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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Phase shift of the displacement operator

According to my professor, the displacement operator $D(α)=e^{\alpha a^†−α^*a}$ can be written, "with a simple phase shift", as $D(α)=e^{i\alpha(a^†+a)}$ which he then proceeds to write as ...
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Shape of the state space under different tensor products

I am currently studying generalized probabilistic theories. Let me roughly recall how such a theory looks like (you can skip this and go to "My question" if you are familiar with this). Recall: In a ...
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Finding the Expectation Value of basis states [on hold]

I am a Mathematician and I am taking a Quantum Computing class. We have been asked to find the expectation value of $X$ tensor $Z$ and $H$ tensor $H$. X is the not operator and switches the state the ...
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Unitarity and measurement

I used to believe that the wavefunction collapse came from the interaction of the system we want to measure {S} with the measurement apparatus {M} : {S} undergoing a non unitary transformation, but ...
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Kraus operator rank

All quantum operations $\mathcal{E}$ on a system of Hilbert space dimension $\mathcal{d}$ can be generated by an operator-sum representation containing at most $\mathcal{d^2}$ elements. Extending ...
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Properties of controlled z-rotations

Given n qubit gate of the form c-z-z-z... (shorthand for c-z between qubit 1 and 2 followed by c-z between 1 and 3 and so on up to n qubits) it seems to be possible to find local unitaries which will ...
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81 views

Question about Hartle and Hawking's universal wavefunction?

My apologies in advance if this question is poorly worded or doesn't make any sense, however I have just finished reading into this theory and it seems as though Hawkings No Boundary Universe is ...
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266 views

Question on hadamard gate and cnot gate circuit tables

I'm trying to solve this problem for homework: Now show that if the CNOT gate is applied in the Hadamard basis - i.e. apply the Hadamard gate to the inputs and outputs of the CNOT gate - then ...
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How to connect these two formulations regarding the need for a density matrix in quantum mechanics?

I found these two formulations: The density matrix is: 1) "needed if we consider a system that is part of a larger closed system." 2) "needed for a system to be ...
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Are universally valid possibilistic theories possible?

This is a spin-off of the following question: Are Thomas Breuer's subjective decoherence and Scott Aaronson's freebits with knightian freedom the same things in essence? Given that Thomas ...
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Physical interpretation of applying a unitary operator to a state

When we apply one of the Pauli matrices $\sigma_y$ on one of its eigen-vectors $| \odot \rangle$, what does the eigen-value tell us about $| \odot \rangle$? Is this considered a measurement of $| ...
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Entropy increase vs Conservation of information (QM)

Unitarity of quantum mechanics prohibits information destruction. On the other hand, the second law of thermodynamics claims entropy to be increasing. If entropy is to be thought of as a measure of ...
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163 views

How does many-worlds interpretation make measurement unitary?

Does many-worlds interpretation of QM make the process of measurement (wavefunction collapse) be an unitary transform? If so, how does it do this? If we have an "object" qubit in state ...
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What is the Philosophy Behind Relational Quantum Mechanics?

I watched this video on Relational Quantum Mechanics yesterday and my brain has been trying to comprehend it since. The interpretation I currently have is this: If an observer O measures the state S ...
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Quantum information references

I was hoping you guys could recommend reading material on quantum information. First off, here's my background. Personally, I started reading Ballentine's Quantum Mechanics and I found it be a very ...
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What exactly happens at the second-order phase transition of the 2D Toric code?

For a 2D Toric code specified by $$H = -J_s\sum_{s} \prod_{j\in s} \sigma^x_j - J_p\sum_{p} \prod_{j\in p} \sigma^z_p - h_x\sum_{l} \sigma^x_l - h_z\sum_{l} \sigma^z_l$$ where $s$ denotes stars, $p$ ...
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33 views

The Simon's Algorithm, confusing equation

I'm approaching the Simon's Algorithm and have troubles with understanding a logic in an introduction. Above the eq. 6.5.4 they introduce that set S which has 2 elements. As far as I understand, ...
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About long range entanglement [closed]

“topologically non-trivial” ground states have long-range entanglement. Is this possible to process the quantum information with help of the studies in topological non-trivial ground states for ...
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Is a quantum channel well behaved under a perturbation of its Choi matrix?

Every completely positive trace preserving quantum channel can be associated with a unique quantum state. Supposing one perturbs the quantum state into a new state. Is there some sense in which one ...
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Definition of Fermion [closed]

Recently, I encounter a problem about the definition of Fermion operator. In our standard textbooks, the Fermions are defined by their exchange/braiding property, that is, if a minus sign appears by ...
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Are there any known continuous (non-lattice) quantum error correction codes?

I come from a hep-th background, but I have noticed that quantum information is becoming increasingly common in discussions of AdS/CFT and black hole information, and so I've begun thinking about it ...
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How would a quantum computer receive input from a classical computer?

One of the potential applications of a quantum computer would be as a coprocessor to a classical computing system, much in the same way as a graphics processing unit (GPU) performs specialized ...
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Would a pair of independent quantum coin tosses be perfectly anti-correlated?

Background Suppose we attach a button to an electronic flip flop such that an LED will toggle when we press the button with 50% probability, where the source of the randomness is a quantum event, ...
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134 views

Significance of 'chiral' form for a qubit?

Say I have a qubit with probability amplitude divided evenly among $|0\rangle$ and $|1\rangle$ $$\frac{1}{\sqrt 2}|0\rangle + \frac{1}{\sqrt 2}|1\rangle$$ So it seems that we have a, loosely ...
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What is the difference between a bit and a qubit?

I am Computer Science student and learning about quantum computing. But, I have a problem in understanding Bit and Qubit relationship. A bit with 2 bits = 4 states 00,01,10,11--- 1 state at a time. ...
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29 views

Wigner-Yanase skew information [closed]

I am reading Eric Carlen's paper on Trace Inequalities and Quantum Entropy. I am currently reading about the Wigner-Yanase skew information which is defined as: $$I_{WY}(\rho)=-\frac{1}{2} ...
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Conjugate of unknown qubit?

I have seen this problem somewhere on stack exchange, but I have a separate question. Given a qubit which is unknown say $\alpha|0\rangle +\beta|1\rangle $ ( $\alpha, \beta$ are unknown ) is there a ...
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Ternary dimensioned density matrix

I am currently reading this paper: Entropy Inequalities by Araki and Lieb (project Euclid link). And I am not able to understand one step: $${\rm Tr}^{123}\left(\rho^{12}\rho^{23}\right)={\rm ...
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How are the field operator and quantum state after a beam splitter and a polarizing beam splitter individually?

How are the field operator $\hat{a}$, $\hat{a}^\dagger$ and the quantum state (like coherent state $|\alpha>$, Fock state $|n>$) changed after a beam splitter and a polarizing beam splitter ...
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How is decoherence due to the environment compatible with the Copenhagen interpretation?

Let's say that "decoherence" is that transition from a pure quantum state to a mixed state due to interactions with the environment. (A reasonable definition?) How is that compatible with the ...
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explaining qubits to beginning CS students

&I have 15 minutes as a guest lecturer to explain the notion of quantum computing to CS students in a Theory of Computation class. There is a lot of information on the web, e.g., ...
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Quantum coherence and decoherence

In Quantum Mechanics coherent states are defined as eigenstates to some annihilation operator. Afaik this notion is due to Roy Glauber. Now, I just read that if you have a spin-state for example, ...
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64 views

Finding the matrix representation of a superoperator

I am trying to express superoperator (e.g. the Liouvillian) as matrices and am having a hard time finding a way to do this. For instance, given the Pauli matrix $\sigma_y$, how do I find the matrix ...
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118 views

Question about the no-clone theorem

The quantum no-clone theorem states that one cannot "build" a perfect cloning device for arbitrary quantum systems. There also exists a famous thought experiment where Alice transmits information to ...
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Could a travelling quantum object transport an on-board monitor to restitute information later? [closed]

Could a pair of identical "automated observers" such as a camera inside a capsule, be made to travel slowly along different paths, and then be recovered to play back a film of its on-board ...
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Entanglement Distillation - Interpretate a protocol

I have a general question to the interpretation of a enganglement distillation protocol. In general you have a set of entanglet qubit pairs in a Werner-state. Point of matter of this is that I can ...
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Query about the proof why non-orthogonal states cannot be reliably distinguished

I have a query regarding the proof given in the book by Nielsen and Chuang on why two non-orthogonal states cannot be perfectly distinguished. The proof is given on page 87 of the 10th edition; here ...
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Is there a unitary, linear bijection between (1) Maximally Entangled and (2) Factorizable States?

Pretty much as the title says. I am interested in the two particle system, each particle having two dimensional quantum states; naturally if there is a generalisation I'd be interested in that too. ...
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Transition rate of two level system subjected to noise

(this question is simpler than its length implies. I did this on purpose to provide a nice complete development for future readers) The setup Suppose we have a two-level quantum system with ...
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how to arrive at first-order correlation function with the above master equation?

My question arose when I was reading a paper called " Multi-photon Blockade of the dressing of the dressed states'. This is the states this paper used: This is the master equation this paper has ...
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Does the superposition principle affect the space of quantum states?

I am confused about the set of quantum states. I have seen it written that in classical physics, the set of all states is a simplex. (I think this refers to the probability simplex.) In quantum ...
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239 views

Heisenberg XXX time evolution operator for three qubits

I've a problem to reproduce the result in equation (4) on page three of this paper: http://arxiv.org/abs/0802.2588. So far I've understood that they apply a Heisenberg XXX interaction between ...
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Can a free falling observer localize the event horizon by calculations?

I'm think that in general relativity we can always pass the one curve in one coordinate system for another coordinate system. My intuition say that the free falling observer locate the event horizon ...
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Superimposed hydrogen electron states

I have been following an Edx.org course on Quantum Computing. The Prof. has started with a Hydrogen atom qubit, assuming that the electron can only be in the ground state and the first excited state. ...
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What's the Cause of Quantum Entanglement? [duplicate]

What is the cause of quantum entanglement? When two particles become entangled what property of them basically changes as to establish a link between them and how the information is exchanged between ...
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How does one devise a Grover quantum oracle despite the no-cloning theorem?

I think I have misunderstood Grover's quantum search algorithm, and would appreciate clarification. From what I understand, the Oracle operator takes an index register of qubits $|x\rangle$ (that ...
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How to write a noisy state as a separable operator

Bipartite operators close enough to the identity are separable. But how does one compute the product operator terms of the separable expansion? In particular, if $\left| \Phi \right> = m^{-1/2} ...
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Group theory and quantum optics

This is a question about application of group theory to physics. The starting point is the group $SU(n)$. I have a representation $R$ of $SU(n)$ that takes values on the unitary group on an infinite ...
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Deutsch's Algorithm. Unitary Transform $U_f$

I'm studying Deutsch's algorithm and I keep coming across the phrase along the lines of "There is a unitary transform (a sequence of quantum gates) $U_f$ that transforms the state $|x\rangle |y\rangle ...
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How does Landauer's Principle apply in quantum (and generally reversible) computing

I understand that a reversible computer does not dissipate heat through the Landauer's principle whilst running - the memory state at all times is a bijective function of the state at any other time. ...