Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels
Open accessAbstract
An unknown quantum state \ensuremath{\Vert}\ensuremath{\varphi}〉 can be disassembled into, then later reconstructed from, purely classical information and purely nonclassical Einstein-Podolsky-Rosen (EPR) correlations. To do so the sender, ``Alice,'' and the receiver, ``Bob,'' must prearrange the sharing of an EPR-correlated pair of particles. Alice makes a joint measurement on her EPR particle and the unknown quantum system, and sends Bob the classical result of this measurement. Knowing this, Bob can convert the state of his EPR particle into an exact replica of the unknown state \ensuremath{\Vert}\ensuremath{\varphi}〉 which Alice destroyed.
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- Findingnone given
An unknown quantum state can be disassembled into, then later reconstructed from, purely classical information and purely nonclassical EPR correlations.
“An unknown quantum state ]P) can be disassembled into, then later reconstructed from, purely classical information and purely nonclassical Einstein-Podolsky-Rosen (EPR) correlations.”
Quote in the paperSubstantial claim - Findingreasoning
After Alice's measurement, Bob's particle 3 is projected into one of four pure states according to the measurement outcome.
“Furthermore, after Alice s measurement, Bob's particle 3 will have been projected into one of the four pure states superposed in Eq. ( 5), according to the measurement outcome.”
Quote in the paperSubstantial claim - Findingreasoning
Each possible resultant state for Bob's EPR particle is related in a simple way to the original state Alice sought to teleport.
“Each of these possible resultant states for Bob's EPR particle is related in a simple way to the original state IP) which Alice sought to teleport.”
Quote in the paperSubstantial claim - Findingreasoning
An accurate teleportation can be achieved in all cases by Alice telling Bob the classical outcome of her measurement, after which Bob applies the required rotation to transform the state of his particle into a replica of the original state.
“Thus an accurate teleportation can be achieved in all cases by having Alice tell Bob the classical outcome of her mea- surement, after which Bob applies the required rotation to transform the state of his particle into a replica of IP).”
Quote in the paperSubstantial claim - Findingreasoning
Regardless of the unknown state, the four measurement outcomes in the Bell-basis measurement are equally likely, each occurring with probability 1/4.
“It follows that, regardless of the unknown state I/i), the four measurement outcomes are equally likely, each occurring with probability 1/4.”
Quote in the paperSubstantial claim
- Findingreasoning
In the three other measurement outcomes, Bob must apply one of the unitary operators corresponding to 180-degree rotations around the z, x, and y axes to convert his EPR particle into a replica of Alice's original state.
“In the three other cases, Bob must apply one of the unitary operators in Eq. ( 6), corresponding, respectively, to 180' rotations around the z, x, and y axes, in order to”
Quote in the paperSubstantial claim - Findingreasoning
Knowing the classical result, Bob can convert the state of his EPR particle into an exact replica of the unknown state which Alice destroyed.
“Knowing this, Bob can convert the state of his EPR particle into an exact replica of the unknown state ]P) which Alice destroyed.”
Quote in the paperSubstantial claim - Findingreasoning
Having received the two transmissions, Bob can construct an accurate replica of the unknown state.
“Having received these two transmissions, Bob can construct an accurate replica of IP).”
Quote in the paperSubstantial claim - Findingreasoning
Teleportation of the unknown state from Alice to Bob has the side effect of producing two bits of random classical information, uncorrelated to the unknown state, which are left behind at the end of the process.
“The teleportation of lg) from Alice to Bob has the side effect of producing two bits of random classical information, uncorrelated to lg), which are left behind at the end of the process.”
Quote in the paperSubstantial claim - Findingreasoning
If Alice's original particle 1 is part of an EPR singlet with another particle 0 far away, then after teleportation particles 0 and 3 would be left in a singlet state, even though they had originally belonged to separate EPR pairs.
“Then, after teleportation, particles 0 and 3 would be left in a singlet state, even though they had originally belonged to separate EPR pairs.”
Quote in the paperSubstantial claim - Findingreasoning
After Alice's measurement, Bob's particle 3 will be related to the original state by four fixed unitary operations if and only if the state of particles 2 and 3 has the specified form.
“It can readily be seen that after Alice's measurement, Bob's particle 3 will be related to IP&) by four fixed unitary operations if and only if IT23) has the form”
Quote in the paperSubstantial claim - Findingreasoning
For any unknown state, this guessed reconstruction is a maximally mixed state, giving no information about the input state.
“For any lg), this is a maximally mixed state, giving no information about the input state IP).”
Quote in the paperSubstantial claim - Interpretationnone given
EPR correlations can assist in teleportation of an intact quantum state from one place to another, by a sender who knows neither the state to be teleported nor the location of the intended receiver.
“Here, we show that EPR correlations can nevertheless assist in the”
Quote in the paperSubstantial claim - Interpretationnone given
Alice can divide the full information encoded in the unknown state into two parts, one purely classical and the other purely nonclassical, and send them to Bob through two different channels.
“Below, we show how Alice can divide the full information encoded in I&/) into two parts, one purely classical and the other purely non- classical, and send them to Bob through two diferent channels.”
Quote in the paperSubstantial claim - Interpretationreasoning
Alice's original unknown state is destroyed in the teleportation process, as required by the no-cloning theorem.
“Of course Alice's original IP) is destroyed in the process, as it must be to obey the no-cloning theorem.”
Quote in the paperSubstantial claim - Interpretationreasoning
Teleportation cannot take place instantaneously or over a spacelike interval, because it requires sending a classical message from Alice to Bob.
“In particular, it cannot take place instantaneously or over a spacelike in- terval, because it requires, among other things, sending a classical message from Alice to Bob.”
Quote in the paperSubstantial claim - Interpretationnone given
To teleport an unknown quantum state, Alice and Bob must prearrange the sharing of an EPR-correlated pair of particles.
“To do so the sender,”
Quote in the paperSubstantial claim - Interpretationreasoning
Any direct product state of particles 2 and 3 is useless as the nonclassical channel, because for such states manipulation of particle 2 has no effect on what can be predicted about particle 3.
“Clearly any direct prod- uct state of particles 2 and 3 is useless, because for such states manipulation of particle 2 has no effect on what can be predicted about particle 3.”
Quote in the paperSubstantial claim - Interpretationnone given
The result of Alice's measurement is purely classical information, which can be transmitted, copied, and stored at will in any suitable physical medium.
“Unlike the quantum correlation of Bob's EPR particle 3 to Alice's particle 2, the result of Alice's measurement is purely classical information, which can be transmit- ted, copied, and stored at will in any suitable physical medium.”
Quote in the paperSubstantial claim - Interpretationreasoning
A full two bits of classical channel capacity are necessary for accurate teleportation of a two-state particle.
“Later we show that a full two bits of classical channel capacity are neces- sary.”
- Also stated in: § Abstract · plain
“therefore reliable teleportation of a two-state particle cannot be achieved with a classical channel of less than two bits of capacity.”
Quote in the paperSubstantial claim - Also stated in: § Abstract · plain
- Interpretationreasoning
The classical message plays an essential role in teleportation.
“The classical message plays an essential role in telepor- tation.”
Quote in the paperSubstantial claim - Interpretationreasoning
Teleportation and 4-way coding can be seen as variations on the same underlying process.
“Teleportation and 4-way coding can be seen as variations on the same un- derlying process, illustrated by the spacetime diagrams in Fig. 1.”
Quote in the paperSubstantial claim - Interpretationreasoning
Since teleportation is a linear operation applied to the quantum state, it will work not only with pure states, but also with mixed or entangled states.
“Since teleportation is a linear operation applied to the quantum state IP), it will work not only with pure states, but also with mixed or entangled states.”
Quote in the paperSubstantial claim - Interpretationreasoning
Alice could then teleport quantum states to Bob over arbitrarily great distances, without worrying about the effects of attenuation and noise on a single photon sent through a long optical fiber.
“Alice could then teleport quantum states to Bob over arbitrarily great distances, without worrying about the eEects of attenuation and noise on, say, a single photon sent through a long op- tical Aber.”
Quote in the paperSubstantial claim - Interpretationreasoning
Reliable teleportation of an N-state particle requires a classical channel of 2 log2 N bits capacity.
“By the same argument, reliable teleportation of an ¹tateparticle requires a classical channel of 21og~ (AI') bits capacity.”
Quote in the paperSubstantial claim - Interpretationreasoning
It could not be otherwise, because any correlation between the input and the guessed output could be used to send a superluminal signal.
“It could not be otherwise, be- cause any correlation between the input and the guessed output could be used to send a superluminal signal.”
Quote in the paperSubstantial claim - Interpretationcitation
Alice and Bob would only need a stockpile of EPR pairs and a channel capable of carrying robust classical messages to teleport quantum states.
“Alice and Bob would only need a stockpile of EPR pairs (whose reliability can be tested by violations of Bell's inequality [7]) and a channel capable of carry- ing robust classical messages.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [7] 7. J. S. Bell, Physics (Long Island City, N. Y. ) 1, 195 (1964);
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Interpretationreasoning
Accurate teleportation using a classical channel of any lesser capacity would allow Bob to send superluminal messages through the teleported particle, by guessing the classical message before it arrived.
“Accurate teleportation using a classical channel of any lesser capacity would allow Bob to send superlumi- nal messages through the teleported particle, by guessing the classical message before it arrived (cf.Fig. 2).”
Quote in the paperSubstantial claim
- May combine two claims. 5
- Classified as probably not a substantial claim. 8
- The quote only partly states this claim. 1
May combine two claims.
FindingreasoningIn the first (singlet) outcome, Bob's state is the same as the original except for an irrelevant phase factor, so Bob need do nothing further to produce a replica.
“In the case of the first (singlet) outcome, Bob's state is the same except for an irrelevant phase factor, so Bob need do nothing further to produce a replica of Alice's spin.”
Quote in the paperSubstantial claimClassified as probably not a substantial claim. May combine two claims.
Findingnone givenAlice makes a joint measurement on her EPR particle and the unknown quantum system, and sends Bob the classical result of this measurement.
“Alice makes a joint measurement on her EPR particle and the unknown quantum system, and sends Bob the classical result of this measurement.”
Quote in the paperSubstantial claimMay combine two claims.
Findingnone givenAlice is left with particles 1 and 2 in one of the Bell states, without any trace of the original state.
“Alice, on the other hand, is left with particles 1 and 2 in one of the states 4~2 ) or IC~~), without any trace of (+) ' (+) the original state I P) .”
Quote in the paperSubstantial claimMay combine two claims.
Findingnone givenStates which are less entangled reduce the fidelity of teleportation, and/or the range of states that can be accurately teleported.
“States which are less entangled reduce the fidelity of teleportation, and/or the range of states lg) that can be accurately tele- ported.”
Quote in the paperSubstantial claimThe quote only partly states this claim.
FindingreasoningIf Bob guesses Alice's classical message before it arrives, the unknown state will be reconstructed (in the spin-1/2 case) as a random mixture of the four states of Eq. (6).
“P) will be reconstructed (in the spin-2 case) as a ran- dom mixture of the four states of Eq. ( 6).”
Quote in the paperSubstantial claimClassified as probably not a substantial claim.
PremisecitationInstantaneous information transfer is impossible.
“It is known that instantaneous information transfer is definitely impossible [3].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [3] 3. A. Einstein, in Albert Einstein, Philosopher Scientist, - edited by P. A. Schilpp (Library of Living Philosophers, Evanston, 1949) p. 85.
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Classified as probably not a substantial claim. May combine two claims.
PremisecitationQuantum information can be swapped from one system to another, but it cannot be duplicated or cloned.
“This”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [5] 5. J. L. Park, Found. Phys. 1, 23 (1970).
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Probably not a substantial claim: may not pass S3 (load-bearing).
Interpretationnone givenTeleportation has the advantage of still being possible in situations where Alice and Bob, after sharing their EPR pairs, have wandered independently and no longer know each other's locations.
“Finally, teleportation has the advantage of still being possible in situations where Alice and Bob, after sharing their EPR pairs, have wandered about independently and no longer know each others' locations.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing), S4 (based).
Interpretationnone givenAll of the above can be generalized to systems having N greater than or equal to 2 orthogonal states.
“All of what we have said above can be generalized to systems having N & 2 orthogonal states.”
Quote in the paperNot a substantial claimClassified as probably not a substantial claim.
Interpretationnone givenThis diagram can be used to show that a full two bits of classical channel capacity are necessary for accurate teleportation of a two-state particle.
“This diagram is of interest because it can be used to show that a full two bits of classical channel capacity are necessary for accurate tele- portation of a two-state particle (cf.caption).”
Quote in the paperSubstantial claimClassified as probably not a substantial claim.
Interpretationnone givenIf it becomes feasible to store separated EPR particles for more than a brief time, quantum teleportation could be quite useful.
“Although it is currently unfeasible to store separated EPR particles for more than a brief time, if it becomes feasible to do so, quantum teleportation could be quite useful.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing), S4 (based).
Interpretationnone givenTrying to draw similar Feynman diagrams with tree structure, rather than loops, would lead to physically impossible processes.
“Trying to draw similar”
Quote in the paperNot a substantial claim
The paper relies on this without support.
If Alice knows beforehand that the unknown state belongs to a given orthonormal set, she can make a measurement whose result will allow her to make an accurate copy.
“Only if Alice knows before- hand that ~qb) belongs to a given orthonormal set can she make a measurement whose result will allow her to make an accurate copy of [P).”
The paper relies on this without support.
If the possibilities for the unknown state include two or more nonorthogonal states, then no measurement will yield sufficient information to prepare a perfectly accurate copy.
“Conversely, if the possibilities for ~P) include two or more nonorthogonal states, then no measurement will yield sufhcient information to prepare a perfectly accurate copy.”
The paper relies on this without support.
In general, there is no way to learn the state vector of an unknown quantum system.
“Knowing the state vector ]P) itself would be sufficient information, but in general there is no way to learn it.”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Quantum teleportation enables a faithful transfer of an unknown quantum state from one location to another, using entangled states as a quantum channel.
“Quantum teleportation (Bennett et al., 1993) enables a faithful transfer of an unknown quantum state from one location to another, using entangled states as a quantum channel.”
From Multiphoton entanglement and interferometry (2012) · cites this paper as Bennett et al., 1993
The projection of two photons into a Bell state lies at the heart of many quantum information processing protocols, such as quantum dense coding, quantum teleportation, and entanglement swapping.
“The projection of two photons into a Bell state lies at the heart for many quantum information processing protocols, such as quantum dense coding (Bennett and Wiesner, 1992), quantum teleportation (Bennett et al., 1993), and entanglement swapping ( Żukowski et al., 1993).”
From Multiphoton entanglement and interferometry (2012) · cites this paper as Bennett et al., 1993
By exploiting entanglement one can efficiently encode classical messages, transfer quantum information to a remote location, entangle remote particles with no common past, and purify less entangled ensembles.
“By exploiting entanglement one can efficiently encode classical messages (Bennett and Wiesner, 1992; section VI.A), transfer quantum information to a remote location (Bennett et al., 1993; section VI.B), entangle two remote particles that have no common past ( Żukowski et al., 1993; section VI.C), and purify a large ensemble in a less entangled states into a smaller ensemble with higher”
From Multiphoton entanglement and interferometry (2012) · cites this paper as Bennett et al., 1993
Quantum teleportation was discovered by Bennett, Brassard, Crépeau, Jozsa, Peres, and Wootters (1993).
“The fascinating possibility of quantum teleportation was discovered by Bennett, Brassard, Crépeau, Jozsa, Peres, and Wootters (1993).”
From Multiphoton entanglement and interferometry (2012) · cites this paper as Bennett, Brassard, Crépeau, Jozsa, Peres, and Wootters (1993)
When particle 1 is a member of an entangled pair, the teleportation leads to entanglement swapping.
“This is the case when, as already remarked by Bennett et al. (1993), particle 1 itself is a member of an entangled pair, ultimately leading to entanglement swapping ( Żukowski et al., 1993;Bose et al., 1998).”
From Multiphoton entanglement and interferometry (2012) · cites this paper as Bennett et al. (1993)
Quantum key distribution (QKD), quantum teleportation, and dense coding are promising quantum communication protocols for expanding classical data transmission in quantum-based systems.
“Some of the promising quantum communication protocols to expand the possibility of classical data transmission in quantum-based systems include quantum key distribution (QKD) [126,127], quantum teleportation [128] and dense coding [129].”
From Quantum Machine Learning for 6G Communication Networks: State-of-the-Art and Vision for the Future (2019) · cites this paper as [129]
Other unique quantum phenomena like teleportation could also be investigated.
“Other unique quantum phenomena like 'teleportation' [30] could also be investigated.”
From Two-bit gates are universal for quantum computation (1995) · cites this paper as [30]
Since quantum teleportation rests entirely on Bell's Theorem, this and all research based upon quantum teleportation requires reassessment.
“Since quantum teleportation [14] rests entirely on Bell's Theorem, then this and all research based upon quantum teleportation requires reassessment.”
From EPR Correlations Using Quaternion Spin (2024) · cites this paper as [14]
The success probability of the nondeterministic CNOT can be boosted by harnessing quantum teleportation.
“Fortunately, the success probability of the nondeterministic CNOT can be boosted by harnessing quantum teleportation [12]-a process whereby the unknown state of a qubit can be transfered to another qubit.”
From Optical Quantum Computing (2007) · cites this paper as [12]
Bennett et al. suggested that it is possible to transfer the quantum state of a particle onto another particle provided one does not get any information about the state in the course of this transformation.
“Bennett et al. [1] have suggested that it is possible to transfer the quantum state of a particle onto another particle - the process of quantum teleportation - provided one does not get any information about the state in the course of this transformation.”
From Experimental quantum teleportation (1997) · cites this paper as [1]
Quantum physics predicts that once particles 1 and 2 are projected into |ψ-〉12, particle 3 is instantaneously projected into the initial state of particle 1.
“Quantum physics predicts [1] that once particles 1 and 2 are projected into | ψ -〉 12 , particle 3 is instantaneously projected into the initial state of particle 1.”
From Experimental quantum teleportation (1997) · cites this paper as [1]
Bennett et al. realised that precisely this projection postulate enables teleportation of |ψ〉 from Alice to Bob.
“Although the projection postulate in quantum mechanics seems to bring Alice's attempts to provide Bob with the state | ψ 〉 to a halt, it was realised by Bennett et al. [1] that precisely this projection postulate enables teleportation of | ψ 〉 from Alice to Bob.”
From Experimental quantum teleportation (1997) · cites this paper as [1]
The photons produced via the down-conversion process share nonclassical correlations.
“It is now well known that the photons produced via the down-conversion process share nonclassical correlations [7].”
From Ultrabright source of polarization-entangled photons (1999) · cites this paper as [7]
An arbitrary unknown qubit can be faithfully transmitted via a pair of maximally entangled qubits previously shared between sender and receiver and a 2-bit classical message.
“Using teleportation, an arbitrary unknown qubit can be faithfully transmitted via a pair of maximally-entangled qubits ( e.g. two spin1 2 particles in a pure singlet state) previously shared between sender and receiver, and a 2-bit classical message from the sender to the receiver.”
From Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels (1996) · cites this paper as [1]
To complete the Gmin gate set so that arbitrary quantum computations can be implemented, it suffices to add HAD and preparation of the state |π/8〉.
“To complete the G min gate set so that we can implement arbitrary quantum computations, it suffices to add HAD and preparation of the state | π/ 8 〉 = cos( π/ 8) | 0 〉 + sin( π/ 8) | 1 〉 . 26, 27”
From Quantum computing with realistically noisy devices (2005) · cites this paper as [26]
The state |φ_3〉 corresponds to a GHZ state of three qubits.
“While | φ 3 〉 corresponds to a GHZ state of three qubits [7]”
From Persistent Entanglement in Arrays of Interacting Particles (2001) · cites this paper as [7]
Entanglement is an important resource in quantum computation, teleportation, and quantum cryptography.
“Be it in quantum computation [1,2], teleportation [3] or quantum cryptography [4], entanglement is viewed as an important resource and, as such, must be quantified.”
From Measures and dynamics of entangled states (2005) · cites this paper as [3]
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“It can also be interpreted as teleportation of entanglement, i.e., teleportation of undefined states (Bennett et al., 1993).”
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- Authors
- Bennett, C. H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., & Wootters, W. K.
- Affiliations
- Technion – Israel Institute of Technology (IL)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1993-03-29
- Volume
- 70
- Issue
- 13
- Pages
- 1895-1899
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W1978553093
- Cited by
- 13,703
- References
- 15
- Citations by year
- 2026: 437 · 2025: 724 · 2024: 696 · 2023: 708 · 2022: 628 · 2021: 640 · 2020: 571 · 2019: 598 · 2018: 477 · 2017: 497 · 2016: 545 · 2015: 500 · 2014: 492 · 2013: 526 · 2012: 492
- FWCI
- 42.66
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- quantum teleportation, unknown quantum states, Einstein-Podolsky-Rosen correlations, EPR pairs, classical information, joint measurement, quantum state tomography, quantum entanglement
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