU { ξðρÞ: ð2:91Þ The transformation (mapping) of initial density operator ρ to the final density operator ρf, denoted as ξ : ρ !

5, for two-qubit input state j00i. We will return to the concept of entanglement in Sect. 3. The quantum parallelism can now be introduced more formally as follows. The QIP device, denoted as QIP, implemented on a quantum register maps the input string i1, . , iN to the output string O1(i), . , ON(i): 0 O1 ðiÞ 1 0 i1 1 B C B C B ⋮ C ¼ UðQIPÞB ⋮ C; @ A @ A ON ðiÞ iN ðiÞ10 ¼ ði1 ; . . ; iN Þ2 : ð2:73Þ i1 , . . , iN 2 f0; 1g: ð2:74Þ The CB states are denoted by ji1 ; . . ; iN i ¼ ji1 i  Á Á Á  jiN i; 42 2 Quantum Information Theory Fundamentals The linear superposition allows us to form the following 2N-qubit state: " # 1 X jψ in i ¼ pffiffiffiffiffiffi ji1 ; .

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