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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Is boson sampling a problem in 'continuous variable' quantum information?

When people generally speak of quantum information in the context of continuous variables, what is generally meant is that observables, like position/momentum or the field quadratures of quantum ...
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Double slit experiment and entanglement

Just wondering, what would happen in this experiment. In the experiment you would first have two entangled particles. Then you fire one of the particles, lets say "Particle A", at a double slit ...
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CNOT gate broken in 2 different quantum simulators? Or am I wrong?

My understanding is that the control qubit in a controlled-not gate remains unchanged after the controlled-not operation is performed on a target-qubit (so the Pauli-X gate is performed only on the ...
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Mapping a given density matrix to the generalized 2-qubit state

The generalized 2-qubit state is given as: $$ \rho = \frac{1}{4}[ I\otimes I + (m_x\sigma_x + m_y\sigma_y + m_z\sigma_z)\otimes I + I \otimes (n_x\sigma_x + n_y\sigma_y + n_z\sigma_z) + ...
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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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Calculating states of entangled and disentangled qubits

I'm writing a quantum computer simulator (about 8 qubits) and I know most of the basics (i.e. how to calculate the effect of a quantum gate on a qubit). But I have hit a wall. Is it possible, with ...
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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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Natural units of information

In physics entropy is usually measured in nats. I wonder is there a possible model of a physical system which has entropy of discrete number of nats? How particles and degrees of freedom should be ...
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What does “decompositions of a mixed state” mean?

I came across an expression for Entanglement of formation for a mixed state $$E_F(\rho_{AB}) = \text{min}\sum_i p_i S(\rho^i_B)\leq S(\rho_B)$$ where minimum is taken over all the decompositions of ...
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on quantum steering

I have become interested in quantum steering after listening a talk and tried to read more about it. I think I am more confused now. My understanding is as follows: Sharing a (entangled) state, ...
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Quantum Eraser under Lorentz Boost

Suppose I am conducting the Quantum Eraser experiment. The results of this experiment are easy to understand with the traditional quantum mechanical interpretation of a pair of entangled photons. ...
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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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How can a qubit superposition state be written to a quantum register?

If a 3 qubit register can simultaneously store all 8 possible values in superposition, then how it is achieved to write 8 values in to the register? And How these 8 values can be processed parallel to ...
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Solving Systems of Partial Trace Equations

Say I specify a quantum state - pure or mixed - by its partial traces on various subsystems. To what degree could one recover the original state, and what are the known methods for doing so? For ...
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Infinite possibilities of you

"The question you are asking appears to be subjective, and is likely to be closed." Challenge . . . ACCEPTED. Okay, here it is. A friend prone to uplifting aphorisms posted on Facebook: "You Are An ...
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Does quantum collapse involve a loss of information? Does it require energy as suggested by the Landauer Limit?

I read in the context of quantum computing or of the minimal energy required for computation that there has to be a minimum possible amount of energy required to change one bit of information, called ...
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A (mundane) CS analogy for quantum teleportation

From my limited understanding of quantum entanglement, it seems like qubits act the same way as pseudo-random-number-generators (except as far as we can tell, these ones really are random). When you ...
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Are coherent states of light 'classical' or 'quantum'?

Coherent states of light, defined as $$|\alpha\rangle=e^{-\frac{|\alpha|^2}{2}}\sum_{n=0}^\infty \frac{\alpha^n}{n!}|n\rangle$$ for a given complex number $\alpha$ and where $|n\rangle$ is a Fock ...
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Super-dense coding protocol with a key

I have this assignment: Show that super-dense coding protocol with the key in the state $\frac{|00⟩⟨00|+|11⟩⟨11|}{2}$ is equivalent (in a sense of transmission rate and security) with ...
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How does a vacancy become mobile during annealing?

The Nitrogen Vacancy (NV) centre is a defect in diamond consisting of a substitutional nitrogen atom accompanied by a vacant nearest-neighbour lattice site. Substitutional nitrogen impurities are ...
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Approaches to Fault tolerant quantum computation

What are the various approaches to fault tolerant quantum computation ? Two examples are 1. topological quantum computation which uses topological phases in quantum states (2-Dimensional for ...
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Can a quantum state with infinite variance of photon number be found in nature or artificially created?

Suppose we have a quantum state $\rho$ and let's denote the photon number operator $\hat{n}=\hat{a}^\dagger\hat{a}$ where $\hat{a}$ is the annihilation operator. Let mean photon number ...
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Smallest number of quantum gates to simulate other gates?

What is the smallest number of Fredkin gates needed to simulate a Toffoli gate? What is the smallest number of Toffoli gates needed to simulate a Fredkin gate? Where the Toffoli's gate is the CCNOT ...
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Explanation for the power of quantum computers

I have seen various explanations for the power of quantum computers: Quantum computers perform operations in parallel universes Quantum computers can use quantum tunneling to reach a global extremum ...
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Discord for partially decohered bell state

To illustrate discord and its use, Zurek in his paper on discord (NB pdf) gives example of a partially decohered bell state i.e. $$\rho_{AB}=\frac{1}{2}(|00\rangle\langle 00|+|11\rangle\langle 11|) + ...
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Continous and Discrete basis, Multiplication of Density Matrix and Hamiltonian

Suppose I have a wave function $\psi(x)$ in position basis. I can make a density function by simply multiplying $\psi(x)$ and its conjugate $\psi^*(x)$. If I operate the density matrix ...
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Is there a formalism for talking about diagonality/commutativity of operators with respect to an overcomplete basis?

Consider a density matrix of a free particle in non-relativistic quantum mechanics. Nice, quasi-classical particles will be well-approximated by a wavepacket or a mixture of wavepackets. The ...
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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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Classical Information carrying capacity of two states

What classical information is carried by $\alpha|0\rangle+\beta|1\rangle$ and $\alpha|00\rangle+\beta|11\rangle$? How to quantify it? To be specific, A GHZ state, $\frac{1}{\sqrt ...
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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. ...
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Usage example of stabilizer codes QEC

This question directly follows the previous one about $X$ stabilizers and phase-flip errors: Practical example of stabilizer codes Let's now consider a second part of the quantum circuit that is ...
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Which model of computation can be viewed as being extended by the currently most relevant models of quantum computation?

Which model of quantum computation resembles most closely the attempts of implementation currently being made? And which non-quantum model of computation is the conceptually closest one to the above ...
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Adiabatic evolution for initial Hamiltonian on Hadamard basis and problem Hamiltonian as diagonal

This is spawned from a comment at the answer to one of my previous questions. Someone suggested to me that claiming the following statement might be NP-hard. Could anyone please help me to figure out ...
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Practical example of stabilizer codes

Given the Steane code $$ \left|0\right\rangle_L \equiv \frac{1}{\sqrt{8}}(\left|0000000\right\rangle + \left|1010101\right\rangle + \left|0110011\right\rangle + \left|1100110\right\rangle + ...
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Confusion about a lemma on the time constraint of an adiabatic evolution (arXiv:quant-ph/0604077)

I am going through the paper Quantum adiabatic evolutions that can't be used to design efficient algorithms by Zhaohui Wei and Mingsheng Ying. On the second page they prove a lemma. The statement goes ...
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Can I usefully interpret a non-unital completely positive (CP) map as a cooling process?

Non-unital completely positive (CP) maps take a maximally mixed quantum state (aka a normalized identity matrix aka an infinite temperature state) and map it to something else. This necessarily ...
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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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Theoretical or experimental violations of the 2nd Law of Thermodynamics? [closed]

Theoretical challenges to the 2nd Law? What are some the theoretical challenges to the 2nd Law? (cf. Čápek, Vladislav, and Daniel P. Sheehan. Challenges to the Second Law of Thermodynamics: Theory ...
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Purposes of QEC stabilizers

I am going through the idea of stabilizer formalism. Defined what is a Pauli group $P_n$ and its properties, we describe a stabilizer set $S$ as: $$S\subset P_n$$ The stabilizer set establishes ...
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Question on quantum computation, entanglement and speed of information propagation

Imagine a following thought experiment. Suppose we have a large amount of entangled particle pairs, several million or billion. Now suppose there are two observers, each carrying one member of ...
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How to obtain stabilizer's generators of a QEC code

The theory of QEC with stabilizer codes defines an alternative way to represent a quantum state in terms of operators. To understand better what I am concerning about, let's consider the 7-qubit ...
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How is quantum superposition different from mixed state?

According to Wikipedia, if a system has $50\%$ chance to be in state $\left|\psi_1\right>$ and $50\%$ to be in state $\left|\psi_2\right>$, then this is a mixed state. Now consider state ...
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Can entanglement with an inaccessible system be useful?

Quantum phenomena in bipartite pure state systems like teleportation are pretty well understood. What I'm interested in is the following situation: Alice, Bob and Charlie hold some general tripartite ...
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Why is Quantum Teleportation important in Cryptography?

I think the physical principle is that (Wikipedia): For every qubit teleported, Alice needs to send Bob two classical bits of information. These two classical bits do not carry complete ...
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Entropy inequality

Assume that you have two bipartite systems $\rho_1^{AB},\rho_2^{AB}$ then I would like to prove the following: $$S(\frac{1}{2}( ...
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Is there a known generalization of the Schmidt decomposition based on a maximal set of “locally recorded branches”?

I came across an unusual multi-partite generalization of the Schmidt decomposition in my work, which I describe below. Usually, when people say "a multi-partite Schmidt decomposition", they mean a ...
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When is an operator subspace the span of Kraus operators?

Let $A$ and $B$ be finite dimensional Hilbert spaces, and let $\mathcal{L}(A \to B)$ be the space of linear operators from $A$ to $B$. Say that a subspace $K \subseteq \mathcal{L}(A \to B)$ is a span ...
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process matrix - physical interpretation

I have a (probably) advanced question, concerning quantum process tomography. Let's say I have made a measurement with a single qubit, and calculated a $\chi$-matrix which looks like ...
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Local decoherence and entropy

Consider a quantum system consisting of two subsystems, $A$ and $B$. Let $\rho$ be the density matrix of the whole system $A\cup B$. Let $|\alpha\rangle$, $\alpha = 1,2\cdots d_B$, be the states of ...
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Is there any problem a quantum finite state machine can do faster than a classical finite state machine?

All of the quantum algorithms I've seen so far require a turing-complete quantum computer, at least as far as I can tell. Are there any quantum algorithms that require only a quantum finite automaton? ...