# Questions tagged [quantum-information]

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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### If you measure one "share" of an entangled pair, will the resulting pair be a product state?

If you do a partial measurement on one "share" of en entangled pair, will the resulting pair no longer be entangled, i.e will be a product state?
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### Why aren't states with 3 basis vectors considered entanglements in two qubit system?

I am going to take out normalization factors for simplicity. $$|00⟩+|11⟩$$ $$|00⟩−|11⟩$$ $$|10⟩+|01⟩$$ $$|10⟩−|01⟩$$ I can see why these states are entangled but I don't see why the following states ...
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### Necessary and sufficient conditions for operator on $\mathbb C^2$ to be a density matrix

Consider a one-qubit system with Hilbert space $\mathscr H\simeq \mathbb C^2$. Define the hermitian operator $$\rho := \alpha\, \sigma_0 + \sum\limits_{i=1}^3 \beta_i\, \sigma_i \quad , \tag{1}$$ ...
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### Find coefficient for pure and mixed states

Consider a generic $2\times 2$ Hermitian matrix written as $$\rho =\alpha\sigma_0+\beta\hat{\vec n}\cdot\vec\sigma\quad ,$$ where $\hat{\vec n}$ is a unit vector and the coefficients are real numbers. ...
1 vote
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### How to prove that every mixed one-qubit state admits a Bloch-sphere representation? [duplicate]

A mixed state $\rho$ can be written as $$\rho=\frac{1}{2}\left(I+r_x\sigma_x+r_y\sigma_y+r_z\sigma_z\right)\qquad\left(\vec{r}:=\left(r_x,r_y,r_z\right)^T\in\mathbb{R}^3; ||\vec{r}||\leq 1\right)$$ ...
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### Given the Symplectic Matrix acting on phase space, find the Gaussian Unitary acting on the Hilbert space

In Gaussian Quantum Mechanics, a unitary preserving the Gaussian nature of the state is a called a Gaussian Unitary. In the phase space picture, a Gaussian state is fully characterized by its first ...
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### Filling factors and implementation for non-Abelian models

Currently reading through Pachos' Introduction to Topological Quantum Computation, and perusing other related articles and papers online. Have seen in many places that the 5/2 filling factor for ...
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### Are most reals fake? Does it make a difference?

There are uncountably many reals. However, there are only countably many definable numbers. Thus, almost all reals are undefinable. Undefinable means that the shortest representation of that number ...
1 vote
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### Qubit system coupled to a bath of quantum harmonic oscillators

It is well known that when we consider a probe harmonic oscillators (called system) that is coupled to a reservoir of N harmonic oscillators, i.e. the Hamiltonian is written as the following, the ...
1 vote
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### Repeating observations in quantum theory

Suppose we prepare a state $\psi$ in a quantum system, represented in some Hilbert space, and suppose $A$ is an observable represented by the matrix $A$ (which possibly has infinite order). QUESTION A ...
1 vote
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### Lower bound on the spectral gap in finite size critical systems with locality

Local quantum systems tuned to criticality are gapless in the thermodynamic limit. The rate at which the ground state spectral gap approaches zero as the system size $L \rightarrow \infty$ carries ...
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### How to compute the Schmidt decomposition of a bipartite pure state?

I'm trying to work out the entropy of entanglement of my state but I'm struggling to put it into a Schmidt decomposition, i.e. in the form: $\sum_i \alpha_i |u_i \rangle |v_i \rangle$. Currently I ...
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### Quantum walk: transition matrix, negative or positive sign in the exponent?

Why is it that in some papers the transition matrix of a continuous-time quantum walk is defined as $\exp(itH)$ and in other papers as $\exp(-itH)$?
1 vote
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### Why is the density matrix of a system has this block form?

In Ficek's paper (http://zon8.physd.amu.edu.pl/~tanas/spis_pub/pdf/04-joptb-S90.pdf), the density matrix of a two two-level atom system has a block form like this. Why does it make sense to assume ...
1 vote
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### Order parameters in topologically ordered systems

Topologically ordered phases are characterized by a non-vanishing ground-state expectation value of a non-local operator. These operators are supported on sites whose number grows with the system size....
1 vote
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### Analog of the Pauli vector for $SU(4)$

In quantum mechanics and representation theory, it is well known that the Pauli matrices transform as a vector due to the special relationship between $SU(2)$ and $SO(3)$. For example, suppose we have ...
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### Boundary condition of dyadic Green’s function for planarly layered media

The dyadic Green’s function of free space in terms of orthonormal system for TE/TM polarized waves is: where, now by applying boundary conditions to the first equation, the dyadic Green’s function ...
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### Question about the energy levels of Rubidium atom - how to understand this energy level diagram?

But today when I try to read some papers working with Alkaline atom, I couldn't figure out how they plot the Rubidium energy level. From my undergraduate study, I thought the diagram of Rubidium atom ...
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### Finding the Kraus Operators of a Quantum Channel from its Choi Matrix

TLDR : What is the form of the projector I need to use to attain a 2X1 vector from $P_i v_k$ with which I can build my Kraus Operator? I am calculating the Kraus Operators for a Quantum Channel ...
161 views

### Examples of quantum systems modelled with Type II von Neumann algebras

What are the examples of quantum systems that should be modelled with a Type $II_1$ or $II_\infty$ von Neumann algebra? I am pretty much a novice at von Neumann algebra, so I have hard time finding ...
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### How to test if a bipartite density matrix violates Bell's inequality?

For a given density matrix $$\rho = \sum_{ijkl=0}^1 r_{ijkl} |i,j\rangle \langle k,l|$$ describing a bipartite two-qubit system, how can I prove for what values $r_{ij}$ the density matrix violates ...
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### Quantum Computer - Rotation Bloch Sphere [closed]

please can anyone help? What gate combination allows moving from the state between |0> and |1> states. In terms of bloch-sphere from the north pole to the south pole as an example. And how can ...
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1 vote
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### Resources for studying quantum metrology

I want to learn about quantum metrology topics like von-Neumann hamiltonian, ABL rule etc., typical case studies of interpretation of measurement, quantum contextuality etc., discussion on what is ...
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1 vote
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### Is there a limit of size for superpositions?

Can objects be always in superposition if there were no environment for decoherence to occur.
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### On the Bell's Theorem / Bell-type Inequalities and the Kochen-Specker Theorem

It appears to me that the Kochen-Specker theorem, if not Gleason’s theorem already, seals the fate of realism / value definiteness (with possibly the additional assumption of non-contextuality, ...
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### Expectation value of $\mathrm{SU(1, 1)}$ parity operator

The $\mathrm{su(1, 1)}$ Lie algebra is spanned by the generators $K_+$, $K_−$ and $K_0$, which satisfy the commutation relations: $$[K_0, K_{±}] = ±K_{±}, [K_−, K_+] = 2K_0.$$ We can define the ...
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### The derivation of the quantum information no-hiding theorem, question 1

I am reading Samuel L. Braunstein, Arun K. Pati, Quantum information cannot be completely hidden in correlations: implications for the black-hole information paradox. I am puzzling over the derivation ...
1 vote
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### Algorithm that checks if a subspace of states contains a product state

Suppose I have two identical qudits, the full Hilbert space is $\mathcal{H}=(\mathbb{C}^{d})^{\otimes 2}$. Say I'm given a supspace of states $\Lambda\subset \mathcal{H}$. What is the fastest ...
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### Higher derivatives of the log-partition function?

I need higher derivatives of the log-partition function $Z(z)=\log \sum_i \exp(z_i)$, has anyone derived the formula? Looking at concrete values of derivatives up to order 8, evaluated at $z=(1,1,1)$ ...
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### Does a subsystem being mixed imply the state is entangled?

If a pure state, $\rho_{AB}$, has subsystems described by mixed density matrices, the overall state is entangled (as far as I understand). Can you conclude the same with an initially mixed bipartite ...
1 vote
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### Concurrence between 2 qubits of tripartite system

If we consider a tripartite system (say of 3 qubits) described by density matrix $\rho_{ABC}$, does the concurrence $C(\rho_{BC})$ still accurately measure the entanglement between subsystems B and C? ...
1 vote
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### Coupled systems and quantum configuration space?

I was watching this PBS Spacetime video. He mentions that quantum particles / wavefunctions (he uses electrons as his example) all have their own set of separate 3D coordinates in a coupled system. ...
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Consider a bipartite system composed of subsystems $A$ and $B$, with corresponding Hilbert spaces $\mathcal{H}_A$ and $\mathcal{H}_B$, spanned by $\{\chi_1,...,\chi_n\}$ and $\{\phi_1,...,\phi_m\}$, ...
Bosonic Case In a bosonic QFT, the Hilbert space associated to a surface $\Sigma$ is the appropriate space of wavefunctionals on $\Sigma$. Hence, if $\Sigma=\Sigma_1 \sqcup \Sigma_2$, we find that the ...