Quantum information is the study of the informational content of quantum states. The most common object of study is the "qubit", the information in a two-state quantum system such as spin-1/2 or photon polarization.

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The role of state space composition in quantum computation

In a paper by Richard Josza and Noah Linden they argue that the way state spaces of composite systems are formed is a key aspect in the benefits of quantum computers. In (classical) phase space, two ...
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Creating matrix Hamiltonian for Feynman's CCNOT [closed]

I'm trying to read Quantum Mechanical Computer and to implement the CCNOT logical gate with Mathematica. Since i wish to use the SWITCH implementation of the CNOT [Fig.8] i've realized that i need to ...
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fiber optic second order PMD as an operator on the tensor product Hilbert space

Second order polarization mode dispersion (SOPMD) is a coupling mechanism between polarization and frequency. Take our photon to be the following tensor product: $\psi = \int \gamma_{\omega} | ...
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decoherence free subspace of a single photon

Take the state vector for a single photon as $\psi = \int \gamma_{\omega} | \omega \rangle \otimes (\alpha |H \rangle + \beta | V \rangle )d \omega$ $H, V, \omega$ are the horizontal polarization, ...
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Looking for description of Helstrom's measurement

I hope someone can help me find the page or chapter where Helstrom discusses his famous measurement for distinguishing between two mixtures in the textbook Quantum Detection and Estimation Theory. ...
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If distant observers never see a black hole form in finite time how can the information paradox be a problem?

So, at least as reported in the media, the physics community is still struggling with the problem of resolving the impossibility of retrieving information from beyond the event horizon of a black hole ...
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Entanglement, superposition, and propositional logic [duplicate]

From what I am understanding, there is entanglement in a system if there is a correlation between elements of that system. For an example that I found, If you have only two cards and know that one is ...
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What is the Reduced Density Matrix?

The difference between pure and mixed states is the difference in their density matrix structure. For density matrix $\rho$ of mixed state the trace of $\rho^{2}$ should be less than 1. For pure ...
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281 views

What is meant by fermionic and bosonic “modes”?

The paper The Dirac quantum automaton: a short review (pdf) starts off by stating: The starting point for the construction of space–time and the physical laws therein is an unstructured, countably ...
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State vector vs density operator

We formulate quantum mechanics using language of state vectors. One alternative formulation is possible using density operator or density matrix. Why we are doing this alternative approach? Is the ...
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What are the practical applications of quantum foundations?

Many quantum foundation researchers keep emphasizing that For All Practical Purposes (FAPP), quantum foundations are irrelevant. They even invented an acronym for it! Does that mean that quantum ...
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280 views

Is a quantum system mandatory for generating true random sequence?

Is a quantum system necessary if we want to generate true random sequence? The mathematical framework used for classical mechanics doesn't involve any random value. But the mathematical framework of ...
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311 views

Why does replacing bra and ket basis vectors by their row and column representations give the wrong matrix representation in a non-orthogonal basis?

I have a Hermitian operator (for a 2D Hilbert space) given by $$H=|\psi\rangle \langle \psi|+|\phi\rangle \langle \phi|$$ where $|\psi\rangle$ and $|\phi\rangle$ are normalized but not necessarily ...
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A machine which copies any object with 100% accuracy?

Does physics allow for a machine that copies an object with 100% accuracy?
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Proof of Pauli group preservation by Clifford group conjugation?

A well know result is that Clifford group preserve the Pauli group under conjugation or, in other words: $C(P_{1} \otimes P_{2})C^{\dagger} = P_{3} \otimes P_{4}$, with $C \in$ Clifford group and ...
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154 views

Quantum violation of Newton's Third Law? [closed]

From this site: http://www.learning-mind.com/5-thought-provoking-quantum-experiments-showing-that-reality-is-an-illusion/ I gained the knowledge that a group of scientists, upon measuring a tiny ...
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How “fundamental” is quantum information/computation?

I am wondering how fundamental the study of quantum information theory and computation is, in the sense of contributing to our understanding of the basic laws of nature. Will quantum information ...
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Application of non maximally entangled state

In quantum information and quantum computation, we generally use Bell type states which are maximally entangled. I find that the set of entangled states as interesting objects from a mathematical ...
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Are physical probabilities also quantized?

In physics there is quanta and energy occurs per this unit. Is it it then reasonable that probability also is quantized since energy is?
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Anybody have example of two-qubit non-Pauli and non-Clifford quantum gate?

A lot of known quantum gates are in the Pauli group (I,X,Z,Y) or in the Clifford group (H,P,Cnot). I need examples of the quantum gates that aren't in this groups. Also, are there are matlab functions ...
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Holonomic and Topological Quantum Computing [closed]

In topological quantum computation, anyons are braided in spacetime, performing non-trivial evolutions of some degenerate groundstate. In holonomic quantum computation, the system is braided in ...
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104 views

Quantum computing, NP complexity [closed]

Hi I have a very limited knowledge of quantum physics and its bothering me trying to understand quantum computing. I want understand how a qubit can return usable data faster then a regular bit, how ...
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1answer
50 views

What is the 'area law' in the context of matrix product states?

I am trying to get into the topic of matrix product states by reading this: A practical introduction to tensor networks: Matrix product states and projected entangled pair states. R. Orús. Ann. ...
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Does this quote from my textbook imply that not all states are superpositions?

I read this at a book; The difference between bits and qubits is that a qubit can be in a state other than $|0\rangle$ or $|1\rangle$. It is also possible to form linear combinations of ...
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Photons have a property from the matter they interact with?

When a photon leaves its source and hits our eye, our brain sees the source of the photon (Like a lightbulb or a star). When a photon is ejected from its source and bounces off of an object we see the ...
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248 views

How to physically prepare a qubit in a certain state?

I earlier asked the question about definition of a qubit. From it I understood that its the experimental setup that actually defines the qubit. But I don't get it's physical realization. How a qubit ...
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BB84 protocol what do they do once they have the key?

In the BB84 protocol Alice and Bob share a key via a method using both quantum and classical channels. I understand how they do this. But I don't understand what they then do with the key? I.e. How do ...
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What is the implication of Schmit decomposition?

According to schmidt decomposition if I have pure state $|\psi\rangle$ in the composite hilbert space $AB$ ( both $A$ and $B$ are hilbert spaces of dimension $n$ ) then it can be writen as ...
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How can I prove following density matrices have same eigenvalues?

I have the following two density operators, the paper I am reading says that these two operators have same eigenvalues $$\rho^i = \frac{1}{3} ( |0\rangle \langle 0 | +|1\rangle \langle 1 |+|2\rangle ...
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Can we have a physical interpretation for a time independent Schrodinger equation of this form?

I am interested in a time independent Schrodinger equation of this form. $$F*\psi - \frac{\hbar^2}{2m} \frac{\partial^2{\psi}}{\partial{x^2}} = E\psi$$ Here the product $V\psi$ is replaced by the ...
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Quantum Computation

Is there any rule or technique so that one can design quantum gate operator from matrix operator? Suppose, what will be the quantum gate operator for this matrix operator : $$ \left( \begin{array}{c ...
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Bell State, if Bob applies a Pauli Gate?

After Alice and Bob share a Bell state, Bob applies a Pauli gate to his qubit. What will be the situation of the Bell state? What happens? Then Alice applies the same gate to her qubit – again, what ...
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448 views

Can we make a Maxwell's Demon using Quantum Computers?

Although I'm reasonably sure that quantum computing advances will not lead to the ability to construct a machine that globally violates the 2nd law of thermodynamics, it feels like a difficult ...
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Two definitions of the density matrix?

There seems to be two different definitions of definitions of density matrices in Physics. In Quantum Information we define a the density matrix associated with a wave function $ | \psi \rangle$ as ...
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Reference for statistical mechanics from information theoretic view

I am interested in knowing if some one here knows book/notes for statistical mechanics from the information theoretic viewpoint.
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Hilbert Schmidt inner product

I am desperately trying to solve the following problem, and would really appreciate help! Suppose $R$ and $Q$ are two quantum systems with the same Hilbert space $\mathcal{H}$ with ...
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How to understand the measurement on entangled state in the following cases? [closed]

Assuming an EPR pair AB, event MA is a measurement on A. My questions are: (1) At MB and MB' (depending on where B is located), if we try to describe the state of B (but not measure B yet), ...
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About quantum measurement problem, proper or improper mixture?

Generally a quantum measurement is regarded as resulting in a definite outcome due to "state collapse" and the post-measurement state is described as a proper mixture with the ignorance of the ...
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Theoretically, how does quantum decoherence induce noise?

The decoherence process has allowed us to explain various (classical and decoherence) sources of measurement noise in quantum systems. I intuitively understand this physical concept of ...
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Separability of density operators on tensor product spaces

Consider a composite system $\mathcal{H}=\mathcal{H}_{A}\otimes\mathcal{H}_{B}$ where $\mathcal{H}_{A}$ and $\mathcal{H}_{B}$ are Hilbert spaces of constituent components (say two qubits). Let ...
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Positive Partial Transposition in Fano form

Cite from "Geometry of Quantum States: An Introduction to Quantum Entanglement 1st Edition by Ingemar Bengtsson (Author), Karol Zyczkowski (Author)": "Partial transposition applied on a density ...
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Bounds on dimension of a purification?

Let $\rho \in H_A$ be a density operator, $H_A$ is finite dimensioal, it is well known that $\rho$ has a purification in some larger hilbert space. Let $b$ be the minimum dimension for $H_B$ such ...
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159 views

What is quantum mysticism? [closed]

Most of my questions on stack physics exchange are being commented on as being quantum mystic. The questions I ask are basically related to device independence and how local hidden variable theory ...
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189 views

What do we mean by Unitary Dynamics in Quantum Computing?

In the afterword to the Tenth Anniversary Edition of the book Quantum Computation and Quantum Information the authors say: For many years, the conventional wisdom was that coherent ...
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Operational difference between separable, entangled, PPT and NPT states

Given two parties Alice and Bob, a state $\rho_{AB}$ is said to be separable if it can be written as $\rho_{AB}=\sum_i p_i\rho^i_A\otimes\rho^i_B$, with $p_i$ being probabilities and ...
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When was Electromagnetically Induced Transparency first introduced?

The oldest paper I know regarding this topic was published in 1997 by Stephen E. Harris. But I am not sure if he is the first to introduce this idea. Could you tell me when and by who did introduce ...
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Quantum Bayesianism and contradictory preditions of two agents

In quantum Bayesianism (QBsim) interpretation, the wave function $| \psi \rangle$, or density operator $\hat{\rho} = | \psi \rangle \langle \psi |$, is not objective. It is instead interpreted as the ...
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77 views

Quantum cloning of orthonormal states

If I understand correctly, for two orthonormal states $\left|\psi_1\right\rangle$ and $\left|\psi_2\right\rangle$ in the Hilbert space H, there must exist a unitary transformation $U$, such that: ...
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202 views

What does it mean that quantum teleportation can be classically simulated?

Quoting here from Quantum Computation by Nielsen and Chuang : (Gottesman–Knill theorem) Suppose a quantum computation is performed which involves only the following elements: state preparations ...
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A question on partial trace and density matrix computation

Consider a Pure state of a two dimensional system $|\psi\rangle={1\over\sqrt{2}}(|e_1\rangle|e_1\rangle+|e_2\rangle|e_2\rangle)$ where $\{|e_i\rangle\}$ is an orthonormal basis. Could any one just ...