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Questions tagged [quantum-state]

Questions about or related to quantum states. Consider using the density-matrix tag when relevant.

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How to convert states |0011⟩, |1100⟩, |0101⟩ to |1111⟩?

How can I use X gate (quantum not) to convert each of the pure states |0011⟩, |1100⟩, |0101⟩ to |1111⟩ with Qiskit? My programming assignment is Using the idea of a multi-controlled phase gate, now ...
Jettapol's user avatar
-1 votes
0 answers
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What is the meaning of $Tr(L^\dagger L\rho)-Tr(L^\dagger\rho L\rho)$?

Consider the non-Hermitian matrix $L$ and the Hermitian positive semidefinite matrix $\rho\geq0$ with $Tr(\rho)=1$. What is the physical meaning of $Tr(L^\dagger L\rho)-Tr(L^\dagger\rho L\rho)$?
Kohei's user avatar
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2 votes
1 answer
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How to apply gates on a subspace of a superposition of qubits?

Let us say that I have the state $a|00\rangle + b|01\rangle + c|10\rangle + d|11\rangle$. I wish to apply a one-qubit unitary (a $2\times2$ matrix) U on the subspace spanned by $|01\rangle$ and $|10\...
Soumyadeep sarma's user avatar
1 vote
1 answer
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How to calculate the number of m-partitions of an N-partite quantum state?

I am reading the structure of multipartite entanglement from section 3.3. It is stated there that the number of possible partitions of $N$ parties into $m$ parts is given by $\frac{m^N}{m!}$. I could ...
Anindita Sarkar's user avatar
1 vote
1 answer
236 views

Why is the Pauli Y gate eigenstate so hard to create?

In a lot of quantum computing formalism, it is relatively easy to create $\vert 0\rangle$, $\vert 1\rangle$, $\vert +\rangle$ and $\vert -\rangle$. However, it is hard to create $\vert i\rangle$. Why ...
Polp's user avatar
  • 13
2 votes
1 answer
21 views

Relation between Rz gate and Phase gate

As I know, the $Rz(\frac{\pi}{2})$ gate is equivalent to the Phase gate $S$ up to the global phase. However, I found using qiskit, the $Rz(\frac{-\pi}{2})$ is also equivalent to the Phase gate $S$. I ...
Amanli's user avatar
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2 votes
2 answers
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Can a SLOCC protocol work only in one direction?

Two states $|\psi\rangle$ and $|\phi\rangle$ are equivalent under SLOCC protocol if $|\psi\rangle$ can be converted to $|\phi\rangle$ and vice versa via LOCC with a finite probability of success. Thus ...
Anindita Sarkar's user avatar
1 vote
0 answers
51 views

Prove that convex combinations of product states admit a hidden variable model

Define product states as simple tensors $\rho_1 \otimes \rho_2$ and separable states to be (trace) norm limits of convex combinations of product states. We say that a state $\rho$ admits a hidden ...
truebaran's user avatar
  • 153
2 votes
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Uniqueness, absolutely maximally entangled states, and the 3 qutrit code

There is a well known $ [[3,1,2]]_3 $ qutrit stabilizer code with stabilizer generators $ XXX $ and $ ZZZ $. This code is related to a $ [[4,0,3]]_3 $ qutrit stabilizer state with stabilizer ...
Ian Gershon Teixeira's user avatar
1 vote
1 answer
69 views

Does measuring the operator $XX$ preserve superpositions in a given two-qubit state?

Suppose I have a state $$\vert\psi\rangle = a\left(\frac{1}{\sqrt{2}}\vert\Phi^+\rangle + \frac{1}{\sqrt{2}}\vert\Phi^-\rangle\right) + b\left(\frac{1}{\sqrt{2}}\vert\Psi^+\rangle + \frac{1}{\sqrt{2}}\...
Vladimir's user avatar
2 votes
3 answers
89 views

Is an unobserved measurement represented by a mixed state?

If I take a $\vert +\rangle$ state and measure it in the $Z$ basis but do not look at the measurement outcome, how should I describe the state? Is it just a mixed state $$\frac{1}{2}\vert 0\rangle\...
Vladimir's user avatar
2 votes
1 answer
43 views

Is there a unitary mapping every state in the upper half of the Bloch sphere to $|0\rangle$?

I am having trouble finding a way to map certain parts of the Bloch sphere to |0> and leave the rest intact. For example, let's think of a state vector $|\psi \rangle = \alpha |0 \rangle + \beta |1 ...
Honza Svoboda's user avatar
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1 answer
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How can I represent quantum states $|0\rangle$ and $|1\rangle$ in $x$ and $y$ bases?

For example, two persons choose at random whether to measure their particle in the $x$ or $y$ direction (basis). We first define $x$ and $y$ eigenstates: $|+x\rangle =\frac1{\sqrt2}(|0\rangle + |1\...
ibtissam's user avatar
2 votes
1 answer
59 views

weird negative sign in a state vector in qiskit

I run the following simple code in qiskit, which get statevector of a quantum circuit. ...
mike_gz's user avatar
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Is there any well defined notion of "the state of a qubit X" if $X$ is a member of a larger qubit system

I'm trying to understand the effect of "measurement" as a gate. But my question is more elementary than that. Consider the following simple quantum circuit: $(X,Y)$ begins in the state $1 ...
Sidharth Ghoshal's user avatar
0 votes
1 answer
32 views

Two Quantum State Density Matrices with Unequal Off-Diagonal Elements but Equal Magnitudes

I recently read Kitaev's paper on magic state distillation. I want to verify whether the circuit for the [5,1,3] encoder can map a single qubit state T_0 to the logical state T_1 in the encoded space. ...
Xiao H's user avatar
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0 votes
1 answer
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How to implement a depolarizing noise channel for qutrits using cirq?

Anyone have any idea how I can implement a depolarizing noise channel for qutrits using cirq? Say using the kraus operators within a class inheriting from cirq.Gate or so?
Son100's user avatar
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1 vote
1 answer
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Quantum circuit of stateful oracle

Suppose I have operator $U_f$ that maps state $|x\rangle|y\rangle|0\rangle$ to another state $|x\rangle|y\rangle|f(x, y)\rangle$. The function $f$ has its internal state, that changes on each ...
Georgy Firsov's user avatar
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0 answers
16 views

Quantum Channel with least disturbance for any input and output dimensions

Let $n$ and $m$ be two arbitrary dimensions of the input Hilbert space and output Hilbert space respectively. What is the quantum channel that preserves information as much as possible (i.e. with the ...
Shadumu's user avatar
  • 321
1 vote
1 answer
90 views

Matrix representation of the symmetric subspace for two copies

Consider two copies of an $n$ qubit Haar random state, given by: \begin{equation} \rho = \mathbb{E}_{U \sim \mathsf{Haar}}\left[U |0^n\rangle \langle 0^n| U^{*}\otimes U |0^n\rangle \langle 0^n| U^{*}\...
BlackHat18's user avatar
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6 votes
2 answers
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If Alice measures a qubit and doesn't tell Bob the result, what's Alice's state from Bob's perspective?

Suppose Alice has a qubit $|\phi\rangle=\alpha|0\rangle+\beta|1\rangle$ and measures it. Bob knows the initial state but not the result of her measurement. So after the measurement, Alice knows what ...
mp12853's user avatar
  • 63
2 votes
2 answers
46 views

Can save_statevector() be used on a real quantum computer?

In a real quantum computer, can the save_statevector function be used to obtain the state vector of a circuit? I attempted to run the following code on a real ...
MrEightL's user avatar
2 votes
1 answer
97 views

What are classical analogies for the notions of superposition, entanglement, and interference?

I'm working on a conceptual explanation of quantum computing properties and have used analogies to make the ideas more accessible. I'd appreciate feedback on the validity of these analogies from those ...
qwerty's user avatar
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3 votes
1 answer
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Is there a quantum circuit to distinguish between $|0 \rangle$ and $\frac{1}{\sqrt{2}} (|0 \rangle + |1 \rangle)$?

Is it possible to construct a quantum circuit, using any unitary and measurement operations, that can distinguish $|0 \rangle$ and $\frac{1}{\sqrt{2}} (|0 \rangle + |1 \rangle)$? In my estimation, the ...
Julia Kim's user avatar
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3 votes
1 answer
157 views

How to understand the idea of maximal entanglement intuitively?

I am trying to understand what it means for 2 qubits to be maximally entangled. When I look for information online or in books all I can find are rigorous mathematical definitions which I find a bit ...
Omeglac's user avatar
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2 votes
1 answer
114 views

Is $\rho = \sum_{j} p_j|n_j\rangle\langle n_j|$ a valid construction for any mixed state?

I have a mixed state $\rho$ and its hamiltonian $H$. Firstly, I find the eigenvalues $\{p_j\}$ of $\rho$, and orthonormal basis of $H$. I write $\rho$ in terms of $H$'s eigenstates and $\rho$'s ...
Việt Nguyễn's user avatar
1 vote
1 answer
135 views

How to represent unitary evolution in Python?

How to represent $U(t)$ (a unitary operator) in a code? Is there any package available for that in Python?
saaru darshini's user avatar
3 votes
1 answer
941 views

Expressing a quantum state as a polynomial

Let us consider the state $\left|\psi\right>$ obtained by applying $m$ 1- and 2-qubit gates to $n$ qubits, starting from the state $\left|0,0,\dots\right>$. Let us express it as: $$ \left|\psi\...
Doriano Brogioli's user avatar
1 vote
1 answer
53 views

What is the input when simulating a quantum state?

Currently I am simulating a quantum gate using verilog. I learned that: $$ |\psi\rangle = \alpha|0\rangle + \beta|1\rangle $$ I want to ask: when simulating, should I let alpha and beta be complex ...
Bakeu's user avatar
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1 vote
1 answer
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How cat state is constructed?

Context: On Wikipedia, a cat state (2-component) is defined as $$ |\text{cat}_+\rangle = C_+(|\alpha\rangle + |-\alpha\rangle) $$ $$ |\text{cat}_-\rangle = C_-(|\alpha\rangle - |-\alpha\rangle), $$ ...
Martin Vesely's user avatar
4 votes
2 answers
227 views

Can a non-local unitary operator preserve separability

Consider a $2$-qubit system with Hilbert space $\mathcal{H} \cong \mathcal{H}_1 \otimes \mathcal{H}_2$. A pure separable state in $\mathcal{H}$ is of the form $\lvert \psi_1 \rangle \otimes \lvert \...
Silly Goose's user avatar
19 votes
6 answers
926 views

Counterexamples in quantum information theory

As was already asked about in this phys.SE question many years ago—which, sadly, got closed and never received an answer—is there a collection of counterexamples in quantum information theory, "...
Frederik vom Ende's user avatar
1 vote
0 answers
53 views

State tomography in Qiskit on a subset of qubits of real QPU

Could anyone please explain how should I carry out a state tomography on a real device in Qiskit (version 0.43.2)? I have access to devices with 127 qubits, but I want to perform a simulation using ...
Andrea's user avatar
  • 11
1 vote
1 answer
66 views

Proability of measuing a qubit in a two qubit system without having a perpendicular basis

I am trying to understand how to apply Born's rule on two qubit systems. From class, the teacher told us that we can write the state like so: only if $\theta_0$ and $\theta_1$ are ortogonal. But now ...
Filat Nicolae's user avatar
2 votes
1 answer
60 views

To understand the notation of $| a, a \oplus b \rangle$

This must be trivial but I can't find a clear explanation of the notation of $| a, a \oplus b \rangle$. It is the resulting state after applying a CNOT gate to $|a,b\rangle$: $\rm{CNOT}|a,b\rangle = | ...
fishjojo's user avatar
3 votes
2 answers
92 views

Are measurements in $X$ and $Z$ bases being equal enough to prove equality of quantum states?

Suppose I have two single qubit states $\rho$ and $\sigma$. In my example, they are pure but I keep it general here. Suppose I know that $$\text{Tr}(\vert +\rangle\langle +\vert\rho) = \text{Tr}(\vert ...
user1936752's user avatar
  • 2,997
0 votes
0 answers
25 views

What is the role of color in color code? ( theoritically and exprimentally)

We know that the color code has an extra element relative toric code . It is color . I want to know what is the role of color ?
Mohsen's user avatar
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7 votes
2 answers
317 views

How can quantum error correction correct small rotations/continuous errors?

I'm having trouble understanding the so-called "digitization of errors" argument in QEC. Suppose I have to encode my logical qubit into $n$ physical qubits to do error correction. I will use ...
Joan's user avatar
  • 73
0 votes
1 answer
58 views

How to convert one state of a quantum system to a desired state?

I have a state of 3 qubits: The first number inside the brackets gives the probability of each state, and the second number gives the phase. $$\begin{align} |000\rangle &= (12.5,0^{°}),\\ |001\...
Root Groves's user avatar
1 vote
2 answers
64 views

How to generate the Bell state $\frac{1}{\sqrt{2}}(|01\rangle+|10\rangle)$ from the state $|00\rangle$ using Qiskit?

I want to generate the Bell state $(|01\rangle+|10\rangle)/\sqrt{2}$ from the state $|00\rangle$ in qiskit, applying the Hadamard gate followed by the $\text{CNOT}$ gate. But it generates $(|11\rangle-...
Xilot Xilot's user avatar
3 votes
1 answer
161 views

Why is the coefficient-squared the probability, and not just the coefficient itself?

Context: I have decided not to accept the postulates of quantum mechanics blindly as gospel. There must be a way someone arrived at those postulates, and I want to know the basic reasoning behind them,...
Abhay Agarwal's user avatar
0 votes
2 answers
75 views

How can I get the state of my quantum circuit like save_statevector() in qiskit 1.0.2?

Just as the title, I want to get the state of my quantum circuit when running simulation locally with fake provider. But I cannot use save_statevector since Aer has been removed from qiskit. My code ...
MrEightL's user avatar
2 votes
2 answers
74 views

How to create a qudit of any dimension $d$ in qiskit?

How to create qudit, not qubit (which is a special case of qudit with $d = 2$) in qiskit of any dimension $d$? Actually, I searched this on chatgpt, but not-so-helpful info was found. It just uses ...
sudhanshu's user avatar
2 votes
1 answer
69 views

Getting rid of extra qubits without changing phase

If I have the state $\frac{1}{\sqrt2}|0000\rangle + \frac{e^{i\phi}}{\sqrt2}|1111\rangle$ and need to get $\frac{1}{\sqrt2}|0\rangle + \frac{e^{i\phi}}{\sqrt2}|1\rangle$, does anyone have any ideas ...
bruhcobell's user avatar
4 votes
2 answers
260 views

Prove that there is no polynomial size quantum algorithm for a Simon's problem with no promise on the input

We look at the following variant of Simon's problem. There is an algorithm $A$ that solves a problem with the following settings: The input is an oracle $f:\{0,1\}^n \to [M]$. The output of the ...
Gabi G's user avatar
  • 229
2 votes
2 answers
58 views

Can Interaction with the environment cause $|0\rangle$ to evolve into a superposition like $|+\rangle$?

We say if a qubit is in state $|0\rangle$, and it is possible if it interacts with the environment it can result in a bit flip to a state $|1\rangle$, so I was wondering why can't it go to a ...
Kutubkhan Bhatiya's user avatar
4 votes
2 answers
101 views

Show that all extensions of $\rho$ can be obtained as a channel applied to its purification

I am struggling with this exercise here: Let $H:A, H_E$ and $H_{E′}$ denote complex Euclidean spaces. Consider a purification $|ψ_{AE}⟩⟨ψ_{AE}| ∈ D(H_A ⊗ H_E)$ of a quantum state $ρ_A ∈ D(H_A)$ and a ...
Pink Elephants's user avatar
1 vote
3 answers
183 views

Equivalence of quantum circuits

I have these 2 quantum circuits: Are they equivalent?I think they are but I cannot understand how this could be possible.Lets assume that the initial condition of the first circuit is:] Lets assume ...
Root Groves's user avatar
2 votes
1 answer
50 views

Existence of a two-outcome measurement $M$ such that the induced distributions differs between different density matrices

Let $\rho \neq \sigma$ be density matrices. I want to show that there exists a two-outcome measurement $M$ such that the induced distributions $M(\rho)$ and $M(\sigma)$ differ. From what I learned, ...
Gabi G's user avatar
  • 229
2 votes
0 answers
19 views

Interested in software helping with projecting multi-qubit states onto irreducible components

My interest in QC comes from a problem in geometry called the Atiyah problem on configurations of points. In short, there is a nice one-to-one correspondence between quantum states of a single qubit ...
Malkoun's user avatar
  • 178

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