Questions tagged [quantum-state]

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

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Almost perfect quantum encryption of a mixed state using only $n + O(log(n) +log(\frac{1}{\epsilon}))$ shared bits

Alice holds a state $\psi$ of $n$-qubits, and wants to send it to Bob using a single quantum message. Bob and Alice share only $n + O(log(n) +log(\frac{1}{\epsilon}))$ random bits, for some value $\...
Gabi G's user avatar
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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
84 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 ...
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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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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
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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
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2 answers
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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
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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
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2 answers
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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
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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
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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
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2 answers
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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. The input is an oracle $f:\{0,1\}^n \to [M]$. The output of the algorithm: if there exists $s \in \{0,1\}^n$ such that for every $x,y \in \{0,1\}^n$...
Gabi G's user avatar
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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
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2 answers
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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
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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
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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
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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
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Efficient computation of probabilities for an N-particle state

Suppose we have a state that is written as: \begin{eqnarray} |\Psi\rangle=\frac{1}{\mathcal{N}}\sum_{\mathcal{P}}e^{i\phi_p}\phi_{1p}(x_{1p})\phi_{2p}(x_{2p})...\phi_{N_p}(x_{N_p})|x_{1p}...x_{Np}\...
Zarathustra's user avatar
2 votes
1 answer
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What is the difference between symmetric states and geometrically uniform states?

On the one hand, in this article, symmetric states are defined as: The $M$ symmetric quantum states which should be distinguished by means of the quantum measurement are described by statistical ...
yosh's user avatar
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1 vote
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State amplification in Grover when starting with W state

I have two 3-qubit registers, each one is prepared in $W$ state, so my two registers are in state: $$\left|W_3\right\rangle\otimes \left|W_3\right\rangle \ ,$$I use this (6-qubits) diffusion operator ...
user12910's user avatar
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Is $|A\rangle = \frac{1}{\sqrt2} |00\rangle + \frac{1}{\sqrt2} |01\rangle$ a valid quantum state?

Is $|A\rangle = \frac{1}{\sqrt2} |00\rangle + \frac{1}{\sqrt2} |01\rangle$ a valid quantum state? Or does a quantum state need to be a superposition of the entire basis, i.e., $$ |A\rangle = \frac{1}{...
user29495's user avatar
1 vote
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How to obtain this measurment result for arbitrary qubits in $X$ basis?

I have seen the following claim. Suppose one has two qubits $\vert\psi\rangle = a\vert 0\rangle + b\vert 1\rangle$ and $\vert\phi\rangle =a'\vert 0\rangle + b'\vert 1\rangle$ and both are measured in ...
Lorraine's user avatar
3 votes
2 answers
237 views

Is it always possible to write the state corresponding to a set of stabilizer generators?

Given a set of stabilizer generators, is it always possible to write down the state corresponding to it? Is there a way to write down the quantum state corresponding to a stabilizer generator?
Dotman's user avatar
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How can I shift elements around in my state vector according to a specific pattern?

Consider the statevector $|\psi_1\rangle=(a_0,...,a_{N-1})^T$. My goal is to shift the elements around to end up with $|\psi_2\rangle=(a_{3N/4},...,a_{N-1},a_0,...a_{N/2},\vec{\phi})^T$ where $\vec{\...
thespaceman's user avatar
1 vote
2 answers
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How to use get_statevector in Qiskit SDK 1.0?

I am Using Qiskit SDK 1.0. I have a problem with get_statevector in qiskit SDK 1.0 and using BasicSimulator. My code is attached ...
Naeem Ullah's user avatar
1 vote
1 answer
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Projective measurement notation

I don't understand how projective measurements work; I think my confusion comes from the notation. How would this be written in matrix notation? Is it just [w row vector] [Ma matrix] [w column vector]^...
researcher101's user avatar
1 vote
1 answer
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On difference in the number of two-qubit stabilizer states that are separable (36) vs those that are maximally entangled (24) and partial entanglement

We have a set of two-qubit stabilizer states. There are 60 of them: 36 separable and 24 maximally entangled (MES). I was wondering whether we can somehow compare the size of the set of partially ...
Sutasu's user avatar
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CCTShift(1) gate for qutrits

What is the matrix for the CCTShift(1) gate? It has to be a $(27 \times 27)$ matrix. Suppose we have two control qutrits and a single target qutrit. If one control qutrit is found in state $|2\rangle$ ...
Root Groves's user avatar
1 vote
1 answer
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Is there a proof that any pure two-qubit Partially entangled state lies somewhere in between a separable and maximally entangled state?

Intuitively this seems true, but is there a proof of the following: We have two-qubit pure state. Given a Partially entangled state (PES) $|P\rangle$ we can always find a separable state $|S\rangle$, ...
Sutasu's user avatar
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0 answers
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Entanglement generation for commuting Hamiltonian

Consider an $n$ qubit Hamiltonian $H$ given by \begin{equation} H = \sum_{i=1}^{m} H_i, \end{equation} where each $H_i$ is a $k$-local term and it holds that \begin{equation} e^{H} = e^{H_m} \cdot e^{...
BlackHat18's user avatar
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-1 votes
1 answer
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How to calculate a density matrix of a given circuit?

I want to find the density matrix of the following quantum circuit, is it correct: [[0.12499999+0.j 0.12499999+0.j 0.12499999+0.j 0.12499999+0.j 0.12499999+0.j 0.12499999+0.j 0.12499999+0.j 0....
Frank Hansen's user avatar
3 votes
1 answer
80 views

A separable pure bipartite quantum state must be a product state

I'm looking for the simple argument to prove that a separable pure bipartite quantum state is in fact a product state. This question comes from a statement in Wikipedia on separable states: In the ...
JMark's user avatar
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0 answers
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Where is my mistake in using a measurement operator instead of Born’s rule to calculate the probability of detecting photons at an arbitrary angle?

As I asked in this question: How can I calculate the measuring probabilities of a two qubit state along a certain axis? From here I know how to calculate the probability of measuring a general state ...
Alex1111's user avatar
-3 votes
1 answer
69 views

How would you name the gate which maps $|x\rangle\rightarrow |(x+1)\text{mod}\hspace{1mm}n\rangle$

Suppose you have a qudit with $n$ decoherent states. How would you name the gate which maps $|x\rangle\rightarrow |(x+1)\text{mod}\hspace{1mm}n\rangle$
Root Groves's user avatar
1 vote
0 answers
38 views

Turn expectation values back into classical data

How are expectation values turned back into classical data for evaluation? I have a circuit performing a regression task that returns the expectation value of the Pauli Z operator. I would like to ...
camaya's user avatar
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4 votes
1 answer
191 views

Why do we have an infinite number of possible quantum gates?

This question came to me during an online lecture by Prof. Nike Dattani, he mentioned that we have "an unlimited number of quantum gates". Simply my question is: why do we have an unlimited ...
JaafarMehrez's user avatar
2 votes
0 answers
23 views

Implement Phase disk in Qiskit

I'm new to qiskit and looking to enhance my output with visualization. Specifically, I'm interested in using the Phase Disk visualization, similar to the one shown in the image below. Can anyone ...
Milen Ninan's user avatar
2 votes
1 answer
30 views

How is the expression $\frac{\|\rho^{T_B}\|-1}{2}$ obtained from the definition of negativity?

In quantum information theory, negativity is defined as summation of the absolute values of negative eigenvalues of the partial transposed density matrix. The expression of negativity is given as $$ \...
Anindita Sarkar's user avatar
2 votes
2 answers
218 views

What is the relation between the purity of a bipartite state and its subsystems?

I know for a separable state $\rho_{AB}$ we have $$P_{AB}= P_{A}=P_{B}=1$$ Where P is purity. What if the relation between the purities when the bipartite state is entangled? Is there any inequality ...
reza's user avatar
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2 votes
1 answer
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Quantum Information Retrieval from Bipartite Mixed States under LOCC: Maximizing Individual State Knowledge

In the context of Local Operations and Classical Communication (LOCC), given a bipartite mixed state represented as $\rho=\frac{1}{n}\sum_{i=1}^n|\psi_i\rangle\langle\psi_i|$, where $|\psi_i\rangle$ ...
Pratapaditya Bej's user avatar
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0 answers
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How to calculate the state vector of a circuit using sampler().run()

I run a circuit using: jobCircuit = Sampler(backend).run(circuit) resultCircuit = jobCircuit.result() How can I access to a state vector of the circuit? I tried ...
alejandra's user avatar
2 votes
1 answer
149 views

Qiskit Runtime forbids reset gate?

Some parts of my quantum circuit uses initialize to prepare specific amplitudes to the qubits. However, the Qiskit Runtime outputs error: ...
Deren  Liu's user avatar
2 votes
2 answers
93 views

How to create the state $(n!)^{-\frac{1}{2}} \sum_{\pi \in S_n} | \pi, \pi (G) \rangle$ when $G$ is an undirected graph and $\pi$ a permutation

Let $G=([n],E)$ be an undirected graph, which is represented by a $n \choose 2$ bit string, by indicating for each $i < j$ if $(i,j) \in E$. We also denote the state $| G \rangle$ as the $n \choose ...
Gabi G's user avatar
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2 votes
1 answer
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Is it possible to modify the QFT circuit to use only 1-qubit gates?

[Measured Quantum Fourier Transform] I've recently learned the Quantum Fourier Transform, and was shown its circuit. The circuit I've seen is composed of Hadamard gates and controlled Rotation gates. ...
Gabi G's user avatar
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1 vote
1 answer
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Pennylane and Qutrit quantum circuit matrix representation bug

I want to find the operator that describes this qutrit quantum circuit. Where a TSub, some TRZ rotations and a TAdd are applied to 2 quitrits. I am using Pennylane 0.34.0. This is the code: ...
Daniele Trisciani's user avatar
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0 answers
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Pseudo telepathy with 3 people that share the state $\frac{1}{2}(|000\rangle -|011\rangle-|101\rangle-|110\rangle)$

The problem is similar to the pseudo-telepathy where Alice, Bob and Charlie are given bits $a,b,c \in \{0,1\}$ such that $a \oplus b \oplus c=0$, and their goal is to output the bits $A,B,C$ without ...
Gabi G's user avatar
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2 votes
1 answer
110 views

Hilbert space of n qubits always has a decoherence free subspace if n is even?

I've heard that a subspace of an $ n $ qubit Hilbert space is called decoherence-free if it is not affected by errors of the form $ g^{\otimes n} $ where $ g \in SU(2) $. Let $ \textbf{2} $ denote the ...
Ian Gershon Teixeira's user avatar
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0 answers
9 views

Transform QLSTM model output expectation values back into classical data

What is the typical procedure for transforming a model's expvals back into the classical data format? I'm new to QML and need some insight. I have some expvals that were the output of model i.e. ...
camaya's user avatar
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1 vote
1 answer
70 views

How to figure out the action of a circuit form its effect on logical operators?

I am looking at the following circuit from "The Heisenberg Representation of Quantum Computers" by Daniel Gottesman. I understand how the circuit acts on the logical operators. I understand ...
am567's user avatar
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5 votes
5 answers
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Evolution of a state vector: Why is the action of $N$ equivalent to the action of $UNU^{†}$?

There is another question asked on this on stack exchange but I did not find any answers there that fully answered the question. In Gottesman's paper "The Heisenberg Representation of Quantum ...
am567's user avatar
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